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Guide for the Use of the 

International System of Units (SI)

Barry N. Taylor

NIST Special Publication 811

1995 Edition

United States Department of Commerce

National Institute of Standards and Technology

kilo

SI 

SI kilo

m

gram 

SI amper

meter SI kilo

logram SI cand

m

gram 

SI amper

meter SI kilo

logram SI cand

er

SI kilo

m SI cand

n

d SI 

elvin SI

ram SI seco

dela SI meter

vin

nd SI 

kelvin SI

gram SI seco

ndela SI meter

vin

nd SI 

kelvin SI

gram SI seco

ndela SI meter

nd

kelvi

gram SI 

ndela SI me

er

SI k

e SI can

nd SI ampe

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SI k

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SI m

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meter SI kilog

logram SI can

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meter SI kilog

logram SI can

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SI kilog

SI can

k

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kelvin SI m

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lvin S

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ela

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SI sec

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SI kel

nd SI am

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ilogram SI se

SI ampere

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con

SI kelvi

nd SI ampe

n SI mole SI 

ilogram SI se

SI ampere

er SI ki

m SI

SI 

se

ere 

mole SI c

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kelvin SI mol

econd SI ampe

kelvin SI m

m SI se

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mole SI c

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kelvin SI mol

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kelvin SI m

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mole SI c

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SI amp

am SI sec

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ter SI k

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SI amper

mole SI k

SI se

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cond SI amper

vin SI mole SI k

logram SI se

I ampere

r SI k

S

cond

SI kelvin

nd SI amper

n SI mole SI k

ogram SI se

ampere

SI k

S

r

SI k

lv

S

pere S

mole SI ca

re SI kelvin S

I kelvin SI mol

ond SI amp

elvin SI

SI s

SI

pere S

mole SI ca

re SI kelvin S

I kelvin SI mol

ond SI amp

elvin SI

SI s

SI

pere S

mole SI ca

re SI kelvin S

I kelvin SI mol

ond SI amp

elvin SI

SI s

SI

r

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SI mole

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n SI mo

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SI mole SI can

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SI mo

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S

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d SI ampere

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SI 

r

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e SI kelvin S

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n SI mole SI

gram SI 

amper

SI

cond 

SI kelvin S

nd SI ampere

SI mole SI

ram SI 

per

r

SI 

elv

S

mpere SI 

I mole SI can

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kelvin SI mo

nd SI amp

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SI 

mpere SI 

I mole SI can

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kelvin SI mo

nd SI amp

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SI 

mpere SI 

I mole SI can

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kelvin SI mo

nd SI amp

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SI 

r

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dela SI

SI mole S

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SI

vin SI mol

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SI kilog

SI can

amp

d

SI mo

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r SI 

ndela

SI 

S

ogram

SI ampere

m SI sec

SI kel

S

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SI kelvin SI

d SI amper

mole S

SI

SI second S

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SI mole S

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SI kelvin SI

d SI amper

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m SI

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SI mole SI cand

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SI mole SI cand

re SI kelvin S

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d SI am

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SI mole SI cand

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d SI am

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lvin SI m

ndela SI m

SI mole S

SI c

SI

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SI candel

SI kilog

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SI

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SI

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SI second SI a

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n

lvin SI mo

ndela SI m

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SI second SI a

SI kelvin S

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SI kelvin

in SI

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I ampere SI kel

mole SI can

SI kelvin

in SI

SI

I ampere SI ke

mole SI ca

SI kelvi

in S

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kil

SI
UNITED STATES OF AMERICA

DEPARTMENT OF COMMERCE

NIST Special Publication 811

1995 Edition

Guide for the Use of the International System

of Units (SI)

Barry N. Taylor

Physics Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-0001

(Supersedes NIST Special Publication 811, September 1991)

April 1995

U.S. Department of Commerce

Ronald H. Brown, Secretary

Technology Administration

Mary L. Good, Under Secretary for Technology

National Institute of Standards and Technology

Arati Prabhakar, Director
National Institute of Standards U.S. Government Printing Office For sale by the Superintendent of

and Technology Washington: 1995 Documents

Special Publication 811 U.S. Government Printing Office

1995 Edition Washington, DC 20402

(Supersedes NIST Special

Publication 811, September 1991)

Natl. Inst. Stand. Technol.

Spec. Publ. 811

1995 Ed.

84 pages (April 1995)

CODEN: NSPUE2
Guide for the Use of the International System of Units (SI)

Preface

The International System of Units, universally abbreviated SI (from the French Le

Syste`me International d’Unite ́s), is the modern metric system of measurement. Long the dominant

measurement system used in science, the SI is becoming the dominant measurement system used in

international commerce.

The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418]

changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards

and Technology (NIST) and gave to NIST the added task of helping United States industry increase

its competitiveness in the global marketplace. It also recognized the rapidly expanding use of the SI

by amending the Metric Conversion Act of 1975 (PL 94-168). In particular, section 5164 (Metric

Usage) of PL 100-418 designates

the metric system of measurement as the preferred system of weights and measures for United

States trade and commerce...

and requires that

each Federal agency, by a date certain and to the extent economically feasible by the end of

fiscal year 1992, use the metric system of measurement in its procurements, grants, and other

business-related activities, except to the extent that such use is impractical or is likely to cause

significant inefficiencies or loss of markets for United States firms...

In January 1991, the Department of Commerce issued an addition to the Code of Federal

Regulations entitled ‘‘Metric Conversion Policy for Federal Agencies,’’ 15 CFR 1170, which removes the voluntary aspect of the conversion to the SI for Federal agencies and gives in detail the

policy for that conversion. Executive Order 12770, issued in July 1991, reinforces that policy by

providing Presidential authority and direction for the use of the metric system of measurement by

Federal agencies and departments.*

Because of the importance of the SI to both science and technology, NIST has over the years

published documents to assist NIST authors and other users of the SI, especially to inform them of

changes in the SI and in SI usage. For example, this second edition of the Guide replaces the first

edition prepared by Arthur O. McCoubrey and published in 1991. That edition, in turn, replaced NBS

Letter Circular LC 1120 (1979), which was widely distributed in the United States and which was

incorporated into the NBS Communications Manual for Scientific, Technical, and Public Information, a manual of instructions issued in 1980 for the preparation of technical publications at NBS.

It is quite natural for NIST to publish documents on the use of the SI. First, NIST coordinates

the Federal Government policy on the conversion to the SI by Federal agencies and on the use of the

SI by United States industry and the public. Second, NIST provides official United States representation in the various international bodies established by the Meter Convention (Convention du Me`tre ,

often called the Treaty of the Meter in the United States), which was signed in Paris in 1875

by seventeen countries, including the United States (nearly 50 countries are now members of the

Convention).

* Executive Order 12770 was published in the Federal Register, Vol. 56, No. 145, p. 35801, July 29, 1991; 15 CFR 1170

was originally published in the Federal Register, Vol. 56, No. 1, p. 160, January 2, 1991 as 15 CFR Part 19, but was

redesignated 15 CFR 1170. Both Executive Order 12770 and 15 CFR 1170 are reprinted in Ref. [1]. (See Appendix D —

Bibliography, which begins on p. 72.)

iii
Guide for the Use of the International System of Units (SI)

One body created by the Meter Convention is the General Conference on Weights and

Measures (CGPM, Confe ́rence Ge ́ne ́rale des Poids et Mesures), a formal diplomatic organization.** The International System was in fact established by the 11th CGPM in 1960, and it is the

responsibility of the CGPM to ensure that the SI is widely disseminated and that it reflects the latest

advances in science and technology.

This 1995 edition of the Guide corrects a number of misprints in the 1991 edition, incorporates

a significant amount of additional material intended to answer frequently asked questions concerning

the SI and SI usage, and updates the bibliography. The added material includes a check list in Chapter

11, which is reproduced immediately after this Preface for easy reference, for reviewing the consistency of NIST manuscripts with the SI. Some changes in format have also been made in an attempt

to improve the ease of use of the Guide .

In keeping with United States and NIST practice (see Sec. C.3), this edition of the Guide continues to use the dot as the decimal marker rather than the comma, the spellings ‘‘meter,’’ ‘‘liter,’’

and ‘‘deka’’ rather than ‘‘metre,’’ ‘‘litre,’’ and ‘‘deca,’’ and the name ‘‘metric ton’’ rather than

‘‘tonne.’’

I should like to take this opportunity to thank James B. McCracken of the NIST Metric Program

for his highly capable assistance in the early stages of the preparation of this Guide .

March 1995

Barry N. Taylor

** See Ref. [2] or [3] for a brief description of the various bodies established by the Meter Convention: The International

Bureau of Weights and Measures (BIPM, Bureau International des Poids et Mesures), the International Committee for Weights

and Measures (CIPM, Comite ́ International des Poids et Mesures), and the CGPM. The BIPM, which is located in Se`vres, a

suburb of Paris, France, and which has the task of ensuring worldwide unification of physical measurements, operates under

the exclusive supervision of the CIPM, which itself comes under the authority of the CGPM. In addition to a complete description of the SI, Refs. [2] and [3] also give the various CGPM and CIPM resolutions on which it is based. With the exception

of Table 8, Tables 1 to 11 of this Guide and their accompanying text are taken or are adapted from these references.

NOTE TO SECOND PRINTING

Since the first printing of this Special Publication (April 1995), the 20th CGPM, which met

October 9-12, 1995, decided to eliminate the class of supplementary units as a separate

class in the SI. Thus the SI now consists of only two classes of units: base units and derived

units, with the radian and steradian, which were the two supplementary units, subsumed

into the class of SI derived units. This decision by the CGPM relates to p. 1, Sec. 1.2, sixth

paragraph; p. 3, Chapter 4, first paragraph; p. 3, last sentence of footnote 2; p. 4, Sec. 4.2.1,

first paragraph; p. 7, Sec. 4.3; p. 11, Sec. 5.4; and p. 40, Sec. A.1. This second printing also

includes some minor typographical corrections.

iv
Guide for the Use of the International System of Units (SI)

Check List for Reviewing Manuscripts

The following check list, which constitutes Chapter 11 of this Guide and is adapted from

Ref. [22], is intended to help NIST authors review the conformity of their manuscripts with proper

SI usage and the basic principles concerning quantities and units. (The chapter or section numbers

in parentheses indicate where additional information may be found.)

(1) u Only units of the SI and those units recognized for use with the SI are used to express the

values of quantities. Equivalent values in other units are given in parentheses following

values in acceptable units only when deemed necessary for the intended audience. (See

Chapter 2.)

(2) u Abbreviations such as sec (for either s or second), cc (for either cm3 or cubic

centimeter), or mps (for either m/s or meter per second), are avoided and only standard

unit symbols, SI prefix symbols, unit names, and SI prefixes are used. (See Sec. 6.1.8.)

(3) u The combinations of letters ‘‘ppm,’’ ‘‘ppb,’’ and ‘‘ppt,’’ and the terms part per million,

part per billion, and part per trillion, and the like, are not used to express the values of

quantities. The following forms, for example, are used instead: 2.0 mL/L or 2.0 3 1026

V, 4.3 nm/m or 4.3 3 1029 l, 7 ps/s or 7 3 10212 t, where V, l, and t are, respectively,

the quantity symbols for volume, length, and time. (See Sec. 7.10.3.)

(4) u Unit symbols (or names) are not modified by the addition of subscripts or other information. The following forms, for example, are used instead. (See Secs. 7.4 and 7.10.2.)

Vmax = 1000 V but not: V = 1000 Vmax

a mass fraction of 10 % but not: 10 % (m/m) or 10 % (by weight)

(5) u Statements such as ‘‘the length l1 exceeds the length l2 by 0.2 %’’ are avoided because

it is recognized that the symbol % represents simply the number 0.01. Instead, forms such

as ‘‘l1 = l2(1 + 0.2 %)’’ or ‘‘D = 0.2 %’’ are used, where D is defined by the relation

D = (l1 2 l2)/l2. (See Sec. 7.10.2.)

(6) u Information is not mixed with unit symbols (or names). For example, the form ‘‘the water

content is 20 mL/kg’’ is used and not ‘‘20 mL H2O/kg’’ or ‘‘20 mL of water/kg.’’ (See

Sec. 7.5.)

(7) u It is clear to which unit symbol a numerical value belongs and which mathematical operation applies to the value of a quantity because forms such as the following are used. (See

Sec. 7.7.)

35 cm 3 48 cm but not: 35 3 48 cm

1 MHz to 10 MHz or (1 to 10) MHz but not: 1 MHz210 MHz or 1 to 10 MHz

20 8C to 30 8C or (20 to 30) 8C but not: 20 8C230 8C or 20 to 30 8C

123 g 6 2 g or (123 6 2) g but not: 123 6 2 g

70 % 6 5 % or (70 6 5) % but not: 70 6 5 %

240 3 (1 6 10 %) V but not: 240 V 6 10 % (one cannot add

240 V and 10 %)

(8) u Unit symbols and unit names are not mixed and mathematical operations are not applied

to unit names. For example, only forms such as kg/m3

, kg • m23, or

kilogram per cubic meter are used and not forms such as kilogram/m3

, kg/cubic meter,

kilogram/cubic meter, kg per m3

, or kilogram per meter3. (See Secs. 6.1.7, 9.5, and 9.8.)

v
Guide for the Use of the International System of Units (SI)

(9) u Values of quantities are expressed in acceptable units using Arabic numerals and the

symbols for the units. (See Sec. 7.6.)

m = 5 kg but not: m = five kilograms or m = five kg

the current was 15 A but not: the current was 15 amperes.

(10) u There is a space between the numerical value and unit symbol, even when the value is used

in an adjectival sense, except in the case of superscript units for plane angle. (See

Sec. 7.2.)

a 25 kg sphere but not: a 25-kg sphere

an angle of 283'4" but not: an angle of 2 83 '4 "

If the spelled-out name of a unit is used, the normal rules of English are applied: ‘‘a roll

of 35-millimeter film.’’ (See Sec. 7.6, note 3.)

(11) u The digits of numerical values having more than four digits on either side of the decimal

marker are separated into groups of three using a thin, fixed space

counting from both the left and right of the decimal marker. For example, 15 739.012 53

is highly preferred to 15739.01253. Commas are not used to separate digits into groups

of three. (See Sec. 10.5.3.)

(12) u Equations between quantities are used in preference to equations between numerical values, and symbols representing numerical values are different from symbols representing

the corresponding quantities. When a numerical-value equation is used, it is properly written and the corresponding quantity equation is given where possible. (See Sec. 7.11.)

(13) u Standardized quantity symbols such as those given in Refs. [6] and [7] are used, for example, R for resistance and Ar for relative atomic mass, and not words, acronyms, or ad hoc

groups of letters. Similarly, standardized mathematical signs and symbols such as are

given in Ref. [6: ISO 31-11] are used, for example, ‘‘tan x ’’ and not ‘‘tg x.’’ More specifically, the base of ‘‘log’’ in equations is specified when required by writing loga x (meaning log to the base a of x ), lb x (meaning log2 x ), ln x (meaning loge x ), or lg x (meaning

log10 x ). (See Secs. 10.1.1 and 10.1.2.)

(14) u Unit symbols are in roman type, and quantity symbols are in italic type with superscripts

and subscripts in roman or italic type as appropriate. (See Sec. 10.2 and Secs. 10.2.1 to

10.2.4.)

(15) u When the word ‘‘weight’’ is used, the intended meaning is clear. (In science and technology, weight is a force, for which the SI unit is the newton; in commerce and everyday use,

weight is usually a synonym for mass, for which the SI unit is the kilogram.) (See

Sec. 8.3.)

(16) u A quotient quantity, for example, mass density, is written ‘‘mass divided by volume’’

rather than ‘‘mass per unit volume.’’ (See Sec. 7.12.)

(17) u An object and any quantity describing the object are distinguished. (Note the difference

between ‘‘surface’’ and ‘‘area,’’ ‘‘body’’ and ‘‘mass,’’ ‘‘resistor’’ and ‘‘resistance,’’

‘‘coil’’ and ‘‘inductance.’’) (See Sec. 7.13.)

(18) u The obsolete term normality and the symbol N, and the obsolete term molarity and the

symbol M, are not used, but the quantity amount-of-substance concentration of B (more

commonly called concentration of B), and its symbol cB and SI unit mol/m3 (or a related

acceptable unit), are used instead. Similarly, the obsolete term molal and the symbol m are

not used, but the quantity molality of solute B, and its symbol bB or mB and SI unit mol/kg

(or a related unit of the SI), are used instead. (See Secs. 8.6.5 and 8.6.8.)

vi
Guide for the Use of the International System of Units (SI)

Contents 

Preface ...................................................................................... iii

Check List for Reviewing Manuscripts...................................................... v

1 Introduction ............................................................................ 1

1.1 Purpose of Guide................................................................ 1

1.2 Outline of Guide ................................................................ 1

2 NIST policy on the Use of the SI....................................................... 2

2.1 Essential data.................................................................... 2

2.1.1 Tables and graphs ...................................................... 2

2.2 Descriptive information ......................................................... 2

3 Other Sources of Information on the SI ................................................ 3

3.1 Publications ..................................................................... 3

3.2 Fundamental Constants Data Center............................................. 3

3.3 Metric Program ................................................................. 3

4 The Three Classes of SI Units and the SI Prefixes..................................... 3

4.1 SI base units .................................................................... 4

4.2 SI derived units.................................................................. 4

4.2.1 SI derived units with special names and symbols....................... 4

4.2.1.1 Degree Celsius ............................................... 5

4.2.2 Use of SI derived units with special names and symbols............... 6

4.3 SI supplementary units .......................................................... 7

4.4 Decimal multiples and submultiples of SI units: SI prefixes .................... 7

5 Units Outside the SI.................................................................... 8

5.1 Units accepted for use with the SI .............................................. 8

5.1.1 Hour, degree, liter, and the like......................................... 8

5.1.2 Neper, bel, shannon, and the like....................................... 9

5.1.3 Electronvolt and unified atomic mass unit.............................. 9

5.1.4 Natural and atomic units ............................................... 9

5.2 Units temporarily accepted for use with the SI.................................. 10

5.3 Units not accepted for use with the SI .......................................... 10

5.3.1 CGS units .............................................................. 11

5.3.2 Other unacceptable units ............................................... 11

5.4 The terms ‘‘units of the SI’’ and ‘‘acceptable units’’ ........................... 11

6 Rules and Style Conventions for Printing and Using Units ............................. 12

6.1 Rules and style conventions for unit symbols .................................... 12

6.1.1 Typeface ............................................................... 12

6.1.2 Capitalization........................................................... 12

6.1.3 Plurals.................................................................. 12

6.1.4 Punctuation............................................................. 12

6.1.5 Unit symbols obtained by multiplication ............................... 12

6.1.6 Unit symbols obtained by division...................................... 13

6.1.7 Unacceptability of unit symbols and unit names together .............. 13

6.1.8 Unacceptability of abbreviations for units.............................. 13

vii
Guide for the Use of the International System of Units (SI)

6.2 Rules and style conventions for SI prefixes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6.2.1 Typeface and spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6.2.2 Capitalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

6.2.3 Inseparability of prefix and unit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

6.2.4 Unacceptability of compound prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

6.2.5 Use of multiple prefixes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

6.2.6 Unacceptability of stand-alone prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

6.2.7 Prefixes and the kilogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

6.2.8 Prefixes with the degree Celsius and units accepted for use

with the SI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

7 Rules and Style Conventions for Expressing Values of Quantities . . . . . . . . . . . . . . . . . . . . . . 15

7.1 Value and numerical value of a quantity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

7.2 Space between numerical value and unit symbol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

7.3 Number of units per value of a quantity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

7.4 Unacceptability of attaching information to units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

7.5 Unacceptability of mixing information with units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

7.6 Symbols for numbers and units versus spelled-out names of numbers and

units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

7.7 Clarity in writing values of quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

7.8 Unacceptability of stand-alone unit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

7.9 Choosing SI prefixes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

7.10 Values of quantities expressed simply as numbers: the unit

one, symbol 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

7.10.1 Decimal multiples and submultiples of the unit one . . . . . . . . . . . . . . . . . . . . 20

7.10.2 %, percentage by, fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

7.10.3 ppm, ppb, and ppt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

7.10.4 Roman numerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

7.11 Quantity equations and numerical-value equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

7.12 Proper names of quotient quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

7.13 Distinction between an object and its attribute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

7.14 Dimension of a quantity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

8 Comments on Some Quantities and Their Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

8.1 Time and rotational frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

8.2 Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

8.3 Weight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

8.4 Relative atomic mass and relative molecular mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

8.5 Temperature interval and temperature difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

8.6 Amount of substance, concentration, molality, and the like. . . . . . . . . . . . . . . . . . . . . . 25

8.6.1 Amount of substance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

8.6.2 Mole fraction of B; amount-of-substance fraction of B . . . . . . . . . . . . . . . . . 25

8.6.3 Molar volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

8.6.4 Molar mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

8.6.5 Concentration of B; amount-of-substance concentration

of B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

8.6.6 Volume fraction of B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

8.6.7 Mass density; density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

8.6.8 Molality of solute B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

8.6.9 Specific volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

8.6.10 Mass fraction of B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

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8.7 Logarithmic quantities and units: level, neper, bel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

8.8 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

8.9 Massic, volumic, areic, lineic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

9 Rules and Style Conventions for Spelling Unit Names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

9.1 Capitalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

9.2 Plurals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

9.3 Spelling unit names with prefixes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

9.4 Spelling unit names obtained by multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

9.5 Spelling unit names obtained by division. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

9.6 Spelling unit names raised to powers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

9.7 Other spelling conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

9.8 Unacceptability of applying mathematical operations to unit names . . . . . . . . . . . . 32

10 More on Printing and Using Symbols and Numbers in Scientific and Technical

Documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

10.1 Kinds of symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

10.1.1 Standardized quantity symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

10.1.2 Standardized mathematical signs and symbols. . . . . . . . . . . . . . . . . . . . . . . . . . 33

10.2 Typefaces for symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

10.2.1 Quantities and variables — italic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

10.2.2 Units — roman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

10.2.3 Descriptive terms—roman. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

10.2.4 Sample equations showing correct type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

10.3 Greek alphabet in roman and italic type. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

10.4 Symbols for the elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

10.4.1 Typeface and punctuation for element symbols. . . . . . . . . . . . . . . . . . . . . . . . . 36

10.4.2 Subscripts and superscripts on element symbols. . . . . . . . . . . . . . . . . . . . . . . . 36

10.5 Printing numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

10.5.1 Typeface for numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

10.5.2 Decimal sign or marker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

10.5.3 Grouping digits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

10.5.4 Multiplying numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

11 Check List for Reviewing Manuscripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Appendix A. Definitions of the SI Base Units and the Radian and Steradian . . . . . . . . . . . . . . . 40

A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

A.2 Meter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

A.3 Kilogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

A.4 Second . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

A.5 Ampere. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

A.6 Kelvin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

A.7 Mole. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

A.8 Candela. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

A.9 Radian. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

A.10 Steradian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

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Appendix B. Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

B.2 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

B.3 Use of conversion factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

B.4 Organization of entries and style . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

B.5 Factor for converting motor vehicle efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

B.6 U.S. survey foot and mile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

B.7 Rules for rounding numbers and converted numerical values of

quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

B.7.1 Rounding numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

B.7.2 Rounding converted numerical values of quantities . . . . . . . . . . . . . . . . . . . . . 45

B.8 Factors for units listed alphabetically. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

B.9 Factors for units listed by kind of quantity or field of science . . . . . . . . . . . . . . . . . . . 57

Appendix C. Comments on the References of Appendix D — Bibliography . . . . . . . . . . . . . . . . 69

C.1 Official interpretation of the SI for the United States:

55 FR 52242-52245 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

C.2 Defining document for the SI: BIPM SI Brochure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

C.3 United States version of defining document for the SI: NIST SP 330 . . . . . . . . . . . 69

C.4 ISO 1000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

C.5 ISO 31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

C.6 IEC 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

C.7 ANSI/IEEE Std 268. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

C.8 Federal Register notices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

C.9 Federal Standard 376B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

C.10 1986 CODATA values of the fundamental constants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

C.11 Uncertainty in measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Appendix D. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

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1 Introduction

1.1 Purpose of Guide

The International System of Units was established in 1960 by the 11th General Conference on

Weights and Measures (CGPM — see Preface). Universally abbreviated SI (from the French

Le Syste`me International d’Unite ́s), it is the modern metric system of measurement used throughout

the world. This Guide has been prepared by the National Institute of Standards and Technology

(NIST) to assist members of the NIST staff, as well as others who may have need of such assistance,

in the use of the SI in their work, including the reporting of results of measurements.

1.2 Outline of Guide

The Preface gives the principal Federal Government actions taken since 1988 regarding the SI

and introduces the international body — the CGPM — that is responsible for the SI.

A check list immediately follows the Preface to help NIST authors review the conformity of

their manuscripts with proper SI usage and the basic principles concerning quantities and units.

A detailed Contents, the aim of which is to simplify the use of the Guide , follows the check list.

This introductory chapter gives the purpose of the Guide and its outline, while Chapter 2 summarizes and clarifies the NIST policy on the use of the SI in NIST publications.

Chapter 3 notes the existence of a number of publications on the SI and gives the two organizational units at NIST to which questions concerning the SI may be directed and from which additional

information about the SI may be obtained.

Chapter 4 discusses the fundamental aspects of the SI, including the three current classes of SI

units: base, derived, and supplementary; those derived units that have special names and symbols,

including the degree Celsius; and the SI prefixes that are used to form decimal multiples and submultiples of SI units.

Chapter 5 discusses units that are outside the SI and indicates those that may be used with it and

those that may not. It also gives (see Sec. 5.4) precise definitions of the terms ‘‘units of the SI’’ and

‘‘acceptable units’’ as used in this Guide .

Chapter 6 gives the rules and style conventions for printing and using units, especially unit symbols and SI prefix symbols.

Chapters 7 and 8, which some readers may view as the most important parts of this Guide ,

provide, respectively, the rules and style conventions for expressing the values of quantities, and

clarifying comments on some often troublesome quantities and their units.

Chapter 9 gives the rules and style conventions for spelling unit names.

Chapter 10 further elaborates on printing and using symbols and numbers in scientific and technical documents and is intended to assist NIST authors prepare manuscripts that are consistent with

accepted typesetting practice.

Chapter 11 gives the check list that is reproduced immediately after the Preface.

Appendix A gives the definitions of the SI base units and the radian and steradian, while

Appendix B gives conversion factors for converting values of quantities expressed in units that are

mainly unacceptable for use with the SI to values expressed mainly in units of the SI. Appendix B

also includes a simplified discussion of rounding numbers and rounding converted numerical values

of quantities.

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Appendix C discusses in some detail most of the references included in Appendix D—Bibliography, which concludes the Guide .

2 NIST Policy on the Use of the SI

In accordance with various Federal Acts, the Code of Federal Regulations, and Executive Order 12770 (see Preface), it is NIST policy that the SI shall be used in all NIST publications.1

When the field of application or the special needs of users of NIST publications require the use of

other units, the values of quantities shall first be expressed in acceptable units, where it is to be understood that acceptable units include the units of the SI and those units recognized for use with the

SI; the corresponding values expressed in the other units shall then follow in parentheses. (For precise definitions of the terms ‘‘units of the SI’’ and ‘‘acceptable units’’ as used in this Guide , see Sec.

5.4.) Exceptions to this policy require the prior approval of the NIST Director. The following three

sections — 2.1 Essential data, 2.1.1 Tables and graphs, and 2.2 Descriptive information — elaborate

upon this policy.

2.1 Essential data

Essential data express or interpret quantitative results. All such data shall be given in acceptable

units. In those cases where

— the sole use of acceptable units would compromise good communication, or

— units other than acceptable units have been specified as a contractual requirement,

values of quantities shall be given in acceptable units followed, in parentheses, by the values of the

same quantities given in the other units.

Exceptions may sometimes be necessary for commercial devices, technical standards, or quantities having special legal significance; examples include commercial weights and measures devices

and the related laws and regulations. However, even in such cases, values of quantities expressed in

acceptable units should be used when possible with the same values expressed in other units following in parentheses.

2.1.1 Tables and graphs

In tables, values of quantities expressed in acceptable units and the corresponding

values expressed in other units may be shown in parallel columns, with the acceptable-unit column

preceding the other-unit column. In graphs, axes labeled in other units shall be given secondary

status. This may preferably be done by placing scale marks on and labeling the left-hand ordinate and

bottom abscissa in acceptable units, and placing scale marks on and labeling the right-hand ordinate

and top abscissa in other units. Alternatively, lighter-weight scale marks and smaller type may be

employed to indicate other units using the same ordinate and abscissa as is used for the acceptable

units.

2.2 Descriptive information

Descriptive information characterizes arrangements, environments, the generalized

dimensions of objects, apparatus, or materials, and other attributes that do not enter directly into

calculations or results. When necessary for effective communication, such information may be

expressed using customary terms that are widely used and recognized. Examples

include common drill sizes and traditional tools used in the United States, U.S. standard fastener

sizes, commercial pipe sizes, and other common terms used in the trades, the professions, the

marketplace, sports, and various social activities. When such descriptive information is given, values

in acceptable units are not required. For example, it is permissible to refer to a ‘‘36-inch pipeline’’

or a ‘‘half-inch drill’’ without first giving the value in an acceptable unit.

1 The NIST policy on the use of the SI is set forth in the NIST Administration Manual, Chapter 4, Communications,

Subchapter 4.09, NIST Technical Communications Program, Appendix D — Use of Metric Units.

2
Guide for the Use of the International System of Units (SI)

3 Other Sources of Information on the SI

3.1 Publications

Appendix C briefly describes a number of publications that deal with the SI and related topics;

citations for these publications are given in Appendix D — Bibliography. Additional information

about the SI is also available from the two NIST organizational units indicated in Secs. 3.2 and 3.3.

3.2 Fundamental Constants Data Center

Questions concerning the more fundamental aspects of the SI and subtle aspects of proper SI

usage may be directed to:

Fundamental Constants Data Center

Physics Laboratory

National Institute of Standards and Technology

Building 245, Room C229

Gaithersburg, MD 20899-0001

Telephone: (301) 975-4220

Fax: (301) 869-7682

3.3 Metric Program

Questions concerning Federal Government use of the SI and Federal Government policy on the

use of the SI by U.S. industry and the public may be directed to:

Metric Program

Technology Services

National Institute of Standards and Technology

Building 820, Room 306

Gaithersburg, MD 20899-0001

Telephone: (301) 975-3690

Fax: (301) 948-1416

4 The Three Classes of SI Units and the SI Prefixes [see p. iv, NOTE TO

SECOND PRINTING]

SI units are currently divided into three classes:

— base units,

— derived units,

— supplementary units,

which together form what is called ‘‘the coherent system of SI units.’’ 2 The SI also includes prefixes

to form decimal multiples and submultiples of SI units.

2 According to Ref. [6: ISO 31-0], a system of units is coherent with respect to a system of quantities and equations if the

system of units is chosen in such a way that the equations between numerical values have exactly the same form (including

the numerical factors) as the corresponding equations between the quantities (see Secs. 7.11 and 7.14). In such a coherent

system, of which the SI is an example, no numerical factor other than the number 1 ever occurs in the expressions for the

derived units in terms of the base units. It should also be noted that the class of supplementary units is likely to be abolished

as a separate class in the SI — see Sec. 4.3.

3
Guide for the Use of the International System of Units (SI)

4.1 SI base units

Table 1 gives the seven base quantities, assumed to be mutually independent, on which the SI is

founded; and the names and symbols of their respective units, called ‘‘SI base units.’’ Definitions of

the SI base units are given in Appendix A. The kelvin and its symbol K are also used to express the

value of a temperature interval or a temperature difference (see Sec. 8.5).

4.2 SI derived units

Derived units are expressed algebraically in terms of base units or other derived units (including

the radian and steradian which are the two supplementary units — see Sec. 4.3). The symbols for

derived units are obtained by means of the mathematical operations of multiplication and division.

For example, the derived unit for the derived quantity molar mass (mass divided by amount of substance) is the kilogram per mole, symbol kg/mol. Additional examples of derived units expressed in

terms of SI base units are given in Table 2. (The rules and style conventions for printing and using

SI unit symbols are given in Secs. 6.1.1 to 6.1.8.)

4.2.1 SI derived units with special names and symbols

Certain SI derived units have special names and symbols; these are given in Tables 3a and 3b.

As discussed in Sec. 4.3, the radian and steradian, which are the two supplementary units, are

included in Table 3a.

Table 1. SI base units

SI base unit

Base quantity Name Symbol

length meter m

mass kilogram kg

time second s

electric current ampere A

thermodynamic temperature kelvin K

amount of substance mole mol

luminous intensity candela cd

Table 2. Examples of SI derived units expressed in terms of SI base units

SI derived unit

Derived quantity Name Symbol

area square meter m2

volume cubic meter m3

speed, velocity meter per second m/s

acceleration meter per second squared m/s2

wave number reciprocal meter m21

mass density (density) kilogram per cubic meter kg/m3

specific volume cubic meter per kilogram m3/kg

current density ampere per square meter A/m2

magnetic field strength ampere per meter A/m

amount-of-substance concentration

(concentration) mole per cubic meter mol/m3

luminance candela per square meter cd/m2

4
Guide for the Use of the International System of Units (SI)

Table 3a. SI derived units with special names and symbols, including the radian and steradian

SI derived unit

Expression Expression

Derived quantity Special name Special symbol in terms in terms

of other of SI base

SI units units

plane angle radian rad m ? m21 = 1

solid angle steradian sr m2 ? m22 = 1

frequency hertz Hz s21

force newton N m ? kg ? s

22

pressure, stress pascal Pa N/m2 m21 ? kg ? s

22

energy, work, quantity

of heat joule J N ? m m2 ? kg ? s

22

power, radiant flux watt W J/s m2 ? kg ? s

23

electric charge,

quantity of electricity coulomb C s ? A

electric potential,

potential difference,

electromotive force volt V W/A m2 ? kg ? s

23 ? A21

capacitance farad F C/V m22 ? kg21 ? s

4 ? A2

electric resistance ohm V V/A m2 ? kg ? s

23 ? A22

electric conductance siemens S A/V m22 ? kg21 ? s

3 ? A2

magnetic flux weber Wb V ? s m2 ? kg ? s

22 ? A21

magnetic flux density tesla T Wb/m2 kg ? s

22 ? A21

inductance henry H Wb/A m2 ? kg ? s

22 ? A22

Celsius temperature(a) degree Celsius 8C K

luminous flux lumen lm cd ? sr cd ? sr(b)

illuminance lux lx lm/m2 m22 ? cd ? sr(b)

(a) See Secs. 4.2.1.1, 6.2.8, and 7.2.

(b) The steradian (sr) is not an SI base unit. However, in photometry the steradian (sr) is maintained in expressions

for units (see Sec. 4.3).

4.2.1.1 Degree Celsius In addition to the quantity thermodynamic temperature (symbol T),

expressed in the unit kelvin, use is also made of the quantity Celsius temperature

(symbol t) defined by the equation

t = T2T0 ,

where T0 = 273.15 K by definition. To express Celsius temperature, the unit degree Celsius, symbol

8C, which is equal in magnitude to the unit kelvin, is used; in this case, ‘‘degree Celsius’’ is a special

name used in place of ‘‘kelvin.’’ An interval or difference of Celsius temperature can, however, be

expressed in the unit kelvin as well as in the unit degree Celsius (see Sec. 8.5). (Note that the thermodynamic temperature T0 is exactly 0.01 K below the thermodynamic temperature of the triple

point of water (see Sec. A.6).)

Table 3b. SI derived units with special names and symbols admitted for reasons of safeguarding human health(a)

SI derived unit

Derived quantity Special Special Expression in terms Expression in terms

name symbol of other SI units of SI base units

activity (of a

radionuclide) becquerel Bq s21

absorbed dose,

specific energy

(imparted), kerma gray Gy J/kg m2 ? s

22

dose equivalent, ambient dose

equivalent, directional dose

equivalent, personal dose

equivalent, equivalent dose sievert Sv J/kg m2 ? s

22

(a) The derived quantities to be expressed in the gray and the sievert have been revised in accordance with the

recommendations of the International Commission on Radiation Units and Measurements (ICRU); see

Ref. [19].

5
Guide for the Use of the International System of Units (SI)

4.2.2 Use of SI derived units with special names and symbols

Examples of SI derived units that can be expressed with the aid of SI derived units having

special names and symbols (including the radian and steradian) are given in Table 4.

The advantages of using the special names and symbols of SI derived units are apparent in Table

4. Consider, for example, the quantity molar entropy: the unit J/(mol ? K) is obviously more easily

understood than its SI base-unit equivalent, m2 ? kg ? s22 ? K21 ? mol21

. Nevertheless, it should

always be recognized that the special names and symbols exist for convenience; either the form in

which special names or symbols are used for certain combinations of units or the form in which they

are not used is correct. For example, because of the descriptive value implicit in the compound-unit

form, communication is sometimes facilitated if magnetic flux (see Table 3a) is expressed in terms

of the volt second (V ? s) instead of the weber (Wb).

Tables 3a, 3b, and 4 also show that the values of several different quantities are expressed in the

same SI unit. For example, the joule per kelvin (J/K) is the SI unit for heat capacity as well as for

entropy. Thus the name of the unit is not sufficient to define the quantity measured.

A derived unit can often be expressed in several different ways through the use of base units and

derived units with special names. In practice, with certain quantities, preference is given to using

certain units with special names, or combinations of units, to facilitate the distinction between quantities whose values have identical expressions in terms of SI base units. For example, the SI unit of

frequency is specified as the hertz (Hz) rather than the reciprocal second (s21

), and the SI unit of

moment of force is specified as the newton meter (N ? m) rather than the joule (J).

Table 4. Examples of SI derived units expressed with the aid of SI derived units having special names and symbols

SI derived unit

Expression

Derived quantity Name Symbol in terms of

SI base units

angular velocity radian per second rad/s m ? m21 ? s21 = s21

angular acceleration radian per second squared rad/s2 m ? m21 ? s22 = s22

dynamic viscosity pascal second Pa ? s m21 ? kg ? s

21

moment of force newton meter N ? m m2 ? kg ? s

22

surface tension newton per meter N/m kg ? s

22

heat flux density,

irradiance watt per square meter W/m2 kg ? s

23

radiant intensity watt per steradian W/sr m2 ? kg ? s

23 ? sr21 (a)

radiance watt per square

meter steradian W/(m2 ? sr) kg ? s

23 ? sr21 (a)

heat capacity, entropy joule per kelvin J/K m2 ? kg ? s

22 ? K21

specific heat capacity, joule per kilogram

specific entropy kelvin J/(kg ? K) m2 ? s

22 ? K21

specific energy joule per kilogram J/kg m2 ? s

22

thermal conductivity watt per meter kelvin W/(m ? K) m ? kg ? s

23 ? K21

energy density joule per cubic meter J/m3 m21 ? kg ? s

22

electric field strength volt per meter V/m m ? kg ? s

23 ? A21

electric charge density coulomb per cubic meter C/m3 m23 ? s ? A

electric flux density coulomb per square meter C/m2 m22 ? s ? A

permittivity farad per meter F/m m23 ? kg21 ? s

4 ? A2

permeability henry per meter H/m m ? kg ? s

22 ? A22

molar energy joule per mole J/mol m2 ? kg ? s

22 ? mol21

molar entropy, molar

heat capacity joule per mole kelvin J/(mol ? K) m2 ? kg ? s

22 ? K21 ? mol21

exposure (x and g rays) coulomb per kilogram C/kg kg21 ? s ? A

absorbed dose rate gray per second Gy/s m2 ? s

23

(a) The steradian (sr) is not an SI base unit. However, in radiometry the steradian (sr) is maintained in expressions

for units (see Sec. 4.3).

6
Guide for the Use of the International System of Units (SI)

Similarly, in the field of ionizing radiation, the SI unit of activity is designated as the becquerel

(Bq) rather than the reciprocal second (s21

), and the SI units of absorbed dose and dose equivalent

are designated as the gray (Gy) and the sievert (Sv), respectively, rather than the joule per kilogram

(J/kg).

4.3 SI supplementary units [see p. iv, NOTE TO SECOND PRINTING]

As previously stated, there are two units in this class: the radian, symbol rad, the SI unit of the

quantity plane angle; and the steradian, symbol sr, the SI unit of the quantity solid angle. Definitions

of these units are given in Appendix A.

The SI supplementary units are now interpreted as so-called dimensionless derived units (see

Sec. 7.14) for which the CGPM allows the freedom of using or not using them in expressions for SI

derived units.3 Thus the radian and steradian are not given in a separate table but have been included

in Table 3a together with other derived units with special names and symbols (see Sec. 4.2.1). This

interpretation of the supplementary units implies that plane angle and solid angle are considered

derived quantities of dimension one (so-called dimensionless quantities — see Sec. 7.14), each of

which has the unit one, symbol 1, as its coherent SI unit. However, in practice, when one expresses

the values of derived quantities involving plane angle or solid angle, it often aids understanding if the

special names (or symbols) ‘‘radian’’ (rad) or ‘‘steradian’’ (sr) are used in place of the number 1. For

example, although values of the derived quantity angular velocity (plane angle divided by time) may

be expressed in the unit s21, such values are usually expressed in the unit rad/s.

Because the radian and steradian are now viewed as so-called dimensionless derived units, the

Consultative Committee for Units (CCU, Comite ́ Consultatif des Unite ́s) of the CIPM (see footnote,

p. iv), as a result of a 1993 request it received from ISO/TC 12 (see Ref. [22]), recommended to the

CIPM that it request the CGPM to abolish the class of supplementary units as a separate class in the

SI. The CIPM accepted the CCU recommendation, and if the abolishment is approved by the CGPM

as is likely (the question will be on the agenda of the 20th CGPM, October 1995), the SI will consist

of only two classes of units: base units and derived units, with the radian and steradian subsumed into

the class of derived units of the SI. (The option of using or not using them in expressions for SI

derived units, as is convenient, would remain unchanged.)

4.4 Decimal multiples and submultiples of SI units: SI prefixes

Table 5 gives the SI prefixes that are used to form decimal multiples and submultiples of SI

units. They allow very large or very small numerical values (see Sec. 7.1) to be avoided. A prefix

attaches directly to the name of a unit, and a prefix symbol attaches directly to the symbol for a unit.

For example, one kilometer, symbol 1 km, is equal to one thousand meters, symbol 1000 m or 103 m.

When prefixes are attached to SI units, the units so formed are called ‘‘multiples and submultiples

of SI units’’ in order to distinguish them from the coherent system of SI units. (See footnote 2 for a

brief discussion of coherence. The rules and style conventions for printing and using SI prefixes are

given in Secs. 6.2.1 to 6.2.8. The special rule for forming decimal multiples and submultiples of the

unit of mass is given in Sec. 6.2.7.)

Note: Alternative definitions of the SI prefixes and their symbols are not permitted. For example,

it is unacceptable to use kilo (k) to represent 210 = 1024, mega (M) to represent

220 = 1 048 576, or giga (G) to represent 230 = 1 073 741 824.

3 See Ref. [2] or [3]. This interpretation was given in 1980 by the CIPM (see footnote, p. iv). It was deemed necessary

because Resolution 12 of the 11th CGPM, which established the SI in 1960 [2, 3], did not specify the nature of the supplementary units. The interpretation is based on two principal considerations: that plane angle is generally expressed as the ratio of

two lengths and solid angle as the ratio of an area and the square of a length, and are thus quantities of dimension one (so-called

dimensionless quantities); and that treating the radian and steradian as SI base units — a possibility not disallowed by Resolution 12 — could compromise the internal coherence of the SI based on only seven base units. (See Ref. [6: ISO 31-0] and

also Sec. 7.14 for a discussion of the concept of dimension, and footnote 2 for a brief discussion of coherence.)

7
Guide for the Use of the International System of Units (SI)

5 Units Outside the SI

Units that are outside the SI may be divided into three categories:

— those units that are accepted for use with the SI;

— those units that are temporarily accepted for use with the SI; and

— those units that are not accepted for use with the SI and thus in the view of this

Guide must strictly be avoided.

5.1 Units accepted for use with the SI

The following four sections discuss in detail the units this Guide accepts for use with the SI.

5.1.1 Hour, degree, liter, and the like

Certain units that are not part of the SI are essential and used so widely that they are accepted

by the CIPM, and thus by this Guide , for use with the SI [2, 3]. These units are given in Table 6. The

combination of units of this table with SI units to form derived units should be restricted to special

cases in order not to lose the advantages of the coherence of SI units. (The use of SI prefixes with

the units of Table 6 is discussed in Sec. 6.2.8.)

Additionally, this Guide recognizes that it may be necessary on occasion to use time-related

units other than those given in Table 6; in particular, circumstances may require that intervals of time

be expressed in weeks, months, or years. In such cases, if a standardized symbol for the unit is not

available, the name of the unit should be written out in full. (See Sec. 8.1 for a suggestion regarding

the symbol for year and Chapter 9 for the rules and style conventions for spelling unit names.)

Table 5. SI prefixes

Factor Prefix Symbol Factor Prefix Symbol

1024 = (103)

8 yotta Y 1021 deci d

1021 = (103)

7 zetta Z 1022 centi c

1018 = (103)

6 exa E 1023 = (103

)

21 milli m

1015 = (103

)

5 peta P 1026 = (103

)

22 micro m

1012 = (103)

4 tera T 1029 = (103

)

23 nano n

109 = (103)

3 giga G 10212 = (103

)

24 pico p

106 = (103

)

2 mega M 10215 = (103

)

25 femto f

103 = (103)

1 kilo k 10218 = (103

)

26 atto a

102 hecto h 10221 = (103

)

27 zepto z

101 deka da 10224 = (103

)

28 yocto y

Table 6. Units accepted for use with the SI

Name Symbol Value in SI units

minute min 1 min = 60 s

hour time h 1 h = 60 min = 3600 s

day d 1 d = 24 h = 86 400 s

degree 8 18 = (p/180) rad

minute plane angle(a) ' 1' = (1/60)8=(p/10 800) rad

second " 1" = (1/60)'=(p/648 000) rad

liter l, L(b) 1 L = 1 dm3 = 1023 m3

metric ton(c) t 1 t = 103 kg

(a) See also Sec. 7.2.

(b) The alternative symbol for the liter, L, was adopted by the CGPM in order to avoid the risk of confusion between the letter

l and the number 1 (see Ref. [2] or [3]). Thus, although both l and L are internationally accepted symbols for the liter, to

avoid this risk the symbol to be used in the United States is L (see Refs. [1] and [8]). The script letter , is not an approved

symbol for the liter.

(c) This is the name to be used for this unit in the United States (see Refs. [1] and [8]); it is also used in some other Englishspeaking countries. However, this unit is called ‘‘tonne’’ in Ref. [2] and is the name used in many countries.

6

6

8
Guide for the Use of the International System of Units (SI)

5.1.2 Neper, bel, shannon, and the like

There are a few highly specialized units not listed in Table 6 that are given by the

International Organization for Standardization (ISO) or the International Electrotechnical Commission (IEC) and which in the view of this Guide are also acceptable for use with the SI. They include

the neper (Np), bel (B), octave, phon, and sone, and units used in information technology, including

the baud (Bd), bit (bit), erlang (E), hartley (Hart), and shannon (Sh).4 It is the position of this Guide

that the only such additional units NIST authors may use with the SI are those given in either the

International Standards on quantities and units of ISO (Ref. [6]) or of IEC (Ref. [7]).

5.1.3 Electronvolt and unified atomic mass unit

The CIPM, and thus this Guide , also finds it necessary to accept for use with the SI the two units

given in Table 7 [2, 3]. These units are used in specialized fields; their values in SI units must be

obtained from experiment and, therefore, are not known exactly. (The use of SI prefixes with the units

of Table 7 is discussed in Sec. 6.2.8.)

Note: In some fields the unified atomic mass unit is called the dalton, symbol Da; however, this

name and symbol are not accepted by the CGPM, CIPM, ISO, or IEC for use with the SI.

Similarly, AMU is not an acceptable unit symbol for the unified atomic mass unit. The only

allowed name is ‘‘unified atomic mass unit’’ and the only allowed symbol is u.

5.1.4 Natural and atomic units

In some cases, particularly in basic science, the values of quantities are expressed in terms of

fundamental constants of nature or so-called natural units. The use of these units with the SI is, in

the view of this Guide, permissible when it is necessary for the most effective communication of

information. In such cases, the specific natural units that are used must be identified. This requirement applies even to the system of units customarily called ‘‘atomic units’’ used in theoretical atomic

physics and chemistry, inasmuch as there are several different systems that have the appellation

‘‘atomic units.’’ Examples of physical quantities used as natural units are given in Table 8.

This Guide also takes the position that while theoretical results intended primarily for other theorists may be left in natural units, if they are also intended for experimentalists, they must also be

given in acceptable units. NIST measurement results must always be given in such units first.

4 The symbol in parentheses following the name of the unit is its internationally accepted unit symbol, but the octave, phon,

and sone have no such unit symbols. For additional information on the neper and bel, see Sec. 0.5 of Ref. [6: ISO 31-2], Ref.

[7: IEC 27-3], and Sec. 8.7 of this Guide . The question of the byte (B) is under international consideration.

Table 7. Units accepted for use with the SI whose values in SI units are obtained experimentally

Name Symbol Definition

electronvolt eV (a)

unified atomic mass unit u (b)

(a) The electronvolt is the kinetic energy acquired by an electron in passing through a potential difference of 1 V in vacuum;

1 eV = 1.602 177 33310219 J with a combined standard uncertainty of 0.000 000 49310219 J [20, 21].

(b) The unified atomic mass unit is equal to 1/12 of the mass of an atom of the nuclide 12C; 1 u = 1.660 540 23

10227 kg with a combined standard uncertainty of 0.000 001 0310227 kg [20, 21].

9
Guide for the Use of the International System of Units (SI)

5.2 Units temporarily accepted for use with the SI

Because of existing practice in certain fields or countries, in 1978 the CIPM considered that it

was permissible for the units given in Table 9 to continue to be used with the SI until the CIPM considers that their use is no longer necessary [2, 3]. However, these units must not be introduced where

they are not presently used. Further, this Guide strongly discourages the continued use of these units

by NIST authors except for the nautical mile, knot, are, and hectare; and except for the curie,

roentgen, rad, and rem until the year 2000 (the cessation date suggested by the Committee for

Interagency Radiation Research and Policy Coordination or CIRRPC, a United States Government

interagency group).5

5.3 Units not accepted for use with the SI

The following two sections briefly discuss units not accepted for use with the SI.

5 In 1993 the CCU (see Sec. 4.3) was requested by ISO/TC 12 (see Ref. [22]) to consider asking the CIPM to deprecate

the use of the units of Table 9 except for the nautical mile and knot, and possibly the are and hectare. The CCU discussed this

request at its February 1995 meeting.

Table 8. Examples of physical quantities sometimes used as natural units

Kind of quantity Physical quantity used as a unit Symbol

action Planck constant divided by 2p |hbar|

electric charge elementary charge e

energy Hartree energy Eh

length Bohr radius a0

length Compton wavelength (electron) lC

magnetic flux magnetic flux quantum F0

magnetic moment Bohr magneton mB

magnetic moment nuclear magneton mN

mass electron rest mass me

mass proton rest mass mp

speed speed of electromagnetic waves in vacuum c

Table 9. Units temporarily accepted for use with the SI(a)

Name Symbol Value in SI units

nautical mile 1 nautical mile = 1852 m

knot 1 nautical mile per hour = (1852/3600) m/s

ångstro ̈m Å 1 Å = 0.1 nm = 10210 m

are(b) a 1 a = 1 dam2 = 102 m2

hectare(b) ha 1 ha = 1 hm2 = 104 m2

barn b 1 b = 100 fm2 = 10228 m2

bar bar 1 bar=0.1 MPa=100 kPa=1000 hPa=105 Pa

gal Gal 1 Gal = 1 cm/s2 = 1022 m/s 2

curie Ci 1 Ci = 3.731010 Bq

roentgen R 1 R = 2.5831024 C/kg

rad rad(c) 1 rad = 1 cGy = 1022 Gy

rem rem 1 rem = 1 cSv = 1022 Sv

(a) See Sec. 5.2 for the position of this Guide regarding the continued use of these units.

(b) This unit and its symbol are used to express agrarian areas.

(c) When there is risk of confusion with the symbol for the radian, rd may be used as the symbol for rad.

10
Guide for the Use of the International System of Units (SI)

5.3.1 CGS units

Table 10 gives examples of centimeter-gram-second (CGS) units having special names. These

units are not accepted for use with the SI. Further, no other units of the various CGS systems of units,

which includes the CGS Electrostatic (ESU), CGS Electromagnetic (EMU), and CGS Gaussian

systems, are accepted for use with the SI except such units as the centimeter, gram, and second that

are also defined in the SI.

5.3.2 Other unacceptable units

There are many units besides CGS units that are outside the SI and not accepted for use with

it, including, of course, all of the U.S. customary (that is, inch-pound) units. In the view of this Guide

such units must strictly be avoided and SI units, their multiples or submultiples, or those units

accepted or temporarily accepted for use with the SI (including their appropriate multiples and submultiples), must be used instead. This restriction also applies to the use of unaccepted special names

for SI units or special names for multiples or submultiples of SI units, such as mho for siemens (S)

and micron for micrometer (mm). Table 11 gives a few examples of some of these other unacceptable

units.

5.4 The terms ‘‘units of the SI’’ and ‘‘acceptable units’’

Consistent with accepted practice [2, 3], this Guide uses the term ‘‘units of the SI’’ to mean

the SI units, that is, the SI base units, SI derived units, and SI supplementary units; and

multiples and submultiples of these units formed by using the SI prefixes. The term

Table 10. Examples of CGS units with special names (not accepted for use with the SI)

Name Symbol Value in SI units

erg erg 1 erg = 1027 J

dyne dyn 1 dyn = 1025 N

poise(a) P 1 P = 1 dyn ? s/cm2 = 0.1 Pa ? s

stokes(b) St 1 St = 1 cm2

/s = 1024 m2/s

gauss(c) Gs, G 1 Gs corresponds to 1024 T

oersted(c) Oe 1 Oe corresponds to (1000/4p) A/m

maxwell(c) Mx 1 Mx corresponds to 1028 Wb

stilb sb 1 sb = 1 cd/cm2 = 104 cd/m2

phot ph 1 ph = 104 lx

(a) The poise (P) is the CGS unit for viscosity (also called dynamic viscosity). The SI unit is the pascal second (Pa ? s).

(b) The stokes (St) is the CGS unit for kinematic viscosity. The SI unit is the meter squared per second (m2

/s).

(c) This unit is part of the so-called electromagnetic three-dimensional CGS system and cannot strictly speaking be compared

to the corresponding unit of the SI, which has four dimensions when only mechanical and electric quantities are considered.

Table 11. Examples of other unacceptable units

Name Symbol Value in SI units

fermi fermi 1 fermi = 1 fm = 10215 m

metric carat metric carat 1 metric carat = 200 mg = 231024 kg

torr Torr 1 Torr = (101 325/760) Pa

standard atmosphere atm 1 atm = 101 325 Pa

kilogram-force kgf 1 kgf = 9.806 65 N

micron m 1 m = 1 mm = 1026 m

calorie (various) calth (thermochemical) 1 calth = 4.184 J

x unit xu 1 xu ≈ 0.1002 pm=1.002310213 m

stere st 1 st=1m3

gamma g 1 g = 1 nT = 1029 T

gamma (mass) g 1 g = 1 mg = 1029 kg

lambda (volume) l 1 l = 1 mL = 1026 L = 1029 m3

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Guide for the Use of the International System of Units (SI)

‘‘acceptable units,’’ which is introduced in this Guide for convenience, is used to mean the units of

the SI plus (a) those units accepted for use with the SI (see Tables 6 and 7 and

Secs. 5.1.1, 5.1.2, and 5.1.3); (b) those units temporarily accepted for use with the SI (see Table 9 and

Sec. 5.2); and (c) appropriate multiples and submultiples of such accepted and temporarily accepted

units. Because natural and atomic units are not widely recognized for use with the SI, they are not

included in the term. However, such units may be used to the extent discussed in Sec. 5.1.4.

6 Rules and Style Conventions for Printing and Using Units

6.1 Rules and style conventions for unit symbols

The following eight sections give rules and style conventions related to the symbols for units.

6.1.1 Typeface

Unit symbols are printed in roman (upright) type regardless of the type used in the surrounding

text. (See also Sec. 10.2 and Secs. 10.2.1 to 10.2.4.)

6.1.2 Capitalization

Unit symbols are printed in lower-case letters except that:

(a) the symbol or the first letter of the symbol is an upper-case letter when the name of the unit is

derived from the name of a person; and

(b) the recommended symbol for the liter in the United States is L [see Table 6, footnote (b)].

Examples: m (meter) s (second) V (volt)

Pa (pascal) lm (lumen) Wb (weber)

6.1.3 Plurals

Unit symbols are unaltered in the plural.

Example : l = 75 cm but not: l = 75 cms

Note: l is the quantity symbol for length. (The rules and style conventions for expressing

the values of quantities are discussed in detail in Chapter 7.)

6.1.4 Punctuation

Unit symbols are not followed by a period unless at the end of a sentence.

Example : ‘‘Its length is 75 cm.’’ or ‘‘It is 75 cm long.’’ but not: ‘‘It is 75 cm. long.’’

6.1.5 Unit symbols obtained by multiplication

Symbols for units formed from other units by multiplication are indicated by means of either a

half-high (that is, centered) dot or a space. However, this Guide , as does Ref. [8], prefers the half-high

dot because it is less likely to lead to confusion.

Example : N ? m or N m

Notes:

1 A half-high dot or space is usually imperative. For example, m ? s21 is the symbol

for the meter per second while ms21 is the symbol for the reciprocal millisecond

(103 s21 — see Sec. 6.2.3).

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Guide for the Use of the International System of Units (SI)

2 Reference [6: ISO 31-0] suggests that if a space is used to indicate units formed by multiplication, the space may be omitted if it does not cause confusion. This possibility is

reflected in the common practice of using the symbol kWh rather than kW ? h or kW h

for the kilowatt hour. Nevertheless, this Guide takes the position that a half-high dot or

a space should always be used to avoid possible confusion; and that for this same reason,

only one of these two allowed forms should be used in any given manuscript.

6.1.6 Unit symbols obtained by division

Symbols for units formed from other units by division are indicated by means of a solidus

(oblique stroke, /), a horizontal line, or negative exponents.

Example : m/s, m

s , or m ? s21

However, to avoid ambiguity, the solidus must not be repeated on the same line unless parentheses

are used.

Examples: m/s2 or m ? s22 but not: m/s/s

m ? kg/(s3 ? A) or m ? kg ? s23 ? A21 but not: m ? kg/s3

/A

Negative exponents should be used in complicated cases.

6.1.7 Unacceptability of unit symbols and unit names together

Unit symbols and unit names are not used together. (See also Secs. 9.5 and 9.8.)

Example : C/kg, C ? kg21, or coulomb per but not: coulomb/kg; coulomb per kg;

kilogram C/kilogram; coulomb ? kg21

;

C per kg; coulomb/kilogram

6.1.8 Unacceptability of abbreviations for units

Because acceptable units generally have internationally recognized symbols and names, it is not

permissible to use abbreviations for their unit symbols or names, such as sec (for either s or second),

sq. mm (for either mm2 or square millimeter), cc (for either cm3 or cubic centimeter), mins (for either

min or minutes), hrs (for either h or hours), lit (for either L or liter), amps (for either A or amperes),

AMU (for either u or unified atomic mass unit), or mps (for either m/s or meter per second).

Although the values of quantities are normally expressed using symbols for numbers and symbols for

units (see Sec. 7.6), if for some reason the name of a unit is more appropriate than the unit symbol

(see Sec. 7.6, note 3), the name of the unit should be spelled out in full.

6.2 Rules and style conventions for SI prefixes

The following eight sections give rules and style conventions related to the SI prefixes.

6.2.1 Typeface and spacing

Prefix symbols are printed in roman (upright) type regardless of the type used in the surrounding text, and are attached to unit symbols without a space between the prefix symbol and the unit

symbol. This last rule also applies to prefixes attached to unit names.

Examples: mL (milliliter) pm (picometer) GV (gigaohm) THz (terahertz)

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Guide for the Use of the International System of Units (SI)

6.2.2 Capitalization

The prefix symbols Y (yotta), Z (zetta), E (exa), P (peta), T (tera), G (giga), and M (mega) are

printed in upper-case letters while all other prefix symbols are printed in lower-case letters (see Table

5). Prefixes are normally printed in lower-case letters.

6.2.3 Inseparability of prefix and unit

The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable

symbol (forming a multiple or submultiple of the unit concerned) which can be raised to a positive

or negative power and which can be combined with other unit symbols to form compound unit symbols.

Examples: 2.3 cm3 = 2.3 (cm)3 = 2.3 (1022 m)3 = 2.3 3 1026 m3

1 cm21 = 1 (cm)21 = 1 (1022 m)21 = 102 m21

5000 ms21 = 5000 (ms)21 = 5000 (1026 s)21 = 5000 3 106 s21 = 5 3 109 s21

1 V/cm = (1 V)/(1022 m) = 102 V/m

Prefixes are also inseparable from the unit names to which they are attached. Thus, for example,

millimeter, micropascal, and meganewton are single words.

6.2.4 Unacceptability of compound prefixes

Compound prefix symbols, that is, prefix symbols formed by the juxtaposition of two or more

prefix symbols, are not permitted. This rule also applies to compound prefixes.

Example : nm (nanometer) but not: mmm (millimicrometer)

6.2.5 Use of multiple prefixes

In a derived unit formed by division, the use of a prefix symbol (or a prefix) in both the numerator and the denominator may cause confusion. Thus, for example, 10 kV/mm is acceptable, but

10 MV/m is often considered preferable because it contains only one prefix symbol and it is in the

numerator.

In a derived unit formed by multiplication, the use of more than one prefix symbol (or more than

one prefix) may also cause confusion. Thus, for example, 10 MV • ms is acceptable, but 10 kV • s is

often considered preferable.

Note: Such considerations usually do not apply if the derived unit involves the kilogram. For example, 0.13 mmol/g is not considered preferable to 0.13 mol/kg.

6.2.6 Unacceptability of stand-alone prefixes

Prefix symbols cannot stand alone and thus cannot be attached to the number 1, the symbol for

the unit one. In a similar vein, prefixes cannot be attached to the name of the unit one, that is, to the

word ‘‘one.’’ (See Sec. 7.10 for a discussion of the unit one.)

Example : the number density of Pb atoms is 5 3 106

/m3 but not: the number density of

Pb atoms is 5 M/m3

6.2.7 Prefixes and the kilogram

For historical reasons, the name ‘‘kilogram’’ for the SI base unit of mass contains the name

‘‘kilo,’’ the SI prefix for 103

. Thus, because compound prefixes are unacceptable (see Sec. 6.2.4),

symbols for decimal multiples and submultiples of the unit of mass are formed by attaching SI prefix

symbols to g, the unit symbol for gram, and the names of such multiples and submultiples are formed

by attaching SI prefixes to the name ‘‘gram.’’

Example : 1026 kg = 1 mg (1 milligram) but not: 1026 kg = 1 mkg (1 microkilogram)

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Guide for the Use of the International System of Units (SI)

6.2.8 Prefixes with the degree Celsius and units accepted for use with the SI

Prefix symbols may be used with the unit symbol 8C and prefixes may be used with the unit

name ‘‘degree Celsius.’’ For example, 12 m8C (12 millidegrees Celsius) is acceptable. However, to

avoid confusion, prefix symbols (and prefixes) are not used with the time- related unit symbols

(names) min (minute), h (hour), d (day); nor with the angle-related symbols (names) 8 (degree), '

(minute), and " (second) (see Table 6).

Prefix symbols (and prefixes) may be used with the unit symbols (names) L (liter),

t (metric ton), eV (electronvolt), and u (unified atomic mass unit) (see Tables 6 and 7). However,

although submultiples of the liter such as mL (milliliter) and dL (deciliter) are in common use,

multiples of the liter such as kL (kiloliter) and ML (megaliter) are not. Similarly, although multiples

of the metric ton such as kt (kilometric ton) are commonly used, submultiples such as mt (millimetric ton), which is equal to the kilogram (kg), are not. Examples of the use of prefix symbols with

eV and u are 80 MeV (80 megaelectronvolts) and 15 nu (15 nanounified atomic mass units).

7 Rules and Style Conventions for Expressing Values of Quantities

7.1 Value and numerical value of a quantity

The value of a quantity is its magnitude expressed as the product of a number and a unit, and

the number multiplying the unit is the numerical value of the quantity expressed in that unit.

More formally, the value of quantity A can be written as A = {A } [A ], where {A } is the numerical value of A when the value of A is expressed in the unit [A ]. The numerical value can therefore

be written as {A } = A /[A ], which is a convenient form for use in figures and tables. Thus, to eliminate the possibility of misunderstanding, an axis of a graph or the heading of a column of a table can

be labeled ‘‘t /8C’’ instead of ‘‘t (8C)’’ or ‘‘Temperature (8C).’’ Similarly, an axis or column heading

can be labeled ‘‘E /(V/m)’’ instead of ‘‘E (V/m)’’ or ‘‘Electric field strength (V/m).’’

Examples:

1 In the SI, the value of the velocity of light in vacuum is c = 299 792 458 m/s

exactly. The number 299 792 458 is the numerical value of c when c is expressed in the

unit m/s, and equals c /(m/s).

2 The ordinate of a graph is labeled T /(103 K), where T is thermodynamic temperature

and K is the unit symbol for kelvin, and has scale marks at 0, 1, 2, 3, 4, and 5. If the

ordinate value of a point on a curve in the graph is estimated to be 3.2, the corresponding

temperature is T /(103 K) = 3.2 or T = 3200 K. Notice the lack of ambiguity in this form

of labeling compared with ‘‘Temperature (103 K).’’

3 An expression such as ln( p /MPa), where p is the quantity symbol for pressure and MPa

is the unit symbol for megapascal, is perfectly acceptable because p /MPa is the numerical value of p when p is expressed in the unit MPa and is simply a number.

Notes:

1 For the conventions concerning the grouping of digits, see Sec. 10.5.3.

2 An alternative way of writing c /(m/s) is {c}m/s, meaning the numerical value

of c when c is expressed in the unit m/s.

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Guide for the Use of the International System of Units (SI)

7.2 Space between numerical value and unit symbol

In the expression for the value of a quantity, the unit symbol is placed after the numerical value

and a space is left between the numerical value and the unit symbol.

The only exceptions to this rule are for the unit symbols for degree, minute, and second for plane

angle: 8, ', and ", respectively (see Table 6), in which case no space is left between the numerical

value and the unit symbol.

Example : a = 30822'8"

Note: a is a quantity symbol for plane angle.

This rule means that:

(a) The symbol 8C for the degree Celsius is preceded by a space when one expresses the values of

Celsius temperatures.

Example : t = 30.2 8C but not: t = 30.28C or t = 30.28 C

(b) Even when the value of a quantity is used in an adjectival sense, a space is left between the

numerical value and the unit symbol. (This rule recognizes that unit symbols are not like ordinary

words or abbreviations but are mathematical entities, and that the value of a quantity should be

expressed in a way that is as independent of language as possible — see Secs. 7.6 and 7.10.3.)

Examples: a 1 m end gauge but not: a 1-m end gauge

a 10 kV resistor but not: a 10-kV resistor

However, if there is any ambiguity, the words should be rearranged accordingly. For example, the

statement ‘‘the samples were placed in 22 mL vials’’ should be replaced with the statement ‘‘the

samples were placed in vials of volume 22 mL.’’

Note: When unit names are spelled out, the normal rules of English apply. Thus, for example, ‘‘a roll of 35-millimeter film’’ is acceptable (see Sec. 7.6, note 3).

7.3 Number of units per value of a quantity

The value of a quantity is expressed using no more than one unit.

Example : l = 10.234 m but not: l = 10 m 23 cm 4 mm

Note: Expressing the values of time intervals and of plane angles are exceptions to this rule.

However, it is preferable to divide the degree decimally. Thus one should write

22.208 rather than 22812', except in fields such as cartography and astronomy.

7.4 Unacceptability of attaching information to units

When one gives the value of a quantity, it is incorrect to attach letters or other symbols to the

unit in order to provide information about the quantity or its conditions of measurement. Instead, the

letters or other symbols should be attached to the quantity.

Example : Vmax = 1000 V but not: V = 1000 Vmax

Note: V is a quantity symbol for potential difference.

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Guide for the Use of the International System of Units (SI)

7.5 Unacceptability of mixing information with units

When one gives the value of a quantity, any information concerning the quantity or its conditions

of measurement must be presented in such a way as not to be associated with the unit. This means

that quantities must be defined so that they can be expressed solely in acceptable units (including the

unit one — see Sec. 7.10).

Examples:

the Pb content is 5 ng/L but not: 5 ng Pb/L or 5 ng of

lead/L

the sensitivity for NO3 molecules is 5 3 1010 /cm3 but not: the sensitivity is 5 3 1010

NO3 molecules/cm3

the neutron emission rate is 5 3 1010 /s but not: the emission rate is

5 3 1010 n/s

the number density of O2 atoms is 3 3 1018 /cm3 but not: the density is 3 3 1018 O2

atoms/cm3

the resistance per square is 100 V but not: the resistance is 100 V/

square

7.6 Symbols for numbers and units versus spelled-out names of numbers and units

This Guide takes the position that the key elements of a scientific or technical paper,

particularly the results of measurements and the values of quantities that influence the measurements, should be presented in a way that is as independent of language as possible. This will allow

the paper to be understood by as broad an audience as possible, including readers with limited knowledge of English. Thus, to promote the comprehension of quantitative information in general and its

broad understandability in particular, values of quantities should be expressed in acceptable units

using

— the Arabic symbols for numbers, that is, the Arabic numerals, not the spelled-out names

of the Arabic numerals; and

— the symbols for the units, not the spelled-out names of the units.

Examples:

the length of the laser is 5 m but not: the length of the laser is five meters

the sample was annealed at a but not: the sample was annealed at a temperature

temperature of 955 K for 12 h of 955 kelvins for 12 hours

Notes:

1 If the intended audience for a publication is unlikely to be familiar with a particular unit

symbol, it should be defined when first used.

2 Because the use of the spelled-out name of an Arabic numeral with a unit symbol can

cause confusion, such combinations must strictly be avoided. For example, one should

never write ‘‘the length of the laser is five m.’’

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Guide for the Use of the International System of Units (SI)

3 Occasionally, a value is used in a descriptive or literary manner and it is fitting to use the

spelled-out name of the unit rather than its symbol. Thus this Guide considers acceptable

statements such as ‘‘the reading lamp was designed to take two 60-watt light bulbs,’’ or

‘‘the rocket journeyed uneventfully across 380 000 kilometers of space,’’ or ‘‘they

bought a roll of 35-millimeter film for their camera.’’

4 The United States Government Printing Office Style Manual (Ref. [4], pp. 165-171)

gives the rule that symbols for numbers are always to be used when one expresses (a) the

value of a quantity in terms of a unit of measurement, (b) time (including dates), and (c)

an amount of money. This publication should be consulted for the rules governing the

choice between the use of symbols for numbers and the spelled-out names of numbers

when numbers are dealt with in general.

7.7 Clarity in writing values of quantities

The value of a quantity is expressed as the product of a number and a unit (see Sec. 7.1). Thus,

to avoid possible confusion, this Guide takes the position that values of quantities must be written so

that it is completely clear to which unit symbols the numerical values of the quantities belong. Also

to avoid possible confusion, this Guide strongly recommends that the word ‘‘to’’ be used to indicate

a range of values for a quantity instead of a range dash (that is, a long hyphen) because the dash could

be misinterpreted as a minus sign. (The first of these recommendations once again recognizes that

unit symbols are not like ordinary words or abbreviations but are mathematical entities — see

Sec. 7.2.)

Examples:

51 mm351 mm325 mm but not: 51351325 mm

225 nm to 2400 nm or (225 to 2400) nm but not: 225 to 2400 nm

0 8C to 100 8C or (0 to 100) 8C but not: 0 8C 2 100 8C

0 V to 5 V or (0 to 5) V but not: 0 2 5 V

(8.2, 9.0, 9.5, 9.8, 10.0) GHz but not: 8.2, 9.0, 9.5, 9.8, 10.0 GHz

63.2 m 6 0.1 m or (63.2 6 0.1) m but not: 63.2 6 0.1 m or 63.2 m 6 0.1

129 s 2 3 s = 126 s or (129 2 3) s = 126 s but not: 129 2 3 s = 126 s

Note: For the conventions concerning the use of the multiplication sign, see Sec. 10.5.4.

7.8 Unacceptability of stand-alone unit symbols

Symbols for units are never used without numerical values or quantity symbols (they are not

abbreviations).

Examples:

there are 106 mm in 1 km but not: there are many mm in a km

it is sold by the cubic meter but not: it is sold by the m3

t /8C, E /(V/m), p /MPa, and the like are perfectly acceptable (see Sec. 7.1)

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Guide for the Use of the International System of Units (SI)

7.9 Choosing SI prefixes

The selection of the appropriate decimal multiple or submultiple of a unit for expressing the

value of a quantity, and thus the choice of SI prefix, is governed by several factors. These include

— the need to indicate which digits of a numerical value are significant,

— the need to have numerical values that are easily understood, and

— the practice in a particular field of science or technology.

A digit is significant if it is required to express the numerical value of a quantity. In the expression

l = 1200 m, it is not possible to tell whether the last two zeroes are significant or only indicate the

magnitude of the numerical value of l. However, in the expression l = 1.200 km, which uses the SI

prefix symbol for 103 (kilo, symbol k), the two zeroes are assumed to be significant because if they

were not, the value of l would have been written l = 1.2 km.

It is often recommended that, for ease of understanding, prefix symbols should be

chosen in such a way that numerical values are between 0.1 and 1000, and that only prefix symbols

that represent the number 10 raised to a power that is a multiple of 3 should be used.

Examples: 3.3 3 107 Hz may be written as 33 3 106 Hz = 33 MHz

0.009 52 g may be written as 9.52 3 1023 g = 9.52 mg

2703 W may be written as 2.703 3 103 W = 2.703 kW

5.8 3 1028 m may be written as 58 3 1029 m = 58 nm

However, the values of quantities do not always allow this recommendation to be followed, nor is it

mandatory to try to do so.

In a table of values of the same kind of quantities or in a discussion of such values, it is usually

recommended that only one prefix symbol should be used even if some of the

numerical values are not between 0.1 and 1000. For example, it is often considered preferable to

write ‘‘the size of the sample is 10 mm 3 3 mm 3 0.02 mm’’ rather than ‘‘the size of the sample is

1 cm 3 3 mm 3 20 mm.’’

In certain kinds of engineering drawings it is customary to express all dimensions in millimeters. This is an example of selecting a prefix based on the practice in a particular field of science or

technology.

7.10 Values of quantities expressed simply as numbers: the unit one, symbol 1

Certain quantities, such as refractive index, relative permeability, and mass fraction, are defined

as the ratio of two mutually comparable quantities and thus are of dimension one (see Sec. 7.14). The

coherent SI unit for such a quantity is the ratio of two identical SI units and may be expressed by the

number 1. However, the number 1 generally does not appear in the expression for the value of a quantity of dimension one. For example, the value of the refractive index of a given medium is expressed

as n = 1.51 3 1 = 1.51.

On the other hand, certain quantities of dimension one have units with special names and symbols which can be used or not depending on the circumstances. Plane angle and solid angle, for which

the SI units are the radian (rad) and steradian (sr), respectively, are examples of such quantities (see

Sec. 4.3).

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Guide for the Use of the International System of Units (SI)

7.10.1 Decimal multiples and submultiples of the unit one

Because SI prefix symbols cannot be attached to the unit one (see Sec. 6.2.6), powers of 10 are

used to express decimal multiples and submultiples of the unit one.

Example : mr = 1.2 3 1026 but not: mr = 1.2 m

Note: mr is the quantity symbol for relative permeability.

7.10.2 %, percentage by, fraction

In keeping with Ref. [6: ISO 31-0], this Guide takes the position that it is acceptable to use the

internationally recognized symbol % (percent) for the number 0.01 with the SI and thus to express

the values of quantities of dimension one (see Sec. 7.14) with its aid. When it is used, a space is left

between the symbol % and the number by which it is multiplied [6: ISO 31-0]. Further, in keeping

with Sec. 7.6, the symbol % should be used, not the name ‘‘percent.’’

Example :

xB = 0.0025 = 0.25 % but not: xB = 0.0025 = 0.25% or xB = 0.25 percent

Note: xB is the quantity symbol for amount-of-substance fraction of B (see Sec. 8.6.2).

Because the symbol % represents simply a number, it is not meaningful to attach information

to it (see Sec. 7.4). One must therefore avoid using phrases such as ‘‘percentage by weight,’’

‘‘percentage by mass,’’ ‘‘percentage by volume,’’ or ‘‘percentage by amount of substance.’’

Similarly, one must avoid writing, for example, ‘‘% (m /m),’’ ‘‘% (by weight),’’

‘‘% (V /V),’’ ‘‘% (by volume),’’ or ‘‘% (mol/mol).’’ The preferred forms are ‘‘the mass fraction is

0.10,’’ or ‘‘the mass fraction is 10 %,’’ or ‘‘wB = 0.10,’’ or ‘‘wB = 10 %’’ (wB is the quantity symbol

for mass fraction of B — see Sec. 8.6.10); ‘‘the volume fraction is 0.35,’’ or ‘‘the volume fraction is

35 %,’’ or ‘‘wB = 0.35,’’ or ‘‘wB = 35 %’’ (wB is the quantity symbol for volume fraction of B — see

Sec. 8.6.6); and ‘‘the amount-of-substance fraction is 0.15,’’ or ‘‘the amount-of-substance fraction

is 15 %,’’ or ‘‘xB = 0.15,’’ or ‘‘xB = 15 %.’’ Mass fraction, volume fraction, and amount-of-substance

fraction of B may also be expressed as in the following examples: wB = 3 g/kg; wB = 6.7 mL/L;

xB = 185 mmol/mol. Such forms are highly recommended. (See also Sec. 7.10.3.)

In the same vein, because the symbol % represents simply the number 0.01, it is incorrect to

write, for example, ‘‘where the resistances R1 and R2 differ by 0.05 %,’’ or ‘‘where the resistance R1

exceeds the resistance R2 by 0.05 %.’’ Instead, one should write, for example, ‘‘where

R1 = R2(1 + 0.05 %),’’ or define a quantity D via the relation D = (R1 2 R2)/R2 and write ‘‘where

D = 0.05 %.’’ Alternatively, in certain cases, the word ‘‘fractional’’ or ‘‘relative’’ can be used. For

example, it would be acceptable to write ‘‘the fractional increase in the resistance of the 10 kV

reference standard in 1994 was 0.002 %.’’

7.10.3 ppm, ppb, and ppt

In keeping with Ref. [6: ISO 31-0], this Guide takes the position that the languagedependent terms part per million, part per billion and part per trillion, and their respective abbreviations ‘‘ppm,’’ ‘‘ppb,’’ and ‘‘ppt’’ (and similar terms and abbreviations), are not acceptable for use

with the SI to express the values of quantities. Forms such as those given in the following examples

should be used instead.

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Guide for the Use of the International System of Units (SI)

Examples:

a stability of 0.5 (mA/A)/min but not: a stability of 0.5 ppm/min

a shift of 1.1 nm/m but not: a shift of 1.1 ppb

a frequency change of 0.35 3 1029 f but not: a frequency change of 0.35 ppb

a sensitivity of 2 ng/kg but not: a sensitivity of 2 ppt

the relative expanded uncertainty of the resistance R is Ur = 3 mV/V

or

the expanded uncertainty of the resistance R is U = 3 3 1026 R

or

the relative expanded uncertainty of the resistance R is Ur = 3 3 1026

but not:

the relative expanded uncertainty of the resistance R is Ur = 3 ppm

Because the names of numbers 109 and larger are not uniform worldwide, it is best that they be

avoided entirely (in most countries, 1 billion = 1 3 1012, not 1 3 109 as in the United States); the

preferred way of expressing large numbers is to use powers of 10. This ambiguity in the names of

numbers is one of the reasons why the use of ppm, ppb, ppt, and the like is deprecated. Another, and

a more important one, is that it is inappropriate to use abbreviations that are language dependent

together with internationally recognized signs and symbols, such as MPa, ln, 1013, and %, to express

the values of quantities and in equations or other mathematical expressions (see also Sec. 7.6).

Note: This Guide recognizes that in certain cases the use of ppm, ppb, and the like may be required

by a law or a regulation. Under these circumstances, Secs. 2.1 and 2.1.1 apply.

7.10.4 Roman numerals

It is unacceptable to use Roman numerals to express the values of quantities. In particular, one

should not use C, M, and MM as substitutes for 102

, 103, and 106, respectively.

7.11 Quantity equations and numerical-value equations

A quantity equation expresses a relation among quantities. An example is l = yt, where l is the

distance a particle in uniform motion with velocity y travels in the time t.

Because a quantity equation such as l = yt is independent of the units used to express the values

of the quantities that compose the equation, and because l, y , and t represent quantities and not

numerical values of quantities, it is incorrect to associate the equation with a statement such as

‘‘where l is in meters, y is in meters per second, and t is in seconds.’’

On the other hand, a numerical value equation expresses a relation among numerical values of

quantities and therefore does depend on the units used to express the values of the quantities. For

example, {l}m = 3.621 {y}km/h {t}s expresses the relation among the numerical values of l, y , and t

only when the values of l, y , and t are expressed in the units meter, kilometer per hour, and second,

respectively. (Here {A }X is the numerical value of quantity A when its value is expressed in the unit

X — see Sec. 7.1, note 2.)

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Guide for the Use of the International System of Units (SI)

An alternative way of writing the above numerical value equation, and one that is preferred because of its simplicity and generality, is l /m = 3.621 [y /(km/h)](t /s). NIST authors

should consider using this preferred form instead of the more traditional form ‘‘l = 3.621 yt, where

l is in meters, y is in kilometers per hour, and t is in seconds.’’ In fact, this form is still ambiguous

because no clear distinction is made between a quantity and its numerical value. The correct statement is, for example, ‘‘l* = 3.621 y* t*, where l* is the numerical value of the distance l travelled

by a particle in uniform motion when l is expressed in meters, y* is the numerical value of the velocity y of the particle when y is expressed in kilometers per hour, and t* is the numerical value of the

time of travel t of the particle when t is expressed in seconds.’’ Clearly, as is done here, it is important

to use different symbols for quantities and their numerical values to avoid confusion.

It is the strong recommendation of this Guide that because of their universality, quantity equations should be used in preference to numerical-value equations. Further, if a numerical value equation is used, it should be written in the preferred form given in the above paragraph and if at all

feasible, the quantity equation from which it was obtained should be given.

Notes:

1 Two other examples of numerical-value equations written in the preferred form are as

follows, where Eg is the gap energy of a compound semiconductor and k is the conductivity of an electrolytic solution:

Eg /eV = 1.425 2 1.337x + 0.270x 2

, 0 < x < 0.15,

where x is an appropriately defined amount-of-substance fraction (see Sec. 8.6.2).

k /(S/cm) = 0.065 135 + 1.7140 3 1023(t /8C) + 6.4141 3 1026(t /8C)2 2

4.5028 3 1028(t /8C)3, 0 8C < t < 50 8C, where t is Celsius temperature.

2 Writing numerical-value equations for quantities expressed in inch-pound units in the

preferred form will simplify their conversion to numerical-value equations for the quantities expressed in units of the SI.

7.12 Proper names of quotient quantities

Derived quantities formed from other quantities by division are written using the words

‘‘divided by’’ rather than the words ‘‘per unit’’ in order to avoid the appearance of associating a

particular unit with the derived quantity.

Example : pressure is force divided by area but not: pressure is force per unit area

7.13 Distinction between an object and its attribute

To avoid confusion, when discussing quantities or reporting their values, one should distinguish

between a phenomenon, body, or substance, and an attribute ascribed to it. For example, one should

recognize the difference between a body and its mass, a surface and its area, a capacitor and its

capacitance, and a coil and its inductance. This means that although it is acceptable to say ‘‘an object

of mass 1 kg was attached to a string to form a pendulum,’’ it is not acceptable to say ‘‘a mass of 1 kg

was attached to a string to form a pendulum.’’

7.14 Dimension of a quantity

Any SI derived quantity Q can be expressed in terms of the SI base quantities length (l), mass

(m), time (t), electric current (I), thermodynamic temperature (T), amount of substance (n), and

luminous intensity (Iv) by an equation of the form

Q=l a m b t g I d T « n z Iv

h O

K

k = 1

ak ,

22
Guide for the Use of the International System of Units (SI)

where the exponents a, b, g, . . . are numbers and the factors ak are also numbers. The dimension

of Q is defined to be

dim Q = La Mb Tg I

d U« Nz Jh ,

where L, M, T, I, U, N, and J are the dimensions of the SI base quantities length, mass, time, electric

current, thermodynamic temperature, amount of substance, and luminous intensity, respectively. The

exponents a, b, g, . . . are called ‘‘dimensional exponents.’’ The SI derived unit of Q is

ma ? kgb ? sg ? Ad ? K« ? molz ? cdh, which is obtained by replacing the dimensions of the SI base

quantities in the dimension of Q with the symbols for the corresponding base units.

Example : Consider a nonrelativistic particle of mass m in uniform motion which travels a

distance l in a time t. Its velocity is y=l /t and its kinetic energy is Ek=my2

/2=

l 2mt22/2. The dimension of Ek is dim Ek = L2MT22 and the dimensional exponents are

2, 1, and 22. The SI derived unit of Ek is then m2 ? kg ? s22

, which is given the special

name ‘‘joule’’ and special symbol J.

A derived quantity of dimension one, which is sometimes called a ‘‘dimensionless quantity,’’ is

one for which all of the dimensional exponents are zero: dim Q = 1. It therefore follows that the

derived unit for such a quantity is also the number one, symbol 1, which is sometimes called a

‘‘dimensionless derived unit.’’

Example : The mass fraction wB of a substance B in a mixture is given by wB = mB/m, where mB

is the mass of B and m is the mass of the mixture (see Sec. 8.6.10). The dimension of

wB is dim wB = M1

M21 = 1; all of the dimensional exponents of wB are zero, and its

derived unit is kg1 ? kg21 = 1 also.

8 Comments on Some Quantities and Their Units

8.1 Time and rotational frequency

The SI unit of time (actually time interval) is the second (s) and should be used in all technical

calculations. When time relates to calendar cycles, the minute (min), hour (h), and day (d) may be

necessary. For example, the kilometer per hour (km/h) is the usual unit for expressing vehicular

speeds. Although there is no universally accepted symbol for the year, Ref. [6: ISO 31-1] suggests the

symbol a.

The rotational frequency n of a rotating body is defined to be the number of revolutions it makes

in a time interval divided by that time interval [6: ISO 31-5]. The SI unit of this quantity is thus the

reciprocal second (s21

). However, as pointed out in Ref. [6: ISO 31-5], the designations ‘‘revolutions

per second’’ (r/s) and ‘‘revolutions per minute’’ (r/min) are widely used as units for rotational

frequency in specifications on rotating machinery.

8.2 Volume

The SI unit of volume is the cubic meter (m3

) and may be used to express the volume of any

substance, whether solid, liquid, or gas. The liter (L) is a special name for the cubic decimeter (dm3

)

but the CGPM recommends that the liter not be used to give the results of high accuracy measurements of volumes [2, 3]. Also, it is not common practice to use the liter to express the volumes of

solids nor to use multiples of the liter such as the kiloliter (kL) [see Sec. 6.2.8, and also Table 6,

footnote (b)].

23
Guide for the Use of the International System of Units (SI)

8.3 Weight

In science and technology, the weight of a body in a particular reference frame is defined as the

force that gives the body an acceleration equal to the local acceleration of free fall in that reference

frame [6: ISO 31-3]. Thus the SI unit of the quantity weight defined in this way is the newton (N).

When the reference frame is a celestial object, Earth for example, the weight of a body is commonly

called the local force of gravity on the body.

Example : The local force of gravity on a copper sphere of mass 10 kg located on the surface

of the Earth, which is its weight at that location, is approximately 98 N.

Note: The local force of gravity on a body, that is, its weight, consists of the resultant of

all the gravitational forces acting on the body and the local centrifugal force due to

the rotation of the celestial object. The effect of atmospheric buoyancy is usually

excluded, and thus the weight of a body is generally the local force of gravity on the

body in vacuum.

In commercial and everyday use, and especially in common parlance, weight is usually used as

a synonym for mass. Thus the SI unit of the quantity weight used in this sense is the kilogram (kg)

and the verb ‘‘to weigh’’ means ‘‘to determine the mass of’’ or ‘‘to have a mass of.’’

Examples: the child’s weight is 23 kg the briefcase weighs 6 kg Net wt. 227 g

Inasmuch as NIST is a scientific and technical organization, the word ‘‘weight’’ used in the

everyday sense (that is, to mean mass) should appear only occasionally in NIST publications; the

word ‘‘mass’’ should be used instead. In any case, in order to avoid confusion, whenever the word

‘‘weight’’ is used, it should be made clear which meaning is intended.

8.4 Relative atomic mass and relative molecular mass

The terms atomic weight and molecular weight are obsolete and thus should be avoided. They

have been replaced by the equivalent but preferred terms relative atomic mass, symbol Ar, and relative

molecular mass, symbol Mr, respectively [6: ISO 31-8], which better reflect their definitions. Like

atomic weight and molecular weight, relative atomic mass and relative molecular mass are quantities

of dimension one and are expressed simply as numbers. The definitions of these quantities are as

follows [6: ISO 31-8]:

Relative atomic mass (formerly atomic weight): ratio of the average mass per atom of an element to

1/12 of the mass of the atom of the nuclide 12C.

Relative molecular mass (formerly molecular weight): ratio of the average mass per molecule or

specified entity of a substance to 1/12 of the mass of an atom of the nuclide 12C.

Examples: Ar(Si) = 28.0855 Mr(H2) = 2.0159 Ar(

12C) = 12 exactly

Notes:

1 It follows from these definitions that if X denotes a specified atom or nuclide and B

a specified molecule or entity (or more generally, a specified substance), then

Ar(X) = m(X)/[m(

12C)/12] and Mr(B) = m(B)/[m(12C)/12], where m(X) is the mass

of X, m(B) is the mass of B, and m(

12C) is the mass of an atom of the nuclide 12C.

It should also be recognized that m(

12C)/12 = u, the unified atomic mass unit, which is

approximately equal to 1.66 3 10227 kg [see Table 7, footnote (b)].

2 It follows from the examples and note 1 that the respective average masses of Si, H2, and 12C are m(Si) = Ar(Si) u, m(H2) = Mr(H2) u, and m(

12C) = Ar(12C) u.

24
Guide for the Use of the International System of Units (SI)

3 In publications dealing with mass spectrometry, one may encounter a statement such as

‘‘the mass-to-charge ratio is 15.’’ What is usually meant in this case is that the ratio of

the nucleon number (that is, mass number — see Sec. 10.4.2) of the ion to its number of

charges is 15. Thus mass-to-charge ratio is a quantity of dimension one, even though it

is commonly denoted by the symbol m /z. For example, the mass-to-charge ratio of the

ion 12C7

1

H7

++ is 91/2 = 45.5.

8.5 Temperature interval and temperature difference

As discussed in Sec. 4.2.1.1, Celsius temperature (t) is defined in terms of thermodynamic temperature (T) by the equation t = T 2 T0, where T0 = 273.15 K by definition. This implies that the

numerical value of a given temperature interval or temperature difference whose value is expressed

in the unit degree Celsius (8C) is equal to the numerical value of the same interval or difference when

its value is expressed in the unit kelvin (K); or in the notation of Sec. 7.1, note 2, {Dt }8C = {DT}K.

Thus temperature intervals or temperature differences may be expressed in either the degree Celsius

or the kelvin using the same numerical value.

Example : The difference in temperature between the freezing point of gallium and the triple point

of water is Dt = 29.7546 8C = DT = 29.7546 K.

8.6 Amount of substance, concentration, molality, and the like

The following section discusses amount of substance, and the subsequent nine sections, which

are based on Ref. [6: ISO 31-8] and which are succinctly summarized in Table 12, discuss quantities

that are quotients involving amount of substance, volume, or mass. In the table and its associated

sections, symbols for substances are shown as subscripts, for example, xB, nB, bB. However, it is generally preferable to place symbols for substances and their states in parentheses immediately after the

quantity symbol, for example n(H2SO4). (For a detailed discussion of the use of the SI in physical

chemistry, see the book cited in Ref. [8], note 5.)

8.6.1 Amount of substance

Quantity symbol: n (also n) . SI unit: mole (mol).

Definition: See Sec. A.7.

Notes:

1 Amount of substance is one of the seven base quantities upon which the SI is founded

(see Sec. 4.1 and Table 1).

2 In general, n(xB) = n(B)/x , where x is a number. Thus, for example, if the amount of

substance of H2SO4 is 5 mol, the amount of substance of (1/3)H2SO4 is 15 mol:

n[(1/3)H2SO4]=3n(H2SO4).

Example : The relative atomic mass of a fluorine atom is Ar(F) = 18.9984. The relative molecular

mass of a fluorine molecule may therefore be taken as Mr(F2)=2Ar(F) = 37.9968. The

molar mass of F2 is then M(F2) = 37.99683 1023 kg/mol = 37.9968 g/mol (see Sec.

8.6.4). The amount of substance of, for example, 100 g of F2 is then n(F2) =

100 g/(37.9968 g/mol) = 2.63 mol.

8.6.2 Mole fraction of B; amount-of-substance fraction of B

Quantity symbol: xB (also yB). SI unit: one (1) (amount-of-substance fraction is a quantity of

dimension one).

Definition: ratio of the amount of substance of B to the amount of substance of the mixture:

xB = nB/n.

25
Guide for the Use of the International System of Units (SI)

Table 12. Summary description of nine quantities that are quotients involving amount of substance,

volume, or mass(a)

(a) Adapted from Canadian Metric Practice Guide (see Ref. [8], note 3; the book cited in Ref. [8], note 5, may also

be consulted).

Notes:

1 This quantity is commonly called ‘‘mole fraction of B’’ but this Guide prefers the name

‘‘amount-of-substance fraction of B’’ because it does not contain the name of the unit

mole (compare kilogram fraction to mass fraction).

2 For a mixture composed of substances A, B, C, ..., n=nA + nB + nC +

... ≡ O

A

nA .

3 A related quantity is amount-of-substance ratio of B (commonly called ‘‘mole ratio of

solute B’’), symbol rB. It is the ratio of the amount of substance of B to the amount of

substance of the solvent substance: rB = nB/nS. For a single solute C in a solvent substance (a one-solute solution), rC = xC/(1 2 xC). This follows from the relations

n = nC + nS, xC = nC/n, and rC = nC/nS, where the solvent substance S can itself be a mixture.

8.6.3 Molar volume

Quantity symbol: Vm. SI unit: cubic meter per mole (m3/mol).

Definition: volume of a substance divided by its amount of substance: Vm = V /n.

Notes:

1 The word ‘‘molar’’ means ‘‘divided by amount of substance.’’

Quantity in numerator

Amount of substance

Symbol: n

SI unit: mol

Volume

Symbol: V

SI unit: m3

Mass

Symbol: m

SI unit: kg

Amount of substance

Symbol: n

SI unit: mol

amount-of-substance

fraction

xB = nB

n

SI unit: mol/mol = 1

molar volume

Vm = V

n

SI unit: m3

/mol

molar mass

M = m

n

SI unit: kg /mol

Volume

Symbol: V

SI unit: m3

amount-of-substance

concentration

cB = nB

V

SI unit: mol/m3

volume fraction

wB = xBV*

m,B

S xAV*

m,A

SI unit: m3/m3 = 1

mass density

r = m

V

SI unit: kg/m3

Mass

Symbol: m

SI unit: kg

molality

bB = nB

mA

SI unit: mol/kg

specific volume

y = V

m

SI unit: m3

/kg

mass fraction

wB = mB

m

SI unit: kg/kg = 1

26

Quantity in denominator
Guide for the Use of the International System of Units (SI)

2 For a mixture, this term is often called ‘‘mean molar volume.’’

3 The amagat should not be used to express molar volumes or reciprocal molar volumes.

(One amagat is the molar volume Vm of a real gas at p = 101 325 Pa and T = 273.15 K

and is approximately equal to 22.4 3 1023 m3

/mol. The name ‘‘amagat’’ is also given to

1/Vm of a real gas at p = 101 325 Pa and T = 273.15 K and in this case is approximately

equal to 44.6 mol/m3

.)

8.6.4 Molar mass

Quantity symbol: M. SI unit: kilogram per mole (kg/mol).

Definition: mass of a substance divided by its amount of substance: M = m /n.

Notes:

1 For a mixture, this term is often called ‘‘mean molar mass.’’

2 The molar mass of a substance B of definite chemical composition is given by

M(B) = Mr(B) 3 1023 kg/mol = Mr(B) kg/kmol = Mr g/mol, where Mr(B) is the relative molecular mass of B (see Sec. 8.4). The molar mass of an atom or nuclide X is

M(X) = Ar(X) 3 1023 kg/mol = Ar(X) kg/kmol = Ar(X) g/mol, where Ar(X) is the

relative atomic mass of X (see Sec. 8.4).

8.6.5 Concentration of B; amount-of-substance concentration of B

Quantity symbol: cB. SI unit: mole per cubic meter (mol/m3).

Definition: amount of substance of B divided by the volume of the mixture: cB = nB/V.

Notes:

1 This Guide prefers the name ‘‘amount-of-substance concentration of B’’ for this quantity

because it is unambiguous. However, in practice, it is often shortened to amount concentration of B, or even simply to concentration of B. Unfortunately, this last form can cause

confusion because there are several different ‘‘concentrations,’’ for example, mass concentration of B, rB = mB/V; and molecular concentration of B, CB = NB/V, where NB is

the number of molecules of B.

2 The term normality and the symbol N should no longer be used because they are

obsolete. One should avoid writing, for example, ‘‘a 0.5 N solution of H2SO4’’

and write instead ‘‘a solution having an amount-of-substance concentration of

c [(1/2)H2SO4]) = 0.5 mol/dm3

’’ (or 0.5 kmol/m3 or 0.5 mol/L since 1 mol/dm3

= 1 kmol/m3 = 1 mol/L).

3 The term molarity and the symbol M should no longer be used because they, too, are

obsolete. One should use instead amount-of-substance concentration of B and such units

as mol/dm3

, kmol/m3, or mol/L. (A solution of, for example, 0.1 mol/dm3 was often

called a 0.1 molar solution, denoted 0.1 M solution. The molarity of the solution was said

to be 0.1 M.)

8.6.6 Volume fraction of B

Quantity symbol: wB. SI unit: one (1) (volume fraction is a quantity of dimension one).

Definition: for a mixture of substances A, B, C, ...,

wB = xB V *

m,B

OxA V *

m,A

,

27
Guide for the Use of the International System of Units (SI)

where xA, xB, xC, . . . are the amount-of-substance fractions of A, B, C,..., V *

m,A, V *m,B , V *m,C , . . . are

the molar volumes of the pure substances A, B, C, . . . at the same temperature and pressure, and

where the summation is over all the substances A, B, C, . . . so that S xA = 1.

8.6.7 Mass density; density

Quantity symbol: r. SI unit: kilogram per cubic meter (kg/m3

).

Definition: mass of a substance divided by its volume: r = m /V.

Notes:

1 This Guide prefers the name ‘‘mass density’’ for this quantity because there are several

different ‘‘densities,’’ for example, number density of particles, n = N /V; and charge

density, r = Q /V.

2 Mass density is the reciprocal of specific volume (see Sec. 8.6.9): r = 1/y .

8.6.8 Molality of solute B

Quantity symbol: bB (also mB). SI unit: mole per kilogram (mol/kg).

Definition: amount of substance of solute B in a solution divided by the mass of the solvent:

bB = nB/mA.

Note: The term molal and the symbol m should no longer be used because they are obsolete. One should use instead the term molality of solute B and the unit

mol/kg or an appropriate decimal multiple or submultiple of this unit. (A solution

having, for example, a molality of 1 mol/kg was often called a 1 molal solution,

written 1 m solution.)

8.6.9 Specific volume

Quantity symbol: y . SI unit: cubic meter per kilogram (m3

/kg).

Definition: volume of a substance divided by its mass: y = V /m.

Note: Specific volume is the reciprocal of mass density (see Sec. 8.6.7): y = 1/r.

8.6.10 Mass fraction of B

Quantity symbol: wB. SI unit: one (1) (mass fraction is a quantity of dimension one).

Definition: mass of substance B divided by the mass of the mixture: wB = mB/m.

8.7 Logarithmic quantities and units: level, neper, bel

This section briefly introduces logarithmic quantities and units. It is based on Refs.

[6: ISO 31-2] and [7: IEC 27-3], which should be consulted for further details.

Two of the most common logarithmic quantities are level of a field quantity, symbol LF , and

level of a power quantity, symbol LP ; and two of the most common logarithmic units are the units in

which the values of these quantities are expressed: the neper, symbol Np, or the bel, symbol B, and

decimal multiples and submultiples of the neper and bel formed by attaching SI prefixes to them,

such as the millineper, symbol mNp (1 mNp = 0.001 Np), and the decibel, symbol dB

(1 dB = 0.1 B).

Level of a field quantity is defined by the relation LF = ln(F /F0), where F /F0 is the ratio

of two amplitudes of the same kind, F0 being a reference amplitude. Level of a power quantity is

defined by the relation LP = (1/2) ln(P /P0), where P /P0 is the ratio of two

powers, P0 being a reference power. (Note that if P /P0 = (F /F0)

2

, then LP = LF .) Similar

28
Guide for the Use of the International System of Units (SI)

names symbols, and definitions apply to levels based on other quantities which are linear or quadratic

functions of the amplitudes, respectively. In practice, the name of the field quantity forms the name

of LF and the symbol F is replaced by the symbol of the field quantity. For example, if the field

quantity in question is electric field strength, symbol E, the name of the quantity is ‘‘level of electric

field strength’’ and it is defined by the relation LE = ln(E /E0).

The difference between two levels of a field quantity (called ‘‘field level difference’’) having the

same reference amplitude F0 is DLF = LF 1 2 LF 2 = ln(F1 /F0) 2 ln(F2 /F0) = ln(F1 /F2), and is

independent of F0. This is also the case for the difference between two levels of a power

quantity (called ‘‘power level difference’’) having the same reference power

P0: DLP = LP 1 2 LP 2 = ln(P1 /P0) 2 ln(P2 /P0) = ln(P1 /P2).

It is clear from their definitions that both LF and LP are quantities of dimension one and thus have

as their units the unit one, symbol 1. However, in this case, which recalls the case of plane angle and

the radian (and solid angle and the steradian), it is convenient to give the unit one the special name

‘‘neper’’ or ‘‘bel’’ and to define these so-called dimensionless units as follows:

One neper (1 Np) is the level of a field quantity when F /F0 = e, that is, when

ln(F /F0) = 1. Equivalently, 1 Np is the level of a power quantity when P /P0 = e2

, that is, when

(1/2) ln(P /P0) = 1. These definitions imply that the numerical value of LF when LF is

expressed in the unit neper is {LF }Np = ln(F /F0), and that the numerical value of LP when LP is

expressed in the unit neper is {LP }Np = (1/2) ln(P /P0); that is

LF = ln(F /F0) Np

LP = (1/2) ln(P /P0) Np .

One bel (1 B) is the level of a field quantity when F /F0 = Ï10, that is, when

2 lg(F /F0) = 1 (note that lg x = log10 x 2 see Sec. 10.1.2). Equivalently, 1 B is the level of a power

quantity when P /P0 = 10, that is, when lg(P /P0) = 1. These definitions imply that the numerical

value of LF when LF is expressed in the unit bel is {LF }B = 2 lg(F /F0) and that the numerical value

of LP when LP is expressed in the unit bel is {LP }B = lg(P /P0); that is

LF = 2 lg(F /F0) B = 20 lg(F /F0) dB

LP = lg(P /P0) B = 10 lg(P /P0) dB .

Since the value of LF (or LP ) is independent of the unit used to express that value, one

may equate LF in the above expressions to obtain ln(F /F0) Np = 2 lg(F /F0) B, which

implies

1B = ln 10

2 Np exactly

≈ 1.151 293 Np

1 dB ≈ 0.115 129 3 Np .

When reporting values of LF and LP , one must always give the reference level. According to Ref.

[7: IEC 27-3], this may be done in one of two ways: Lx (re xref) or Lx/x ref, where x is the quantity

symbol for the quantity whose level is being reported, for example, electric field strength E or sound

pressure p; and xref is the value of the reference quantity, for example, 1 mV/m for E0, and 20 mPa

for p0. Thus

LE (re 1 mV/m) = 2 0.58 Np or LE/(1 mV/m) = 2 0.58 Np

29
Guide for the Use of the International System of Units (SI)

means that the level of a certain electric field strength is 0.58 Np below the reference electric field

strength E0 = 1 mV/m. Similarly

Lp (re 20 mPa) = 25 dB or Lp/20 mPa = 25 dB

means that the level of a certain sound pressure is 25 dB above the reference pressure p0 = 20 mPa.

Notes:

1 When such data are presented in a table or in a figure, the following condensed notation

may be used instead: 2 0.58 Np (1 mV/m); 25 dB (20 mPa).

2 When the same reference level applies repeatedly in a given context, it may be omitted

if its value is clearly stated initially and if its planned omission is pointed out.

3 The rules of Ref. [7: IEC 27-3] preclude, for example, the use of the symbol dBm to

indicate a reference level of power of 1 mW. This restriction is based on the rule of

Sec. 7.4, which does not permit attachments to unit symbols.

8.8 Viscosity

The proper SI units for expressing values of viscosity h (also called dynamic viscosity) and

values of kinematic viscosity n are, respectively, the pascal second (Pa ? s) and the meter squared per

second (m2/s) (and their decimal multiples and submultiples as appropriate). The CGS units

commonly used to express values of these quantities, the poise (P) and the stokes (St), respectively

[and their decimal submultiples the centipoise (cP) and the centistoke (cSt)], are not to be used; see

Sec. 5.3.1 and Table 10, which gives the relations 1 P = 0.1 Pa ? s and 1 St = 1024 m2

/s.

8.9 Massic, volumic, areic, lineic

Reference [6: ISO 31-0] has introduced the new adjectives ‘‘massic,’’ ‘‘volumic,’’ ‘‘areic,’’ and

‘‘lineic’’ into the English language based on their French counterparts: ‘‘massique,’’ ‘‘volumique,’’

‘‘surfacique,’’ and ‘‘line ́ique.’’ They are convenient and NIST authors may wish to use them.

They are equivalent, respectively, to ‘‘specific,’’ ‘‘density,’’ ‘‘surface... density,’’ and

‘‘linear... density,’’ as explained below.

(a) The adjective massic, or the adjective specific, is used to modify the name of a quantity to

indicate the quotient of that quantity and its associated mass.

Examples: massic volume or specific volume: y = V /m

massic entropy or specific entropy: s = S /m

(b) The adjective volumic is used to modify the name of a quantity, or the term density is added to

it, to indicate the quotient of that quantity and its associated volume.

Examples: volumic mass or (mass) density: r = m /V

volumic number or number density: n = N/V

Note: Parentheses around a word means that the word is often omitted.

(c) The adjective areic is used to modify the name of a quantity, or the terms surface

... density are added to it, to indicate the quotient of that quantity (a scalar) and its associated surface

area.

Examples: areic mass or surface (mass) density: rA = m /A

areic charge or surface charge density: s = Q /A

30
Guide for the Use of the International System of Units (SI)

(d) The adjective lineic is used to modify the name of a quantity, or the terms linear

. . . density are added to it, to indicate the quotient of that quantity and its associated length.

Examples: lineic mass or linear (mass) density: rl = m /l

lineic electric current or linear electric current density: A = I /b

9 Rules and Style Conventions for Spelling Unit Names

The following eight sections give rules and style conventions related to spelling the names of

units.

9.1 Capitalization

When spelled out in full, unit names are treated like ordinary English nouns. Thus the names

of all units start with a lower-case letter, except at the beginning of a sentence or in capitalized

material such as a title.

In keeping with this rule, the correct spelling of the name of the unit 8C is ‘‘degree Celsius’’

(the unit ‘‘degree’’ begins with a lower case ‘‘d’’ and the modifier ‘‘Celsius’’ begins with an uppercase ‘‘C’’ because it is the name of a person).

9.2 Plurals

Plural unit names are used when they are required by the rules of English grammar. They are

normally formed regularly, for example, ‘‘henries’’ is the plural of henry. According to Ref. [8],

the following plurals are irregular: Singular — lux, hertz, siemens; Plural — lux, hertz, siemens.

(See also Sec. 9.7.)

9.3 Spelling unit names with prefixes

When the name of a unit containing a prefix is spelled out, no space or hyphen is used between

the prefix and unit name (see Sec. 6.2.3).

Examples: milligram but not: milli-gram kilopascal but not: kilo-pascal

Reference [8] points out that there are three cases where the final vowel of an SI prefix is

commonly omitted: megohm (not megaohm), kilohm (not kiloohm), and hectare (not

hectoare). In all other cases where the unit name begins with a vowel, both the final vowel of the

prefix and the vowel of the unit name are retained and both are pronounced.

9.4 Spelling unit names obtained by multiplication

When the name of a derived unit formed from other units by multiplication is spelled out, a

space, which is preferred by Ref. [8] and this Guide , or a hyphen is used to separate the names of

the individual units.

Example : pascal second or pascal-second

9.5 Spelling unit names obtained by division

When the name of a derived unit formed from other units by division is spelled out, the word

‘‘per’’ is used and not a solidus. (See also Secs. 6.1.7 and 9.8.)

Example : ampere per meter (A/m) but not: ampere/meter

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Guide for the Use of the International System of Units (SI)

9.6 Spelling unit names raised to powers

When the names of units raised to powers are spelled out, modifiers such as ‘‘squared’’ or

‘‘cubed’’ are used and are placed after the unit name.

Example : meter per second squared (m/s2)

The modifiers ‘‘square’’ or ‘‘cubic’’ may, however, be placed before the unit name in the case of area

or volume.

Examples: square centimeter (cm2) cubic millimeter (mm3)

ampere per square meter (A/m2

) kilogram per cubic meter (kg/m3)

9.7 Other spelling conventions

A derived unit is usually singular in English, for example, the value 3 m2 ? K/W is usually

spelled out as ‘‘three square meter kelvin per watt,’’ and the value 3 C ? m2/V is usually spelled out

as ‘‘three coulomb meter squared per volt.’’ However, a ‘‘single’’ unit may be plural; for example,

the value 5 kPa is spelled out as ‘‘five kilopascals,’’ although ‘‘five kilopascal’’ is acceptable. If in

such a single-unit case the number is less than one, the unit is always singular when spelled out; for

example, 0.5 kPa is spelled out as ‘‘five-tenths kilopascal.’’

Note: These other spelling conventions are given for completeness; as indicated in Sec. 7.6,

it is the position of this Guide that symbols for numbers and units should be used to

express the values of quantities, not the spelled-out names of numbers and units.

Reference [4] also requires that a symbol for a number be used whenever the value

of a quantity is expressed in terms of a unit of measurement.

9.8 Unacceptability of applying mathematical operations to unit names

Because it could possibly lead to confusion, mathematical operations are not applied to unit

names but only to unit symbols. (See also Secs. 6.1.7 and 9.5.)

Example : joule per kilogram or J/kg or J ? kg21 but not: joule/kilogram or

joule ? kilogram21

10 More on Printing and Using Symbols and Numbers in Scientific and

Technical Documents 6

By following the guidance given in this chapter, NIST authors can prepare manuscripts that are

consistent with accepted typesetting practice.

10.1 Kinds of symbols

Letter symbols are of three principal kinds: (a) symbols for quantities, (b) symbols for units, and

(c) symbols for descriptive terms. Quantity symbols, which are always printed in italic (that is, sloping) type, are, with few exceptions, single letters of the Latin or Greek alphabets which may have

subscripts or superscripts or other identifying signs. Symbols for units, in particular those for acceptable units, have been discussed in detail in earlier portions of this Guide . Symbols for descriptive

terms include the symbols for the chemical elements, certain mathematical symbols, and modifying

superscripts and subscripts on quantity symbols.

6 This chapter is adapted in part from Refs. [5], [6: ISO 31-0], and [6: ISO 31-11].

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Guide for the Use of the International System of Units (SI)

10.1.1 Standardized quantity symbols

The use of words, acronyms, or other ad hoc groups of letters as quantity symbols should be

avoided by NIST authors. For example, use the quantity symbol Zm for mechanical impedance, not

MI. In fact, there are nationally and internationally accepted symbols for literally hundreds of quantities used in the physical sciences and technology. Many of these are given in Refs. [6] and [7], and

it is likely that symbols for the quantities used in most NIST publications can be found in these international standards or can readily be adapted from the symbols and principles given in these standards.

Because of their international acceptance, NIST authors are urged to use the symbols of Refs. [6] and

[7] to the fullest extent possible.7

Examples: V (solid angle) Zm (mechanical impedance)

LP (level of a power quantity) Dr (relative mass excess)

p (pressure) stot (total cross-section)

kT (isothermal compressibility) Eu (Euler number)

E (electric field strength) TN (Ne ́el temperature)

10.1.2 Standardized mathematical signs and symbols

As is the case for quantity symbols, most of the mathematical signs and symbols used in the

physical sciences and technology are standardized. They may be found in Ref. [6: ISO 31-11] and

should be used by NIST authors to the fullest possible extent.7

Examples: ∧ (conjunction sign, p ∧ q means p and q)

Þ (a Þ b, a is not equal to b)

­

def (adef b, a is by definition equal to b)

≈ (a ≈ b, a is approximately equal to b)

, (a , b, a is proportional to b)

arcsin x (arc sine of x )

loga x (logarithm to the base a of x)

lb x (lb x = log2 x )

ln x (ln x = loge x )

lg x (lg x = log10 x )

10.2 Typefaces for symbols

Most word processing systems now in use at NIST are capable of producing lightface (that is,

regular) or boldface letters of the Latin or Greek alphabets in both roman (upright) and italic (sloping) types. The understandability of NIST typed and typeset scientific and technical publications is

facilitated if symbols are in the correct typeface.

The typeface in which a symbol appears helps to define what the symbol represents. For example, irrespective of the typeface used in the surrounding text, ‘‘A’’ would be typed or typeset in

— italic type for the scalar quantity area: A;

— roman type for the unit ampere: A;

— italic boldface for the vector quantity vector potential: A .

7 In addition to Refs. [6] and [7], quantity symbols may also be found in ANSI/IEEE Std 280-1985, IEEE

Standard Letter Symbols for Quantities Used in Electrical Science and Electrical Engineering. Similarly, in addition to

Ref. [6: ISO 31-11], mathematical signs and symbols are also given in ANSI/IEEE Std 260.3-1993, Mathematical Signs and

Symbols for Use in Physical Sciences and Technology. (See Ref. [8], note 1.) The book cited in Ref. [8], note 5, and Document

I.U.P.A.P.-25 (SUNAMCO 87-1), Symbols, Units, Nomenclature and Fundamental Constants in Physics, 1987 Revision, by

E. R. Cohen and P. Giacomo, International Union of Pure and Applied Physics, SUNAMCO Commission [reprinted from

Physica, Vol. 146A, Nos. 1-2, p. 1 (November, 1987)], also give quantity symbols and mathematical signs and symbols.

33
Guide for the Use of the International System of Units (SI)

More specifically, the three major categories of symbols found in scientific and technical publications

should be typed or typeset in either italic or roman type, as follows:

— symbols for quantities and variables: italic;

— symbols for units: roman;

— symbols for descriptive terms: roman.

These rules imply that a subscript or superscript on a quantity symbol is in roman type if it is descriptive (for example, if it is a number or represents the name of a person or a particle); but it is in italic

type if it represents a quantity, or is a variable such as x in Ex or an index such as i in Si xi that

represents a number (see Secs. 10.2.1, 10.2.3, and 10.2.4). An index that represents a number is also

called a ‘‘running number’’ [6: ISO 31-0].

Notes:

1 The above rules also imply, for example, that m, the symbol for the SI prefix

micro (1026

), that V, the symbol for the SI derived unit ohm, and that F, the symbol for

the SI derived unit farad, are in roman type; but they are in italic type if they represent

quantities (m, V, and F are the recommended symbols for the quantities magnetic

moment of a particle, solid angle, and force, respectively).

2 The typeface for numbers is discussed in Sec. 10.5.1.

The following four sections give examples of the proper typefaces for these three major

categories.

10.2.1 Quantities and variables — italic

Symbols for quantities are italic, as are symbols for functions in general, for example, f (x ):

t=3 s t time, s second T=22 K T temperature, K kelvin

r=11 cm r radius, cm centimeter l=633 nm l wavelength, nm nanometer

Constants are usually physical quantities and thus their symbols are italic; however, in general,

symbols used as subscripts and superscripts are roman if descriptive (see Sec. 10.2.3):

NA Avogadro constant, A Avogadro R molar gas constant

u D Debye temperature, D Debye Z atomic number

e elementary charge me m mass, e electron

Running numbers and symbols for variables in mathematical equations are italic, as are symbols for

parameters such as a and b that may be considered constant in a given context:

y=O

m

i=1

xizi x 2 = ay 2+bz 2

Symbols for vectors are boldface italic, symbols for tensors are sans-serif bold italic, and symbols for

matrices are italic:

A?B =C (vectors) T (tensors) A = S

a11 a12

a21 a22D (matrices)

Symbols used as subscripts and superscripts are italic if they represent quantities or variables:

cp p pressure qm m mass sV V solid angle vz z z coordinate

10.2.2 Units — roman

The symbols for units and SI prefixes are roman:

m meter g gram L liter

cm centimeter mg microgram mL milliliter

34
Guide for the Use of the International System of Units (SI)

10.2.3 Descriptive terms — roman

Symbols representing purely descriptive terms (for example, the chemical elements) are

roman, as are symbols representing mathematical constants that never change (for example, p) and

symbols representing explicitly defined functions or well defined operators (for example, G(x ) or

div):

Chemical elements:

Ar argon B boron C carbon

Mathematical constants, functions, and operators:

e base of natural logarithms Sxi S sum of

exp x exp exponential of loga x loga logarithm to the base a of

dx /dt d 1st derivative of sin x sin sine of

Symbols used as subscripts and superscripts are roman if descriptive:

«0

(ir) ir irrational Ek k kinetic

Vm

l m molar, l liquid phase mB B Bohr

10.2.4 Sample equations showing correct type

F = q1 q2

4p«0 r 2 F = ma pV = nRT

wB = xBV*

m,B/ S

A

xAV*

m,A Ea = RT2 d(ln k )/dT c1 = l25

/[exp(c2 /lT)21]

E = mc 2 ,pB = lB lim

p→0

(xB p /lB) F

Q = 2grad V

10.3 Greek alphabet in roman and italic type

Table 13 shows the proper form, in both roman and italic type, of the upper-case and lower-case

letters of the Greek alphabet.

Table 13. Greek alphabet in roman and italic type

alpha A a A a

beta B b B b

gamma G g G g

delta D d D d

epsilon E «, e E «, e

zeta Z z Z z

eta H h H h

theta Q, U(a) u, q(b) Q ,U(a) u , q(b)

iota I i I i

kappa K k , û(b) K k, û(b)

lambda L l L l

mu M m M m

nu N n N n

xi J j J j

omicron O o O o

pi P p, Ã P p, Ã

rho P r, (b) P r , (b)

sigma S s S s

tau T t T t

upsilon Y y Y y

phi F w, f F w, f

chi X x X x

psi C c C c

omega V v V v

(a) ISO (see Ref. [6: ISO 31-0]) gives only the first of these two letters.

(b) ISO (see Ref. [6: ISO 31-0]) gives these two letters in the reverse order.

35
Guide for the Use of the International System of Units (SI)

10.4 Symbols for the elements

The following two sections give the rules and style conventions for the symbols for the elements.

10.4.1 Typeface and punctuation for element symbols

Symbols for the elements are normally printed in roman type without regard to the type used

in the surrounding text (see Sec. 10.2.3). They are not followed by a period unless at the end of a

sentence.

10.4.2 Subscripts and superscripts on element symbols

The nucleon number (mass number) of a nuclide is indicated in the left superscript position: 28Si.

The number of atoms in a molecule of a particular nuclide is shown in the right subscript position: 1

H2.

The proton number (atomic number) is indicated in the left subscript position: 29Cu.

The state of ionization or excitation is indicated in the right superscript position, some examples

of which are as follows:

State of ionization: Ba++

Co(NO2)6

222 or Co(NO2)

32

6 or [Co(NO2)6]

32

Electronic excited state: Ne*, CO*

Nuclear excited state: 15N* or 15Nm

10.5 Printing numbers

The following three sections give rules and style conventions related to the printing of numbers.

10.5.1 Typeface for numbers

Arabic numerals expressing the numerical values of quantities (see Sec. 7.6) are generally

printed in lightface (that is, regular) roman type irrespective of the type used for the surrounding text.

Arabic numerals other than numerical values of quantities may be printed in lightface or bold italics,

or in bold roman type, but lightface roman type is usually preferred.

10.5.2 Decimal sign or marker

The recommended decimal sign or marker for use in the United States is the dot on the line

[4, 8]. For numbers less than one, a zero is written before the decimal marker. For example, 0.25 s

is the correct form, not .25 s.

36
Guide for the Use of the International System of Units (SI)

10.5.3 Grouping digits

Because the comma is widely used as the decimal marker outside the United States, it should

not be used to separate digits into groups of three. Instead, digits should be separated into groups of

three, counting from the decimal marker towards the left and right, by the use of a thin, fixed space.

However, this practice is not usually followed for numbers having only four digits on either side of

the decimal marker except when uniformity in a table is desired.

Examples: 76 483 522 but not: 76,483,522

43 279.168 29 but not: 43,279.168 29

8012 or 8 012 but not: 8,012

0.491 722 3 is highly preferred to: 0.4917223

0.5947 or 0.594 7 but not: 0.59 47

8012.5947 or 8 012.594 7 but not: 8 012.5947 or 8012.594 7

Note: The practice of using a space to group digits is not usually followed in certain specialized

applications, such as engineering drawings and financial statements.

10.5.4 Multiplying numbers

When the dot is used as the decimal marker as in the United States, the preferred sign for the

multiplication of numbers or values of quantities is a cross (that is, multiplication sign) (3), not a

half-high (that is, centered) dot ( ? ).

Examples: 25 3 60.5 but not: 25 ? 60.5

53 m/s 3 10.2 s but not: 53 m/s ? 10.2 s

15 3 72 kg but not: 15 ? 72 kg

Notes:

1 When the comma is used as the decimal marker, the preferred sign for the

multiplication of numbers is the half-high dot. However, even when the comma is so

used, this Guide prefers the cross for the multiplication of values of quantities.

2 The multiplication of quantity symbols (or numbers in parentheses or values of

quantities in parentheses) may be indicated in one of the following ways: ab,

a b, a? b, a3 b.

37
Guide for the Use of the International System of Units (SI)

11 Check List for Reviewing Manuscripts

The following check list, adapted from Ref. [22], is intended to help NIST authors review the

conformity of their manuscripts with proper SI usage and the basic principles concerning quantities

and units. For easy reference, this check list also appears immediately after the Preface.

(1) u Only units of the SI and those units recognized for use with the SI are used to express the

values of quantities. Equivalent values in other units are given in parentheses following

values in acceptable units only when deemed necessary for the intended audience. (See

Chapter 2.)

(2) u Abbreviations such as sec (for either s or second), cc (for either cm3 or cubic

centimeter), or mps (for either m/s or meter per second), are avoided and only standard

unit symbols, SI prefix symbols, unit names, and SI prefixes are used. (See Sec. 6.1.8.)

(3) u The combinations of letters ‘‘ppm,’’ ‘‘ppb,’’ and ‘‘ppt,’’ and the terms part per million,

part per billion, and part per trillion, and the like, are not used to express the values of

quantities. The following forms, for example, are used instead: 2.0 mL/L or 2.0 3 1026

V, 4.3 nm/m or 4.3 3 1029 l, 7 ps/s or 7 3 10212 t, where V, l, and t are, respectively, the

quantity symbols for volume, length, and time. (See Sec. 7.10.3.)

(4) u Unit symbols (or names) are not modified by the addition of subscripts or other information. The following forms, for example, are used instead. (See Secs. 7.4 and 7.10.2.)

Vmax = 1000 V but not: V = 1000 Vmax

a mass fraction of 10 % but not: 10 % (m/m) or 10 % (by weight)

(5) u Statements such as ‘‘the length l1 exceeds the length l2 by 0.2 %’’ are avoided because

it is recognized that the symbol % represents simply the number 0.01. Instead, forms such

as ‘‘l1 = l2(1 + 0.2 %)’’ or ‘‘D = 0.2 %’’ are used, where D is defined by the relation

D = (l1 2 l2)/l2. (See Sec. 7.10.2.)

(6) u Information is not mixed with unit symbols (or names). For example, the form ‘‘the water

content is 20 mL/kg’’ is used and not ‘‘20 mL H2O/kg’’ or ‘‘20 mL of water/kg.’’ (See

Sec. 7.5.)

(7) u It is clear to which unit symbol a numerical value belongs and which mathematical operation applies to the value of a quantity because forms such as the following are used. (See

Sec. 7.7.)

35 cm 3 48 cm but not: 35 3 48 cm

1 MHz to 10 MHz or (1 to 10) MHz but not: 1 MHz210 MHz or 1 to 10 MHz

20 8C to 30 8C or (20 to 30) 8C but not: 20 8C230 8C or 20 to 30 8C

123 g 6 2 g or (123 6 2) g but not: 123 6 2 g

70 % 6 5 % or (70 6 5) % but not: 70 6 5 %

240 3 (1 6 10 %) V but not: 240 V 6 10 % (one cannot add

240 V and 10 %)

(8) u Unit symbols and unit names are not mixed and mathematical operations are not applied

to unit names. For example, only forms such as kg/m3

, kg • m23, or

kilogram per cubic meter are used and not forms such as kilogram/m3

, kg/cubic meter,

kilogram/cubic meter, kg per m3

, or kilogram per meter3. (See Secs. 6.1.7, 9.5, and 9.8.)

38
Guide for the Use of the International System of Units (SI)

(9) u Values of quantities are expressed in acceptable units using Arabic numerals and the

symbols for the units. (See Sec. 7.6.)

m = 5 kg but not: m = five kilograms or m = five kg

the current was 15 A but not: the current was 15 amperes.

(10) u There is a space between the numerical value and unit symbol, even when the value is used

in an adjectival sense, except in the case of superscript units for plane angle. (See

Sec. 7.2.)

a 25 kg sphere but not: a 25-kg sphere

an angle of 283'4" but not: an angle of 2 83 '4 "

If the spelled-out name of a unit is used, the normal rules of English are applied: ‘‘a roll

of 35-millimeter film.’’ (See Sec. 7.6, note 3.)

(11) u The digits of numerical values having more than four digits on either side of the decimal

marker are separated into groups of three using a thin, fixed space

counting from both the left and right of the decimal marker. For example, 15 739.012 53

is highly preferred to 15739.01253. Commas are not used to separate digits into groups

of three. (See Sec. 10.5.3.)

(12) u Equations between quantities are used in preference to equations between numerical

values, and symbols representing numerical values are different from symbols representing the corresponding quantities. When a numerical-value equation is used, it is properly

written and the corresponding quantity equation is given where possible. (See Sec. 7.11.)

(13) u Standardized quantity symbols such as those given in Refs. [6] and [7] are used, for example, R for resistance and Ar for relative atomic mass, and not words, acronyms, or ad hoc

groups of letters. Similarly, standardized mathematical signs and symbols such as are

given in Ref. [6: ISO 31-11] are used, for example, ‘‘tan x ’’ and not ‘‘tg x.’’ More specifically, the base of ‘‘log’’ in equations is specified when required by writing loga x (meaning log to the base a of x ), lb x (meaning log2 x ), ln x (meaning loge x ), or lg x (meaning

log10 x ). (See Secs. 10.1.1 and 10.1.2.)

(14) u Unit symbols are in roman type, and quantity symbols are in italic type with superscripts

and subscripts in roman or italic type as appropriate. (See Sec. 10.2 and Secs. 10.2.1 to

10.2.4.)

(15) u When the word ‘‘weight’’ is used, the intended meaning is clear. (In science and technology, weight is a force, for which the SI unit is the newton; in commerce and everyday use,

weight is usually a synonym for mass, for which the SI unit is the kilogram.) (See

Sec. 8.3.)

(16) u A quotient quantity, for example, mass density, is written ‘‘mass divided by volume’’

rather than ‘‘mass per unit volume.’’ (See Sec. 7.12.)

(17) u An object and any quantity describing the object are distinguished. (Note the difference

between ‘‘surface’’ and ‘‘area,’’ ‘‘body’’ and ‘‘mass,’’ ‘‘resistor’’ and ‘‘resistance,’’

‘‘coil’’ and ‘‘inductance.’’) (See Sec. 7.13.)

(18) u The obsolete term normality and the symbol N, and the obsolete term molarity and the

symbol M, are not used, but the quantity amount-of-substance concentration of B (more

commonly called concentration of B), and its symbol cB and SI unit mol/m3 (or a related

acceptable unit), are used instead. Similarly, the obsolete term molal and the symbol m are

not used, but the quantity molality of solute B, and its symbol bB or mB and SI unit mol/kg

(or a related unit of the SI), are used instead. (See Secs. 8.6.5 and 8.6.8.)

39
Guide for the Use of the International System of Units (SI)

Appendix A. Definitions of the SI Base Units and the Radian and Steradian

A.1 Introduction

The following definitions of the SI base units are taken from Ref. [3]; the definitions of the SI

supplementary units, the radian and steradian, which are now interpreted as SI derived units (see

Sec. 4.3), are those generally accepted and are the same as those given in Ref. [8]. It should be noted

that SI derived units are uniquely defined only in terms of SI base units; for example,

1V=1m2 ? kg ? s23 ? A21

.

A.2 Meter (17th CGPM, 1983)

The meter is the length of the path travelled by light in vacuum during a time interval of

1/299 792 458 of a second.

A.3 Kilogram (3d CGPM, 1901)

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the

kilogram.

A.4 Second (13th CGPM, 1967)

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the

transition between the two hyperfine levels of the ground state of the cesium-133 atom.

A.5 Ampere (9th CGPM, 1948)

The ampere is that constant current which, if maintained in two straight parallel conductors of

infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would

produce between these conductors a force equal to 2 3 1027 newton per meter of length.

A.6 Kelvin (13th CGPM, 1967)

The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic

temperature of the triple point of water.

A.7 Mole (14th CGPM, 1971)

1. The mole is the amount of substance of a system which contains as many elementary entities

as there are atoms in 0.012 kilogram of carbon 12.

2. When the mole is used, the elementary entities must be specified and may be atoms, molecules,

ions, electrons, other particles, or specified groups of such particles.

In the definition of the mole, it is understood that unbound atoms of carbon 12, at rest and in their

ground state, are referred to.

Note that this definition specifies at the same time the nature of the quantity whose unit is the

mole.

A.8 Candela (16th CGPM, 1979)

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic

radiation of frequency 540 3 1012 hertz and that has a radiant intensity in that direction of (1/683)

watt per steradian.

A.9 Radian

The radian is the plane angle between two radii of a circle that cut off on the circumference an

arc equal in length to the radius.

A.10 Steradian

The steradian is the solid angle that, having its vertex in the center of a sphere, cuts off an area

of the surface of the sphere equal to that of a square with sides of length equal to the radius of the

sphere.

40
Guide for the Use of the International System of Units (SI)

Appendix B. Conversion Factors8

B.1 Introduction

Sections B.8 and B.9 give factors for converting values of quantities expressed in various

units — predominantly units outside the SI that are unacceptable for use with it — to values

expressed either in (a) SI units, (b) units that are accepted for use with the SI (especially units that

better reflect the nature of the unconverted units), (c) units formed from such accepted units and SI

units, or (d) decimal multiples or submultiples of the units of (a) to (c) that yield numerical values

of convenient magnitudes.

An example of (d) is the following: the values of quantities expressed in ångstro ̈ms, such as the

wavelengths of visible laser radiations, are usually converted to values expressed in nanometers, not

meters. More generally, if desired, one can eliminate powers of 10 that appear in converted values

as a result of using the conversion factors (or simply factors for brevity) of Secs. B.8 and B.9 by

selecting an appropriate SI prefix (see Sec. B.3).

B.2 Notation

The factors given in Secs. B.8 and B.9 are written as a number equal to or greater than 1 and

less than 10, with 6 or fewer decimal places. The number is followed by the letter E, which stands

for exponent, a plus (+) or minus (2) sign, and two digits which indicate the power of 10 by which

the number is multiplied.

Examples: 3.523 907 E202 means 3.523 907 3 1022 = 0.035 239 07

3.386 389 E+03 means 3.386 389 3 103 = 3386.389

A factor in boldface is exact. All other factors have been rounded to the significant digits given

in accordance with accepted practice (see Secs. 7.9, B.7.2, and Refs. [6: ISO 31-0] and [8]). Where

less than six digits after the decimal place are given, the unit does not warrant a greater number of

digits in its conversion. However, for the convenience of the user, this practice is not followed for all

such units, including the cord, cup, quad, and teaspoon.

B.3 Use of conversion factors

Each entry in Secs. B.8 and B.9 is to be interpreted as in these two examples:

To convert from to Multiply by

atmosphere, standard (atm) ......................... pascal (Pa)..................................... 1.013 25 E+05

cubic foot per second (ft3

/s) . . . . . . . . . . . . . . . . . . . . . . . . cubic meter per second (m3/s). . . . . . . . . . . . . . . . . 2.831 685 E202

means 1 atm = 101 325 Pa (exactly);

1 ft3

/s = 0.028 316 85 m3/s.

Thus to express, for example, the pressure p = 11.8 standard atmospheres (atm) in pascals (Pa), write

p = 11.8 atm 3 101 325 Pa/atm

and obtain the converted numerical value 11.8 3 101 325 = 1 195 635 and the converted value

p = 1.20 MPa.

8 Appendix B is a significantly revised version of Appendix C of the 1991 edition of this NIST Special Publication (see

Preface). Appendix C of the 1991 edition was reprinted from ANSI/IEEE Std 268-1982, American National Standard Metric

Practice, 1982 by the Institute of Electrical and Electronics Engineers, Inc., with the permission of the IEEE. The origin

of this material is E. A. Mechtly, The International System of Units — Physical Constants and Conversion Factors, NASA

SP-7012, Second Revision, National Aeronautics and Space Administration (U.S. Government Printing Office, Washington,

DC, 1973).

41
Guide for the Use of the International System of Units (SI)

Notes:

1 Guidance on rounding converted numerical values of quantities is given in Sec. B.7.2.

2 If the value of a quantity is expressed in a unit of the center column of Sec. B.8 or B.9

and it is necessary to express it in the corresponding unit of the first column, divide by

the factor.

The factors for derived units not included in Secs. B.8 and B.9 can readily be found from the

factors given.

Examples: To find the factor for converting values in lb ? ft/s to values in kg ? m/s, obtain from

Sec. B.8 or B.9

1 lb = 4.535 924 E201 kg

1 ft = 3.048 E201 m

and substitute these values into the unit lb ? ft/s to obtain

1 lb ? ft/s = 0.453 592 4 kg 3 0.3048 m/s

= 0.138 255 0 kg ? m/s

and the factor is 1.382 550 E201.

To find the factor for converting values in (avoirdupois) oz ? in2 to values in kg ? m2

, obtain from

Sec. B.8 or B.9

1 oz = 2.834 952 E202 kg

1 in2 = 6.4516 E204 m2

and substitute these values into the unit oz ? in2 to obtain

1 oz ? in2 = 0.028 349 52 kg 3 0.000 645 16 m2

= 0.000 018 289 98 kg ? m2

and the factor is 1.828 998 E205.

B.4 Organization of entries and style

In Sec. B.8 the units for which factors are given are listed alphabetically, while in Sec B.9 the

same units are listed alphabetically within the following alphabetized list of kinds of quantities and

fields of science:

ACCELERATION

ANGLE

AREA AND SECOND MOMENT

OF AREA

CAPACITY (see VOLUME)

DENSITY (that is, MASS DENSITY —

(see MASS DIVIDED BY VOLUME)

ELECTRICITY and MAGNETISM

ENERGY (includes WORK)

ENERGY DIVIDED BY AREA TIME

FLOW (see MASS DIVIDED BY TIME

or VOLUME DIVIDED BY TIME)

FORCE

FORCE DIVIDED BY AREA

(see PRESSURE)

FORCE DIVIDED BY LENGTH

HEAT

Available Energy

Coefficient of Heat Transfer

Density of Heat

Density of Heat Flow Rate

Fuel Consumption

Heat Capacity and Entropy

Heat Flow Rate

Specific Heat Capacity and

Specific Entropy

Thermal Conductivity

Thermal Diffusivity

Thermal Insulance

Thermal Resistance

Thermal Resistivity

42
Guide for the Use of the International System of Units (SI)

LENGTH

LIGHT

MASS and MOMENT OF INERTIA

MASS DENSITY (see MASS DIVIDED

BY VOLUME)

MASS DIVIDED BY AREA

MASS DIVIDED BY CAPACITY

(see MASS DIVIDED BY VOLUME)

MASS DIVIDED BY LENGTH

MASS DIVIDED BY TIME

(includes FLOW)

MASS DIVIDED BY VOLUME

(includes MASS DENSITY and

MASS CONCENTRATION)

MOMENT OF FORCE or TORQUE

MOMENT OF FORCE or TORQUE,

DIVIDED BY LENGTH

PERMEABILITY

POWER

In Secs. B.8 and B.9, the units in the left-hand columns are written as they are often used

customarily; the rules and style conventions recommended in this Guide are not necessarily observed.

Further, many are obsolete and some are not consistent with good technical practice. The corresponding units in the center columns are, however, written in accordance with the rules and style

conventions recommended in this Guide .

B.5 Factor for converting motor vehicle efficiency

The efficiency of motor vehicles in the United States is commonly expressed in miles per U.S.

gallon, while in most other countries it is expressed in liters per one hundred kilometers. To convert

fuel economy stated in miles per U.S. gallon to fuel consumption expressed in L/(100 km), divide

235.215 by the numerical value of the stated fuel economy. Thus 24 miles per gallon corresponds to

9.8 L/(100 km).

B.6 U.S. survey foot and mile

The U.S. Metric Law of 1866 gave the relationship 1 m = 39.37 in (in is the unit symbol for the

inch). From 1893 until 1959, the yard was defined as being exactly equal to (3600/3937) m, and thus

the foot was defined as being exactly equal to (1200/3937) m.

In 1959 the definition of the yard was changed to bring the U.S. yard and the yard used in other

countries into agreement. Since then the yard has been defined as exactly equal to 0.9144 m, and thus

the foot has been defined as exactly equal to 0.3048 m. At the same time it was decided that any data

expressed in feet derived from geodetic surveys within the United States would continue to bear the

relationship as defined in 1893, namely, 1 ft = (1200/3937) m (ft is the unit symbol for the foot). The

name of this foot is ‘‘U.S. survey foot,’’ while the name of the new foot defined in 1959 is ‘‘international foot.’’ The two are related to each other through the expression 1 international

foot = 0.999 998 U.S. survey foot exactly.

PRESSURE or STRESS (FORCE

DIVIDED BY AREA)

RADIOLOGY

SPEED (see VELOCITY)

STRESS (see PRESSURE)

TEMPERATURE

TEMPERATURE INTERVAL

TIME

TORQUE (see MOMENT

OF FORCE)

VELOCITY (includes SPEED)

VISCOSITY, DYNAMIC

VISCOSITY, KINEMATIC

VOLUME (includes CAPACITY)

VOLUME DIVIDED BY TIME

(includes FLOW)

WORK (see ENERGY)

43
Guide for the Use of the International System of Units (SI)

In Secs. B.8 and B.9, the factors given are based on the international foot unless otherwise

indicated. Users of this Guide may also find the following summary of exact relationships helpful,

where for convenience the symbols ft and mi, that is, ft and mi in italic type, indicate that it is the U.S.

survey foot or U.S. survey mile that is meant rather than the international foot (ft) or international mile

(mi), and where rd is the unit symbol for the rod and fur is the unit symbol for the furlong.

1 ft = (1200/3937) m

1 ft = 0.3048 m

1 ft = 0.999 998 ft

1 rd, pole, or perch = 161

2 ft

40 rd = 1 fur = 660 ft

8 fur = 1 U.S. survey mile (also called ‘‘statute mile’’) = 1 mi = 5280 ft

1 fathom = 6 ft

1 international mile = 1 mi = 5280 ft

272 1/4 ft 2 = 1 rd2

160 rd2 = 1 acre = 43 560 ft 2

640 acre = 1 mi 2

B.7 Rules for rounding numbers and converted numerical values of quantities

Rules for rounding numbers are discussed in Refs. [6: ISO 31-0] and [8]; the latter reference also

gives rules for rounding the converted numerical values of quantities whose values expressed in units

that are not accepted for use with the SI (primarily customary or inch-pound units) are converted to

values expressed in acceptable units. This Guide gives the principal rules for rounding numbers in

Sec. B.7.1, and the basic principle for rounding converted numerical values of quantities in

Sec. B.7.2. The cited references should be consulted for additional details.

B.7.1 Rounding numbers

To replace a number having a given number of digits with a number (called the rounded number)

having a smaller number of digits, one may follow these rules:

(1) If the digits to be discarded begin with a digit less than 5, the digit preceding the 5 is not changed.

Example : 6.974 951 5 rounded to 3 digits is 6.97

(2) If the digits to be discarded begin with a 5 and at least one of the following digits is greater than

0, the digit preceding the 5 is increased by 1.

Examples: 6.974 951 5 rounded to 2 digits is 7.0

6.974 951 5 rounded to 5 digits is 6.9750

(3) If the digits to be discarded begin with a 5 and all of the following digits are 0, the digit preceding

the 5 is unchanged if it is even and increased by 1 if it is odd. (Note that this means that the final digit

is always even.)

Examples: 6.974 951 5 rounded to 7 digits is 6.974 952

6.974 950 5 rounded to 7 digits is 6.974 950

44
Guide for the Use of the International System of Units (SI)

B.7.2 Rounding converted numerical values of quantities

The use of the factors given in Secs. B.8 and B.9 to convert values of quantities was demonstrated in Sec. B.3. In most cases the product of the unconverted numerical value and the factor will

be a numerical value with a number of digits that exceeds the number of significant digits (see

Sec. 7.9) of the unconverted numerical value. Proper conversion procedure requires rounding this

converted numerical value to the number of significant digits that is consistent with the maximum

possible rounding error of the unconverted numerical value.

Example : To express the value l = 36 ft in meters, use the factor 3.048 E201 from Sec. B.8 or

Sec. B.9 and write

l = 36 ft 3 0.3048 m/ft = 10.9728 m = 11.0 m.

The final result, l = 11.0 m, is based on the following reasoning: The numerical value ‘‘36’’ has two

significant digits, and thus a relative maximum possible rounding error (abbreviated RE in this Guide

for simplicity) of 6 0.5/36 = 6 1.4 % because it could have resulted from rounding the number 35.5,

36.5, or any number between 35.5 and 36.5. To be consistent with this RE, the converted numerical

value ‘‘10.9728’’ is rounded to 11.0 or three significant digits because the number 11.0 has an RE

of 6 0.05/11.0 = 6 0.45 %. Although this 6 0.45 % RE is one-third of the 6 1.4 % RE of the unconverted numerical value ‘‘36,’’ if the converted numerical value ‘‘10.9728’’ had

been rounded to 11 or two significant digits, information contained in the unconverted

numerical value ‘‘36’’ would have been lost. This is because the RE of the numerical value ‘‘11’’ is

6 0.5/11 = 6 4.5 %, which is three times the 6 1.4 % RE of the unconverted numerical value

‘‘36.’’ This example therefore shows that when selecting the number of digits to retain in the numerical value of a converted quantity, one must often choose between discarding information or providing unwarranted information. Consideration of the end use of the converted value can often help one

decide which choice to make.

Note: Consider that one had been told initially that the value l = 36 ft had been rounded to the

nearest inch. Then in this case, since l is known to within 6 1 in, the RE of the numerical

value ‘‘36’’ is 6 1 in/(36 ft 3 12 in/ft) = 6 0.23 %. Although this is less than

the 6 0.45 % RE of the number 11.0, it is comparable to it. Therefore, the result l = 11.0 m

is still given as the converted value. (Note that the numerical value ‘‘10.97’’ would give

excessive unwarranted information because it has an RE that is one-fifth of 6 0.23 %.)

45
Guide for the Use of the International System of Units (SI)

B.8 Factors for units listed alphabetically

Caution: The units listed in column 1 are in general not to be used in NIST publications, with the

exception of those few in italic type.

Factors in boldface are exact

To convert from to Multiply by

abampere............................................ ampere (A) .................................... 1.0 E+01

abcoulomb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+01

abfarad .............................................. farad (F) ....................................... 1.0 E+09

abhenry ............................................. henry (H) ...................................... 1.0 E209

abmho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . siemens (S) .................................... 1.0 E+09

abohm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm (V) ....................................... 1.0 E209

abvolt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . volt (V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E208

acceleration of free fall, standard (gn)............... meter per second squared (m/s2

) .............. 9.806 65 E+00

acre (based on U.S. survey foot)9 . . . . . . . . . . . . . . . . . . . square meter (m2

).............................. 4.046 873 E+03

acre foot (based on U.S. survey foot)9 .............. cubic meter (m3)............................... 1.233 489 E+03

ampere hour (A ? h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 E+03

ångstro ̈m (Å). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m)...................................... 1.0 E210

ångstro ̈m (Å). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nanometer (nm)................................ 1.0 E201

are (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2

).............................. 1.0 E+02

astronomical unit (AU).............................. meter (m)...................................... 1.495 979 E+11

atmosphere, standard (atm).......................... pascal (Pa)..................................... 1.013 25 E+05

atmosphere, standard (atm). . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 1.013 25 E+02

atmosphere, technical (at)10......................... pascal (Pa)..................................... 9.806 65 E+04

atmosphere, technical (at)10. . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 9.806 65 E+01

bar (bar)............................................. pascal (Pa)..................................... 1.0 E+05

bar (bar). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 1.0 E+02

barn (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2

).............................. 1.0 E228

barrel [for petroleum, 42 gallons (U.S.)](bbl) ....... cubic meter (m3

)............................... 1.589 873 E201

barrel [for petroleum, 42 gallons (U.S.)](bbl) ....... liter (L) ........................................ 1.589 873 E+02

biot (Bi)............................................. ampere (A) .................................... 1.0 E+01

British thermal unitIT (BtuIT)

11. . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.055 056 E+03

British thermal unitth (Btuth)

11 . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.054 350 E+03

British thermal unit (mean) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.055 87 E+03

British thermal unit (39 8F) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.059 67 E+03

British thermal unit (59 8F) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.054 80 E+03

British thermal unit (60 8F) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.054 68 E+03

British thermal unitIT foot per hour square foot degree Fahrenheit

[BtuIT ? ft/(h ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m ? K)]. . . . . . . . . . . . . 1.730 735 E+00

British thermal unitth foot per hour square foot degree Fahrenheit

[Btuth ? ft/(h ? ft2 ? 8F)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m ? K)]. . . . . . . . . . . . . 1.729 577 E+00

British thermal unitIT inch per hour square foot degree Fahrenheit

[BtuIT ? in/(h ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m ? K)]. . . . . . . . . . . . . 1.442 279 E201

British thermal unitth inch per hour square foot degree Fahrenheit

[Btuth ? in/(h ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m ? K)]. . . . . . . . . . . . . 1.441 314 E201

British thermal unitIT inch per second square foot degree Fahrenheit

[BtuIT ? in/(s ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m ? K)]. . . . . . . . . . . . . 5.192 204 E+02

9 See Sec. B.6. 10 One technical atmosphere equals one kilogram-force per square centimeter (1 at = 1 kgf/cm2

). 11 The Fifth International Conference on the Properties of Steam (London, July 1956) defined the International Table calorie as 4.1868 J. Therefore the exact conversion factor for the International Table Btu is 1.055 055 852 62 kJ. Note that the notation for International Table used in this

listing is subscript ‘‘IT’’. Similarily, the notation for thermochemical is subscript ‘‘th.’’ Further, the thermochemical Btu, Btuth, is based on

the thermochemical calorie, calth, where calth = 4.184 J exactly.

46
Guide for the Use of the International System of Units (SI)

To convert from to Multiply by

British thermal unitth inch per second square foot degree Fahrenheit

[Btuth ? in/(s ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m ? K)]. . . . . . . . . . . . . 5.188 732 E+02

British thermal unitIT per cubic foot

(BtuIT /ft3

). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per cubic meter (J/m3)................... 3.725 895 E+04

British thermal unitth per cubic foot

(Btuth /ft3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per cubic meter (J/m3)................... 3.723 403 E+04

British thermal unitIT per degree Fahrenheit

(BtuIT /8F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kelvin (J/ k) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.899 101 E+03

British thermal unitth per degree Fahrenheit

(Btuth /8F). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kelvin (J/ k) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.897 830 E+03

British thermal unitIT per degree Rankine

(BtuIT /8R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kelvin (J/ k) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.899 101 E+03

British thermal unitth per degree Rankine

(Btuth /8R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kelvin (J/ k) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.897 830 E+03

British thermal unitIT per hour (BtuIT /h) . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.930 711 E201

British thermal unitth per hour (Btuth /h). . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.928 751 E201

British thermal unitIT per hour square foot degree Fahrenheit

[BtuIT /(h ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter kelvin

[W/(m2 ? K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.678 263 E+00

British thermal unitth per hour square foot degree Fahrenheit

[Btuth /(h ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter kelvin

[W/(m2 ? K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.674 466 E+00

British thermal unitth per minute (Btuth /min) . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.757 250 E+01

British thermal unitIT per pound (BtuIT /lb). . . . . . . . . . joule per kilogram (J/kg) ...................... 2.326 E+03

British thermal unitth per pound (Btuth /lb) . . . . . . . . . . joule per kilogram (J/kg) ...................... 2.324 444 E+03

British thermal unitIT per pound degree Fahrenheit

[BtuIT /(lb ? 8F)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin (J/(kg ? K)]. . . . . . . . . . 4.1868 E+03

British thermal unitth per pound degree Fahrenheit

[Btuth /(lb ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)]. . . . . . . . . . 4.184 E+03

British thermal unitIT per pound degree Rankine

[BtuIT /(lb ? 8R)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)]. . . . . . . . . . 4.1868 E+03

British thermal unitth per pound degree Rankine

[Btuth /(lb ? 8R)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)]. . . . . . . . . . 4.184 E+03

British thermal unitIT per second (BtuIT /s) . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.055 056 E+03

British thermal unitth per second (Btuth /s) . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.054 350 E+03

British thermal unitIT per second square foot degree Fahrenheit

[BtuIT /(s ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter kelvin

[W/(m2 ? K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.044 175 E+04

British thermal unitth per second square foot degree Fahrenheit

[Btuth /(s ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter kelvin

[W/(m2 ? K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.042 808 E+04

British thermal unitIT per square foot

(BtuIT /ft2

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per square meter (J/m2).................. 1.135 653 E+04

British thermal unitth per square foot

(Btuth /ft2

). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per square meter (J/m2).................. 1.134 893 E+04

British thermal unitIT per square foot hour

[(BtuIT /(ft2 ? h)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2)................. 3.154 591 E+00

British thermal unitth per square foot hour

[Btuth /(ft2 ? h)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2

)................. 3.152 481 E+00

British thermal unitth per square foot minute

[Btuth /(ft2 ? min)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2)................. 1.891 489 E+02

British thermal unitIT per square foot second

[(BtuIT /(ft2 ? s)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2)................. 1.135 653 E+04

British thermal unitth per square foot second

[Btuth /(ft2 ? s)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2)................. 1.134 893 E+04

British thermal unitth per square inch second

[Btuth /(in2 ? s)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2)................. 1.634 246 E+06

47
Guide for the Use of the International System of Units (SI)

To convert from to Multiply by

bushel (U.S.) (bu) ................................... cubic meter (m3)............................... 3.523 907 E202

bushel (U.S.) (bu) ................................... liter (L) ........................................ 3.523 907 E+01

calorieIT (calIT)

11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1868 E+00

calorieth (calth)

11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.184 E+00

calorie (cal) (mean) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.190 02 E+00

calorie (15 8C) (cal15) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.185 80 E+00

calorie (20 8C) (cal20) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.181 90 E+00

calorieIT, kilogram (nutrition)12 . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1868 E+03

calorieth, kilogram (nutrition)12 . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.184 E+03

calorie (mean), kilogram (nutrition)12. . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.190 02 E+03

calorieth per centimeter second degree Celsius

[calth /(cm ? s ? 8C)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m ? K)]. . . . . . . . . . . . . 4.184 E+02

calorieIT per gram (calIT /g). . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram (J/kg) ...................... 4.1868 E+03

calorieth per gram (calth /g) . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram (J/kg) ...................... 4.184 E+03

calorieIT per gram degree Celsius

[calIT /(g ? 8C)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)]. . . . . . . . . . 4.1868 E+03

calorieth per gram degree Celsius

[calth /(g ? 8C)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)]. . . . . . . . . . 4.184 E+03

calorieIT per gram kelvin [calIT/(g ? K)] . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)] . . . . . . . . . 4.1868 E+03

calorieth per gram kelvin [calth /(g ? K)] . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)] . . . . . . . . . 4.184 E+03

calorieth per minute (calth /min). . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.973 333 E202

calorieth per second (calth /s). . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.184 E+00

calorieth per square centimeter (calth /cm2

). . . . . . . . . . . joule per square meter (J/m2).................. 4.184 E+04

calorieth per square centimeter minute

[calth /(cm2 ? min)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2)................. 6.973 333 E+02

calorieth per square centimeter second

[calth /(cm2 ? s)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2

)................. 4.184 E+04

candela per square inch (cd/in2

) . . . . . . . . . . . . . . . . . . . . candela per square meter (cd/m2).............. 1.550 003 E+03

carat, metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 2.0 E204

carat, metric ........................................ gram (g) ....................................... 2.0 E201

centimeter of mercury (0 8C)13 ...................... pascal (Pa)..................................... 1.333 22 E+03

centimeter of mercury (0 8C)13 . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 1.333 22 E+00

centimeter of mercury, conventional (cmHg)13 ....... pascal (Pa)..................................... 1.333 224 E+03

centimeter of mercury, conventional (cmHg)13 . . . . . . . kilopascal (kPa)................................ 1.333 224 E+00

centimeter of water (4 8C)13 ......................... pascal (Pa)..................................... 9.806 38 E+01

centimeter of water, conventional (cmH2O)13 ........ pascal (Pa)..................................... 9.806 65 E+01

centipoise (cP) ...................................... pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E203

centistokes (cSt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter squared per second (m2

/s). . . . . . . . . . . . . . . 1.0 E206

chain (based on U.S. survey foot) (ch)9 ............. meter (m)...................................... 2.011 684 E+01

circular mil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2

).............................. 5.067 075 E210

circular mil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square millimeter (mm2)....................... 5.067 075 E204

clo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter kelvin per watt (m2 ? K /W). . . . . . . 1.55 E201

cord (128 ft3)....................................... cubic meter (m3) .............................. 3.624 556 E+00

cubic foot (ft3

) ...................................... cubic meter (m3)............................... 2.831 685 E202

cubic foot per minute (ft3

/min) ..................... cubic meter per second (m3/s) . . . . . . . . . . . . . . . . . 4.719 474 E204

cubic foot per minute (ft3/min) ..................... liter per second (L/s).......................... 4.719 474 E201

cubic foot per second (ft3/s) . . . . . . . . . . . . . . . . . . . . . . . . cubic meter per second (m3/s) . . . . . . . . . . . . . . . . . 2.831 685 E202

12 The kilogram calorie or ‘‘large calorie’’ is an obsolete term used for the kilocalorie, which is the calorie used to express the energy content

of foods. However, in practice, the prefix ‘‘kilo’’ is usually omitted.

13 Conversion factors for mercury manometer pressure units are calculated using the standard value for the acceleration of gravity and the

density of mercury at the stated temperature. Additional digits are not justified because the definitions of the units do not take into account the

compressibility of mercury or the change in density caused by the revised practical temperature scale, ITS-90. Similar comments also apply

to water manometer pressure units. Conversion factors for conventional mercury and water manometer pressure units are based on

Ref. [6: ISO 31-3].

48
Guide for the Use of the International System of Units (SI)

To convert from to Multiply by

cubic inch (in3)

14 ................................... cubic meter (m3

)............................... 1.638 706 E205

cubic inch per minute (in3

/min)..................... cubic meter per second (m3/s) . . . . . . . . . . . . . . . . . 2.731 177 E207

cubic mile (mi3

)..................................... cubic meter (m3)............................... 4.168 182 E+09

cubic yard (yd3

)..................................... cubic meter (m3)............................... 7.645 549 E201

cubic yard per minute (yd3

/min) .................... cubic meter per second (m3/s) . . . . . . . . . . . . . . . . . 1.274 258 E202

cup (U.S.)........................................... cubic meter (m3

)............................... 2.365 882 E204

cup (U.S.)........................................... liter (L) ........................................ 2.365 882 E201

cup (U.S.)........................................... milliliter (mL) ................................. 2.365 882 E+02

curie (Ci) ........................................... becquerel (Bq)................................. 3.7 E+10

darcy15 .............................................. meter squared (m2) ............................ 9.869 233 E213

day (d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s)...................................... 8.64 E+04

day (sidereal)........................................ second (s)...................................... 8.616 409 E+04

debye (D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb meter (C ? m) ........................ 3.335 641 E230

degree (angle) (8).................................... radian (rad) .................................... 1.745 329 E202

degree Celsius (temperature) (8C). . . . . . . . . . . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T / K = t /8C+273.15

degree Celsius (temperature interval) (8C) . . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+00

degree centigrade (temperature)16................... degree Celsius (8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t /8C ≈ t /deg. cent.

degree centigrade (temperature interval)16 .......... degree Celsius (8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+00

degree Fahrenheit (temperature) (8F). . . . . . . . . . . . . . . . degree Celsius (8C) . . . . . . . . . . . . . . . . . . . . . . . . . . .t/ 8C=(t/ 8F 2 32)/ 1.8

degree Fahrenheit (temperature) (8F). . . . . . . . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T / K=(t / 8F + 459.67)/1.8

degree Fahrenheit (temperature interval)(8F) . . . . . . . . degree Celsius (8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.555 556 E201

degree Fahrenheit (temperature interval)(8F) . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.555 556 E201

degree Fahrenheit hour per British thermal unitIT

(8F ? h/BtuIT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin per watt (K/W). . . . . . . . . . . . . . . . . . . . . . . . . 1.895 634 E+00

degree Fahrenheit hour per British thermal unitth

(8F ? h/Btuth). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin per watt (K/W). . . . . . . . . . . . . . . . . . . . . . . . . 1.896 903 E+00

degree Fahrenheit hour square foot per British thermal unitIT

(8F ? h ? ft2/BtuIT). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter kelvin per watt (m2 ? K /W) . . . . . . 1.761 102 E201

degree Fahrenheit hour square foot per British thermal unitth

(8F ? h ? ft2/Btuth) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter kelvin per watt (m2 ? K /W) . . . . . . 1.762 280 E201

degree Fahrenheit hour square foot per British thermal unitIT inch

[8F ? h ? ft2

/(BtuIT ? in)]........................... meter kelvin per watt (m ? K/W) . . . . . . . . . . . . . . 6.933 472 E+00

degree Fahrenheit hour square foot per British thermal unitth inch

[8F ? h ? ft2

/(Btuth ? in)] ........................... meter kelvin per watt (m ? K/W) . . . . . . . . . . . . . . 6.938 112 E+00

degree Fahrenheit second per British thermal unitIT

(8F ? s/BtuIT). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin per watt (K/W). . . . . . . . . . . . . . . . . . . . . . . . . 5.265 651 E204

degree Fahrenheit second per British thermal unitth

(8F ? s/Btuth) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin per watt (K/W). . . . . . . . . . . . . . . . . . . . . . . . . 5.269 175 E204

degree Rankine (8R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T/ K=(T/ 8R) /1.8

degree Rankine (temperature interval) (8R) . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.555 556 E201

denier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) .................... 1.111 111 E207

denier ............................................... gram per meter (g/m) ......................... 1.111 111 E204

dyne (dyn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 1.0 E205

dyne centimeter (dyn ? cm). . . . . . . . . . . . . . . . . . . . . . . . . . newton meter (N ? m). . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E207

dyne per square centimeter (dyn/cm2

) .............. pascal (Pa)..................................... 1.0 E201

electronvolt (eV) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.602 177 E219

EMU of capacitance (abfarad) ...................... farad (F) ....................................... 1.0 E+09

EMU of current (abampere)......................... ampere (A) .................................... 1.0 E+01

EMU of electric potential (abvolt) . . . . . . . . . . . . . . . . . . volt (V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E208

EMU of inductance (abhenry) ...................... henry (H) ...................................... 1.0 E209

14 The exact conversion factor is 1.638 706 4 E205. 15 The darcy is a unit for expressing the permeability of porous solids, not area. 16 The centigrade temperature scale is obsolete; the degree centigrade is only approximately equal to the degree Celsius.

49
Guide for the Use of the International System of Units (SI)

To convert from to Multiply by

EMU of resistance (abohm) . . . . . . . . . . . . . . . . . . . . . . . . . ohm (V) ....................................... 1.0 E209

erg (erg). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E207

erg per second (erg/s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E207

erg per square centimeter second

|1obrktl1ru|/(cm2 ? s)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2

)................. 1.0 E203

ESU of capacitance (statfarad) ...................... farad (F) ....................................... 1.112 650 E212

ESU of current (statampere) ........................ ampere (A) .................................... 3.335 641 E210

ESU of electric potential (statvolt) . . . . . . . . . . . . . . . . . . volt (V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.997 925 E+02

ESU of inductance (stathenry) ...................... henry (H) ...................................... 8.987 552 E+11

ESU of resistance (statohm). . . . . . . . . . . . . . . . . . . . . . . . . ohm (V) ....................................... 8.987 552 E+11

faraday (based on carbon 12) . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.648 531 E+04

fathom (based on U.S. survey foot)9 ................ meter (m)...................................... 1.828 804 E+00

fermi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m)...................................... 1.0 E215

fermi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . femtometer (fm) ............................... 1.0 E+00

fluid ounce (U.S.) (fl oz)............................ cubic meter (m3

)............................... 2.957 353 E205

fluid ounce (U.S.) (fl oz)............................ milliliter (mL) ................................. 2.957 353 E+01

foot (ft) ............................................. meter (m)...................................... 3.048 E201

foot (U.S. survey) (ft)9 .............................. meter (m)...................................... 3.048 006 E201

footcandle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lux (lx) ........................................ 1.076 391 E+01

footlambert. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . candela per square meter (cd/m2

).............. 3.426 259 E+00

foot of mercury, conventional (ftHg)13 .............. pascal (Pa)..................................... 4.063 666 E+04

foot of mercury, conventional (ftHg)13 . . . . . . . . . . . . . . kilopascal (kPa)................................ 4.063 666 E+01

foot of water (39.2 8F)13 ............................ pascal (Pa)..................................... 2.988 98 E+03

foot of water (39.2 8F)13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 2.988 98 E+00

foot of water, conventional (ftH2O)13 ............... pascal (Pa)..................................... 2.989 067 E+03

foot of water, conventional (ftH2O)13 . . . . . . . . . . . . . . . kilopascal (kPa)................................ 2.989 067 E+00

foot per hour (ft/h). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) ........................ 8.466 667 E205

foot per minute (ft/min) ............................ meter per second (m/s) ........................ 5.08 E203

foot per second (ft/s)................................ meter per second (m/s) ........................ 3.048 E201

foot per second squared (ft/s2

)...................... meter per second squared (m/s2). . . . . . . . . . . . . . . 3.048 E201

foot poundal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.214 011 E202

foot pound-force (ft ? lbf) . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.355 818 E+00

foot pound-force per hour (ft ? lbf/h). . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.766 161 E204

foot pound-force per minute (ft ? lbf/min) . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.259 697 E202

foot pound-force per second (ft ? lbf/s) . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.355 818 E+00

foot to the fourth power (ft4)

17 ...................... meter to the fourth power (m4

) ................ 8.630 975 E203

franklin (Fr). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.335 641 E210

gal (Gal) ............................................ meter per second squared (m/s2

). . . . . . . . . . . . . . . 1.0 E202

gallon [Canadian and U.K. (Imperial)] (gal) ........ cubic meter (m3

)............................... 4.546 09 E203

gallon [Canadian and U.K. (Imperial)] (gal) ........ liter (L) ........................................ 4.546 09 E+00

gallon (U.S.) (gal)................................... cubic meter (m3)............................... 3.785 412 E203

gallon (U.S.) (gal)................................... liter (L) ........................................ 3.785 412 E+00

gallon (U.S.) per day (gal/ d) ........................ cubic meter per second (m3

/s) . . . . . . . . . . . . . . . . . 4.381 264 E208

gallon (U.S.) per day (gal / d)........................ liter per second (L / s).......................... 4.381 264 E205

gallon (U.S.) per horsepower hour

[gal / (hp ? h)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter per joule (m3/J) . . . . . . . . . . . . . . . . . . . 1.410 089 E209

gallon (U.S.) per horsepower hour

[gal / (hp ? h)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . liter per joule (L /J) ............................ 1.410 089 E206

gallon (U.S.) per minute (gpm)(gal / min) ........... cubic meter per second (m3/s) . . . . . . . . . . . . . . . . . 6.309 020 E205

gallon (U.S.) per minute (gpm)(gal / min) ........... liter per second (L / s).......................... 6.309 020 E202

17 This is a unit for the quantity second moment of area, which is sometimes called the ‘‘moment of section’’ or ‘‘area moment of

inertia’’ of a plane section about a specified axis.

50
Guide for the Use of the International System of Units (SI)

To convert from to Multiply by

gamma (g) .......................................... tesla (T) ....................................... 1.0 E209

gauss (Gs, G) ....................................... tesla (T) ....................................... 1.0 E204

gilbert (Gi).......................................... ampere (A) .................................... 7.957 747 E201

gill [Canadian and U.K. (Imperial)] (gi) ............ cubic meter (m3

)............................... 1.420 653 E204

gill [Canadian and U.K. (Imperial)] (gi) ............ liter (L) ........................................ 1.420 653 E201

gill (U.S.) (gi)....................................... cubic meter (m3

)............................... 1.182 941 E204

gill (U.S.) (gi)....................................... liter (L) ........................................ 1.182 941 E201

gon (also called grade) (gon)........................ radian (rad) .................................... 1.570 796 E202

gon (also called grade) (gon)........................ degree (angle) (8) .............................. 9.0 E201

grain (gr). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 6.479 891 E205

grain (gr)............................................ milligram (mg) ................................ 6.479 891 E+01

grain per gallon (U.S.) (gr / gal) . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3

) ............. 1.711 806 E202

grain per gallon (U.S.) (gr / gal) ..................... milligram per liter (mg/ L)..................... 1.711 806 E+01

gram-force per square centimeter (gf/cm2). . . . . . . . . . pascal (Pa)..................................... 9.806 65 E+01

gram per cubic centimeter (g/cm3) . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 1.0 E+03

hectare (ha) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2

).............................. 1.0 E+04

horsepower (550 ft ? lbf/s) (hp) . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.456 999 E+02

horsepower (boiler) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.809 50 E+03

horsepower (electric). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.46 E+02

horsepower (metric). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.354 988 E+02

horsepower (U.K.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4570 E+02

horsepower (water). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.460 43 E+02

hour (h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s)...................................... 3.6 E+03

hour (sidereal) ...................................... second (s)...................................... 3.590 170 E+03

hundredweight (long, 112 lb). . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 5.080 235 E+01

hundredweight (short, 100 lb). . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 4.535 924 E+01

inch (in)............................................. meter (m)...................................... 2.54 E202

inch (in). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . centimeter (cm)................................ 2.54 E+00

inch of mercury (32 8F)13 ........................... pascal (Pa)..................................... 3.386 38 E+03

inch of mercury (32 8F)13 . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 3.386 38 E+00

inch of mercury (60 8F)13 ........................... pascal (Pa)..................................... 3.376 85 E+03

inch of mercury (60 8F)13 . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 3.376 85 E+00

inch of mercury, conventional (inHg)13 ............. pascal (Pa)..................................... 3.386 389 E+03

inch of mercury, conventional (inHg)13 . . . . . . . . . . . . . kilopascal (kPa)................................ 3.386 389 E+00

inch of water (39.2 8F)13 ............................ pascal (Pa)..................................... 2.490 82 E+02

inch of water (60 8F)13 .............................. pascal (Pa)..................................... 2.4884 E+02

inch of water, conventional (inH2O)13 .............. pascal (Pa)..................................... 2.490 889 E+02

inch per second (in/s)............................... meter per second (m/s) ........................ 2.54 E202

inch per second squared (in/s2) ..................... meter per second squared (m/s2). . . . . . . . . . . . . . . 2.54 E202

inch to the fourth power (in4)

17 ..................... meter to the fourth power (m4

) ................ 4.162 314 E207

kayser (K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reciprocal meter (m21) ........................ 1.0 E+02

kelvin (K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . degree Celsius (8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . .t / 8C = T / K 2 273.15

kilocalorieIT (kcalIT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1868 E+03

kilocalorieth (kcalth) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.184 E+03

kilocalorie (mean) (kcal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.190 02 E+03

kilocalorieth per minute (kcalth /min) . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.973 333 E+01

kilocalorieth per second (kcalth /s) . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.184 E+03

kilogram-force (kgf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 9.806 65 E+00

kilogram-force meter (kgf ? m). . . . . . . . . . . . . . . . . . . . . . newton meter (N ? m). . . . . . . . . . . . . . . . . . . . . . . . . . 9.806 65 E+00

51
Guide for the Use of the International System of Units (SI)

To convert from to Multiply by

kilogram-force per square centimeter

(kgf/cm2)......................................... pascal (Pa)..................................... 9.806 65 E+04

kilogram-force per square centimeter

(kgf/cm2

). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 9.806 65 E+01

kilogram-force per square meter (kgf/m2)........... pascal (Pa)..................................... 9.806 65 E+00

kilogram-force per square millimeter

(kgf/mm2

)........................................ pascal (Pa)..................................... 9.806 65 E+06

kilogram-force per square millimeter

(kgf/mm2

). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . megapascal (MPa) ............................. 9.806 65 E+00

kilogram-force second squared per meter

(kgf ? s2

/m). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 9.806 65 E+00

kilometer per hour (km/h) . . . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) ........................ 2.777 778 E201

kilopond (kilogram-force) (kp) . . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 9.806 65 E+00

kilowatt hour (kW ? h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 E+06

kilowatt hour (kW ? h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . megajoule (MJ) ................................ 3.6 E+00

kip (1 kip=1000 lbf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 4.448 222 E+03

kip (1 kip=1000 lbf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilonewton (kN) ............................... 4.448 222 E+00

kip per square inch (ksi) (kip/in2

)................... pascal (Pa)..................................... 6.894 757 E+06

kip per square inch (ksi) (kip/in2

). . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 6.894 757 E+03

knot (nautical mile per hour)........................ meter per second (m/s) ........................ 5.144 444 E201

lambert18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . candela per square meter (cd/m2).............. 3.183 099 E+03

langley (calth /cm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per square meter (J/m2).................. 4.184 E+04

light year (l.y.)19 .................................... meter (m)...................................... 9.460 73 E+15

liter (L)20 ........................................... cubic meter (m3

)............................... 1.0 E203

lumen per square foot (lm/ft2

) . . . . . . . . . . . . . . . . . . . . . . lux (lx) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.076 391 E+01

maxwell (Mx)....................................... weber (Wb).................................... 1.0 E208

mho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . siemens (S) .................................... 1.0 E+00

microinch ........................................... meter (m)...................................... 2.54 E208

microinch ........................................... micrometer (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.54 E202

micron (m) .......................................... meter (m)...................................... 1.0 E206

micron (m) .......................................... micrometer (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+00

mil (0.001 in)....................................... meter (m)...................................... 2.54 E205

mil (0.001 in)....................................... millimeter (mm) ............................... 2.54 E202

mil (angle) .......................................... radian (rad) .................................... 9.817 477 E204

mil (angle) .......................................... degree (8)...................................... 5.625 E202

mile (mi)............................................ meter (m)...................................... 1.609 344 E+03

mile (mi). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilometer (km)................................. 1.609 344 E+00

mile (based on U.S. survey foot) (mi)9 .............. meter (m)...................................... 1.609 347 E+03

mile (based on U.S. survey foot) (mi)9 . . . . . . . . . . . . . . kilometer (km)................................. 1.609 347 E+00

mile, nautical 21 ..................................... meter (m)...................................... 1.852 E+03

mile per gallon (U.S.) (mpg) (mi/gal)............... meter per cubic meter (m/m3)................. 4.251 437 E+05

mile per gallon (U.S.) (mpg) (mi/gal). . . . . . . . . . . . . . . kilometer per liter (km/L) ..................... 4.251 437 E201

mile per gallon (U.S.) (mpg) (mi/gal)22 ............. liter per 100 kilometer (L/100 km) . . . . . . . .divide 235.215 by number

of miles per gallon

mile per hour (mi/h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) ........................ 4.4704 E201

mile per hour (mi/h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilometer per hour (km/h)..................... 1.609 344 E+00

18 The exact conversion factor is 104

/p. 19 This conversion factor is based on 1 d = 86 400 s; and 1 Julian century = 36 525 d. (See The Astronomical Almanac for the Year 1995, page

K6, U.S. Government Printing Office, Washington, DC, 1994).

20 In 1964 the General Conference on Weights and Measures reestablished the name ‘‘liter’’ as a special name for the cubic decimeter. Between

1901 and 1964 the liter was slightly larger (1.000 028 dm3

); when one uses high-accuracy volume data of that time, this fact must be kept in

mind.

21 The value of this unit, 1 nautical mile = 1852 m, was adopted by the First International Extraordinary Hydrographic

Conference, Monaco, 1929, under the name ‘‘International nautical mile.’’

22 See Sec. B.5.

52
Guide for the Use of the International System of Units (SI)

To convert from to Multiply by

mile per minute (mi/min).......................... . meter per second (m/s) ....................... . 2.682 24 E+01

mile per second (mi/s) ............................. . meter per second (m/s) ....................... . 1.609 344 E+03

millibar (mbar)..................................... . pascal (Pa).................................... . 1.0 E+02

millibar (mbar)..................................... . kilopascal (kPa)............................... . 1.0 E201

millimeter of mercury, conventional (mmHg)

13 ...... . pascal (Pa).................................... . 1.333 224 E+02

millimeter of water, conventional (mmH2O)13 ....... . pascal (Pa).................................... . 9.806 65 E+00

minute (angle) (')................................... . radian (rad) ................................... . 2.908 882 E204

minute (min)....................................... . second (s)..................................... . 6.0 E+01

minute (sidereal) ................................... . second (s)..................................... . 5.983 617 E+01

oersted (Oe)........................................ . ampere per meter (A/m)...................... . 7.957 747 E+01

ohm centimeter (V ? cm)........................... . ohm meter (V ? m)............................ . 1.0 E202

ohm circular-mil per foot .......................... . ohm meter (V ? m)............................ . 1.662 426 E209

ohm circular-mil per foot .......................... . ohm square millimeter per meter

(V ? mm2

/m)............................... . 1.662 426 E203

ounce (avoirdupois) (oz)............................ . kilogram (kg) ................................. . 2.834 952 E202

ounce (avoirdupois) (oz)............................ . gram (g) ...................................... . 2.834 952 E+01

ounce (troy or apothecary) (oz) .................... . kilogram (kg) ................................. . 3.110 348 E202

ounce (troy or apothecary) (oz) .................... . gram (g) ...................................... . 3.110 348 E+01

ounce [Canadian and U.K. fluid (Imperial)]

(fl oz)............................................ . cubic meter (m3

).............................. . 2.841 306 E205

ounce [Canadian and U.K. fluid (Imperial)]

(fl oz) ........................................... . milliliter (mL) ................................ . 2.841 306 E+01

ounce (U.S. fluid) (fl oz)........................... . cubic meter (m3

).............................. . 2.957 353 E205

ounce (U.S. fluid) (fl oz)........................... . milliliter (mL) ................................ . 2.957 353 E+01

ounce (avoirdupois)-force (ozf)..................... . newton (N) ................................... . 2.780 139 E201

ounce (avoirdupois)-force inch (ozf ? in) ........... . newton meter (N ? m)......................... . 7.061 552 E203

ounce (avoirdupois)-force inch (ozf ? in) ........... . millinewton meter (mN ? m).................. . 7.061 552 E+00

ounce (avoirdupois) per cubic inch (oz/in3

)........ . kilogram per cubic meter (kg/m3) ............ . 1.729 994 E+03

ounce (avoirdupois) per gallon [Canadian and

U.K. (Imperial)] (oz/gal)........................ . kilogram per cubic meter (kg/m3

) ............ . 6.236 023 E+00

ounce (avoirdupois) per gallon [Canadian and

U.K. (Imperial)] (oz/gal)........................ . gram per liter (g/L) .......................... . 6.236 023 E+00

ounce (avoirdupois) per gallon(U.S.)(oz/gal) ...... . kilogram per cubic meter (kg/m3) ............ . 7.489 152 E+00

ounce (avoirdupois) per gallon(U.S.)(oz/gal)....... . gram per liter (g/L) .......................... . 7.489 152 E+00

ounce (avoirdupois) per square foot (oz/ft2

)........ . kilogram per square meter (kg/m2) ........... . 3.051 517 E201

ounce (avoirdupois) per square inch (oz/in2

)....... . kilogram per square meter (kg/m2) ........... . 4.394 185 E+01

ounce (avoirdupois) per square yard (oz/yd2) ....... . kilogram per square meter (kg/m2) ........... . 3.390 575 E202

parsec (pc) ......................................... . meter (m)..................................... . 3.085 678 E+16

peck (U.S.) (pk) ................................... . cubic meter (m3).............................. . 8.809 768 E203

peck (U.S.) (pk) ................................... . liter (L) ....................................... . 8.809 768 E+00

pennyweight (dwt)................................. . kilogram (kg) ................................. . 1.555 174 E203

pennyweight (dwt)................................. . gram (g) ...................................... . 1.555 174 E+00

perm (0 8C) ........................................ . kilogram per pascal second square meter

[kg/(Pa ? s ? m2

)] ........................... . 5.721 35 E211

perm (23 8C) ....................................... . kilogram per pascal second square meter

[kg/(Pa ? s ? m2

)] ........................... . 5.745 25 E211

perm inch (0 8C) ................................... . kilogram per pascal second meter

[kg/(Pa ? s ? m)]............................ . 1.453 22 E212

perm inch (23 8C).................................. . kilogram per pascal second meter

[kg/(Pa ? s ? m)]............................ . 1.459 29 E212

53
Guide for the Use of the International System of Units (SI)

To convert from to Multiply by

phot (ph) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lux (lx) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+04

pica (computer) (1/6 in)............................ meter (m) ..................................... 4.233 333 E203

pica (computer) (1/6 in)............................ millimeter (mm) ............................... 4.233 333 E+00

pica (printer’s) ...................................... meter (m)...................................... 4.217 518 E203

pica (printer’s) ...................................... millimeter (mm) ............................... 4.217 518 E+00

pint (U.S. dry) (dry pt).............................. cubic meter (m3)............................... 5.506 105 E204

pint (U.S. dry) (dry pt).............................. liter (L) ........................................ 5.506 105 E201

pint (U.S. liquid) (liq pt) ............................ cubic meter (m3)............................... 4.731 765 E204

pint (U.S. liquid) (liq pt) ............................ liter (L) ........................................ 4.731 765 E201

point (computer) (1/72 in).......................... meter (m) ..................................... 3.527 778 E204

point (computer) (1/72 in).......................... millimeter (mm) ............................... 3.527 778 E201

point (printer’s) ..................................... meter (m)...................................... 3.514 598 E204

point (printer’s) ..................................... millimeter (mm) ............................... 3.514 598 E201

poise (P) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E201

pound (avoirdupois) (lb)23 . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 4.535 924 E201

pound (troy or apothecary) (lb) . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 3.732 417 E201

poundal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 1.382 550 E201

poundal per square foot ............................. pascal (Pa)..................................... 1.488 164 E+00

poundal second per square foot ..................... pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.488 164 E+00

pound foot squared (lb ? ft2

) . . . . . . . . . . . . . . . . . . . . . . . . . kilogram meter squared (kg ? m2).............. 4.214 011 E202

pound-force (lbf)24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 4.448 222 E+00

pound-force foot (lbf ? ft) . . . . . . . . . . . . . . . . . . . . . . . . . . . newton meter (N ? m). . . . . . . . . . . . . . . . . . . . . . . . . . 1.355 818 E+00

pound-force foot per inch (lbf ? ft/in) . . . . . . . . . . . . . . . newton meter per meter (N ? m/m) . . . . . . . . . . . . 5.337 866 E+01

pound-force inch (lbf ? in). . . . . . . . . . . . . . . . . . . . . . . . . . . newton meter (N ? m). . . . . . . . . . . . . . . . . . . . . . . . . . 1.129 848 E201

pound-force inch per inch (lbf ? in/in) . . . . . . . . . . . . . . newton meter per meter (N ? m/m) . . . . . . . . . . . . 4.448 222 E+00

pound-force per foot (lbf/ft) . . . . . . . . . . . . . . . . . . . . . . . . newton per meter (N/m)....................... 1.459 390 E+01

pound-force per inch (lbf/in). . . . . . . . . . . . . . . . . . . . . . . . newton per meter (N/m)....................... 1.751 268 E+02

pound-force per pound

(lbf/lb) (thrust to mass ratio) . . . . . . . . . . . . . . . . . . . . . newton per kilogram (N/kg)................... 9.806 65 E+00

pound-force per square foot (lbf/ft2) ................ pascal (Pa)..................................... 4.788 026 E+01

pound-force per square inch (psi) (lbf/in2

).......... pascal (Pa)..................................... 6.894 757 E+03

pound-force per square inch (psi) (lbf/in2) . . . . . . . . . . kilopascal (kPa)................................ 6.894 757 E+00

pound-force second per square foot

(lbf ? s/ft2)........................................ pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . . 4.788 026 E+01

pound-force second per square inch

(lbf ? s/in2) ....................................... pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . . 6.894 757 E+03

pound inch squared (lb ? in2

) . . . . . . . . . . . . . . . . . . . . . . . . kilogram meter squared (kg ? m2).............. 2.926 397 E204

pound per cubic foot (lb/ft3

) . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 1.601 846 E+01

pound per cubic inch (lb/in3) . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 2.767 990 E+04

pound per cubic yard (lb/yd3) . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 5.932 764 E201

pound per foot (lb/ft) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) .................... 1.488 164 E+00

pound per foot hour [lb/(ft ? h)]. . . . . . . . . . . . . . . . . . . . . pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . . 4.133 789 E204

pound per foot second [lb/(ft ? s)]. . . . . . . . . . . . . . . . . . . pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.488 164 E+00

pound per gallon [Canadian and

U.K. (Imperial)] (lb/gal) . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 9.977 637 E+01

pound per gallon [Canadian and

U.K. (Imperial)] (lb/gal) . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per liter (kg/L) ...................... 9.977 637 E202

pound per gallon (U.S.) (lb/gal). . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 1.198 264 E+02

pound per gallon (U.S.) (lb/gal). . . . . . . . . . . . . . . . . . . . . kilogram per liter (kg/L) ...................... 1.198 264 E201

pound per horsepower hour [lb/(hp ? h)] . . . . . . . . . . . . kilogram per joule (kg/J) ...................... 1.689 659 E207

pound per hour (lb/h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per second (kg/s) .................... 1.259 979 E204

23 The exact conversion factor is 4.535 923 7 E201. All units in Secs. B.8 and B.9 that contain the pound refer to the avoirdupois

pound.

24 If the local value of the acceleration of free fall is taken as gn=9.806 65 m/s2 (the standard value), the exact conversion factor

is 4.448 221 615 260 5 E+00.

54
Guide for the Use of the International System of Units (SI)

To convert from to Multiply by

pound per inch (lb/in). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) .................... 1.785 797 E+01

pound per minute (lb/min). . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per second (kg/s) .................... 7.559 873 E203

pound per second (lb/s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per second (kg/s) .................... 4.535 924 E201

pound per square foot (lb/ft2) . . . . . . . . . . . . . . . . . . . . . . . kilogram per square meter (kg/m2)............ 4.882 428 E+00

pound per square inch (not pound-force)

(lb/in2

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per square meter (kg/m2)............ 7.030 696 E+02

pound per yard (lb/yd) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) .................... 4.960 546 E201

psi (pound-force per square inch) (lbf/in2

).......... pascal (Pa)..................................... 6.894 757 E+03

psi (pound-force per square inch) (lbf/in2

) . . . . . . . . . . kilopascal (kPa)................................ 6.894 757 E+00

quad (1015 BtuIT)

11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.055 056 E+18

quart (U.S. dry) (dry qt) ............................ cubic meter (m3)............................... 1.101 221 E203

quart (U.S. dry) (dry qt) ............................ liter (L) ........................................ 1.101 221 E+00

quart (U.S. liquid) (liq qt)........................... cubic meter (m3

)............................... 9.463 529 E204

quart (U.S. liquid) (liq qt)........................... liter (L) ........................................ 9.463 529 E201

rad (absorbed dose) (rad) . . . . . . . . . . . . . . . . . . . . . . . . . . . gray (Gy) ...................................... 1.0 E202

rem (rem) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sievert (Sv) .................................... 1.0 E202

revolution (r) ........................................ radian (rad) .................................... 6.283 185 E+00

revolution per minute (rpm) (r/min)................. radian per second (rad/s) ...................... 1.047 198 E201

rhe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reciprocal pascal second [(Pa ? s)21

]........... 1.0 E+01

rod (based on U.S. survey foot) (rd)9................ meter (m)...................................... 5.029 210 E+00

roentgen (R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb per kilogram (C/kg).................. 2.58 E204

rpm (revolution per minute) (r/min)................. radian per second (rad/s) ...................... 1.047 198 E201

second (angle) (") ................................... radian (rad) .................................... 4.848 137 E206

second (sidereal) .................................... second (s)...................................... 9.972 696 E201

shake................................................ second (s)...................................... 1.0 E208

shake................................................ nanosecond (ns) ............................... 1.0 E+01

slug (slug). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 1.459 390 E+01

slug per cubic foot (slug/ft3). . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 5.153 788 E+02

slug per foot second [slug/(ft ? s)] . . . . . . . . . . . . . . . . . . pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . . 4.788 026 E+01

square foot (ft2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2).............................. 9.290 304 E202

square foot per hour (ft2

/h) . . . . . . . . . . . . . . . . . . . . . . . . . square meter per second (m2/s). . . . . . . . . . . . . . . . 2.580 64 E205

square foot per second (ft2

/s) . . . . . . . . . . . . . . . . . . . . . . . square meter per second (m2/s). . . . . . . . . . . . . . . . 9.290 304 E202

square inch (in2

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2).............................. 6.4516 E204

square inch (in2

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square centimeter (cm2)........................ 6.4516 E+00

square mile (mi2

). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2).............................. 2.589 988 E+06

square mile (mi2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square kilometer (km2). . . . . . . . . . . . . . . . . . . . . . . . . 2.589 988 E+00

square mile

(based on U.S. survey foot) (mi2)

9. . . . . . . . . . . . . . . . square meter (m2

).............................. 2.589 998 E+06

square mile

(based on U.S. survey foot) (mi2)

9. . . . . . . . . . . . . . . . square kilometer (km2

). . . . . . . . . . . . . . . . . . . . . . . . . 2.589 998 E+00

square yard (yd2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2).............................. 8.361 274 E201

statampere .......................................... ampere (A) .................................... 3.335 641 E210

statcoulomb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.335 641 E210

statfarad............................................. farad (F) ....................................... 1.112 650 E212

stathenry ............................................ henry (H) ...................................... 8.987 552 E+11

statmho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . siemens (S) .................................... 1.112 650 E212

statohm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm (V) ....................................... 8.987 552 E+11

statvolt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . volt (V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.997 925 E+02

stere (st)............................................. cubic meter (m3

)............................... 1.0 E+00

stilb (sb). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . candela per square meter (cd/m2

).............. 1.0 E+04

stokes (St) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter squared per second (m2

/s). . . . . . . . . . . . . . . 1.0 E204

55
Guide for the Use of the International System of Units (SI)

To convert from to Multiply by

tablespoon........................................... cubic meter (m3)............................... 1.478 676 E205

tablespoon........................................... milliliter (mL) ................................. 1.478 676 E+01

teaspoon ............................................ cubic meter (m3)............................... 4.928 922 E206

teaspoon ............................................ milliliter (mL) ................................. 4.928 922 E+00

tex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) .................... 1.0 E206

therm (EC)25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.055 06 E+08

therm (U.S.)25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.054 804 E+08

ton, assay (AT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 2.916 667 E202

ton, assay (AT) ...................................... gram (g) ....................................... 2.916 667 E+01

ton-force (2000 lbf). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 8.896 443 E+03

ton-force (2000 lbf). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilonewton (kN) ............................... 8.896 443 E+00

ton, long (2240 lb) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 1.016 047 E+03

ton, long, per cubic yard . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3

) ............. 1.328 939 E+03

ton, metric (t). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 1.0 E+03

tonne (called ‘‘metric ton’’ in U.S.) (t) . . . . . . . . . . . . . kilogram (kg) .................................. 1.0 E+03

ton of refrigeration (12 000 BtuIT /h) . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.516 853 E+03

ton of TNT (energy equivalent)26 . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.184 E+09

ton, register ........................................ cubic meter (m3)............................... 2.831 685 E+00

ton, short (2000 lb) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 9.071 847 E+02

ton, short, per cubic yard . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 1.186 553 E+03

ton, short, per hour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per second (kg/s) .................... 2.519 958 E201

torr (Torr) ........................................... pascal (Pa)..................................... 1.333 224 E+02

unit pole............................................. weber (Wb).................................... 1.256 637 E207

watt hour (W ? h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 E+03

watt per square centimeter (W/cm2). . . . . . . . . . . . . . . . watt per square meter (W/m2)................. 1.0 E+04

watt per square inch (W/in2

). . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2)................. 1.550 003 E+03

watt second (W ? s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+00

yard (yd) ............................................ meter (m)...................................... 9.144 E201

year (365 days)...................................... second (s)...................................... 3.1536 E+07

year (sidereal)....................................... second (s)...................................... 3.155 815 E+07

year (tropical)....................................... second (s)...................................... 3.155 693 E+07

25 The therm (EC) is legally defined in the Council Directive of 20 December 1979, Council of the European Communities (now the European

Union, EU). The therm (U.S.) is legally defined in the Federal Register of July 27, 1968. Although the therm (EC), which is based on the

International Table Btu, is frequently used by engineers in the United States, the therm (U.S.) is the legal unit used by the U.S. natural gas

industry.

26 Defined (not measured) value.

56
Guide for the Use of the International System of Units (SI)

B.9 Factors for units listed by kind of quantity or field of science

Caution: The units listed in column 1 are in general not to be used in NIST publications, with the

exception of those few in italic type.

Factors in boldface are exact

To convert from to Multiply by

ACCELERATION

acceleration of free fall, standard (gn )............... meter per second squared (m/s2). . . . . . . . . . . . . . . 9.806 65 E+00

foot per second squared (ft/s2)...................... meter per second squared (m/s2). . . . . . . . . . . . . . . 3.048 E201

gal (Gal)............................................ meter per second squared (m/s2

). . . . . . . . . . . . . . . 1.0 E202

inch per second squared (in/s2) ..................... meter per second squared (m/s2). . . . . . . . . . . . . . . 2.54 E202

ANGLE

degree (8)........................................... radian (rad) .................................... 1.745 329 E202

gon (also called grade) (gon) ....................... radian (rad) .................................... 1.570 796 E202

gon (also called grade) (gon) ....................... degree ( 8 )..................................... 9.0 E201

mil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . radian (rad) .................................... 9.817 477 E204

mil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . degree ( 8 )..................................... 5.625 E202

minute ('). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . radian (rad) .................................... 2.908 882 E204

revolution (r) ........................................ radian (rad) .................................... 6.283 185 E+00

second (") . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . radian (rad) .................................... 4.848 137 E206

AREA AND SECOND MOMENT OF AREA

acre (based on U.S. survey foot)9 . . . . . . . . . . . . . . . . . . . square meter (m2).............................. 4.046 873 E+03

are (a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2).............................. 1.0 E+02

barn (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2

).............................. 1.0 E228

circular mil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2

).............................. 5.067 075 E210

circular mil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square millimeter (mm2

)....................... 5.067 075 E204

foot to the fourth power (ft4

)

17...................... meter to the fourth power (m4

) ................ 8.630 975 E203

hectare (ha) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2).............................. 1.0 E+04

inch to the fourth power (in4

)

17 ..................... meter to the fourth power (m4

) ................ 4.162 314 E207

square foot (ft2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2).............................. 9.290 304 E202

square inch (in2

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2).............................. 6.4516 E204

square inch (in2

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square centimeter (cm2)........................ 6.4516 E+00

square mile (mi2

). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2).............................. 2.589 988 E+06

square mile (mi2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square kilometer (km2). . . . . . . . . . . . . . . . . . . . . . . . . 2.589 988 E+00

square mile

(based on U.S. survey foot) (mi2

)

9. . . . . . . . . . . . . . . . square meter (m2

).............................. 2.589 998 E+06

square mile

(based on U.S. survey foot) (mi2

)

9. . . . . . . . . . . . . . . . square kilometer (km2

). . . . . . . . . . . . . . . . . . . . . . . . . 2.589 998 E+00

square yard (yd2

). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2).............................. 8.361 274 E201

CAPACITY (see VOLUME)

DENSITY (that is, MASS DENSITY — see MASS DIVIDED BY VOLUME)

ELECTRICITY and MAGNETISM

abampere............................................ ampere (A) .................................... 1.0 E+01

abcoulomb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+01

abfarad .............................................. farad (F) ....................................... 1.0 E+09

abhenry ............................................. henry (H) ...................................... 1.0 E209

abmho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . siemens (S) .................................... 1.0 E+09

abohm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm (V) ....................................... 1.0 E209

abvolt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . volt (V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E208

ampere hour (A ? h). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 E+03

57
Guide for the Use of the International System of Units (SI)

To convert from to Multiply by

biot (Bi)............................................. ampere (A) .................................... 1.0 E+01

EMU of capacitance (abfarad) ...................... farad (F) ....................................... 1.0 E+09

EMU of current (abampere)......................... ampere (A) .................................... 1.0 E+01

EMU of electric potential (abvolt) . . . . . . . . . . . . . . . . . . volt (V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E208

EMU of inductance (abhenry) ...................... henry (H) ...................................... 1.0 E209

EMU of resistance (abohm) . . . . . . . . . . . . . . . . . . . . . . . . . ohm (V) ....................................... 1.0 E209

ESU of capacitance (statfarad) ...................... farad (F) ....................................... 1.112 650 E212

ESU of current (statampere) ........................ ampere (A) .................................... 3.335 641 E210

ESU of electric potential (statvolt) . . . . . . . . . . . . . . . . . . volt (V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.997 925 E+02

ESU of inductance (stathenry) ...................... henry (H) ...................................... 8.987 552 E+11

ESU of resistance (statohm). . . . . . . . . . . . . . . . . . . . . . . . . ohm (V) ....................................... 8.987 552 E+11

faraday (based on carbon 12) . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.648 531 E+04

franklin (Fr). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.335 641 E210

gamma (g).......................................... tesla (T) ....................................... 1.0 E209

gauss (Gs, G)....................................... tesla (T) ....................................... 1.0 E204

gilbert (Gi).......................................... ampere (A) .................................... 7.957 747 E201

maxwell (Mx) ...................................... weber (Wb).................................... 1.0 E208

mho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . siemens (S) .................................... 1.0 E+00

oersted (Oe) ........................................ ampere per meter (A/m)....................... 7.957 747 E+01

ohm centimeter (V ? cm) . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm meter (V ? m). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E202

ohm circular-mil per foot . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm meter (V ? m). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.662 426 E209

ohm circular-mil per foot . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm square millimeter per meter

(V ? mm2

/m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.662 426 E203

statampere .......................................... ampere (A) .................................... 3.335 641 E210

statcoulomb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.335 641 E210

statfarad............................................. farad (F) ....................................... 1.112 650 E212

stathenry ............................................ henry (H) ...................................... 8.987 552 E+11

statmho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . siemens (S) .................................... 1.112 650 E212

statohm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm (V) ....................................... 8.987 552 E+11

statvolt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . volt (V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.997 925 E+02

unit pole............................................. weber (Wb).................................... 1.256 637 E207

ENERGY (includes WORK)

British thermal unitIT (BtuIT)

11 . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.055 056 E+03

British thermal unitth (Btuth)

11 . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.054 350 E+03

British thermal unit (mean) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.055 87 E+03

British thermal unit (39 8F) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.059 67 E+03

British thermal unit (59 8F) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.054 80 E+03

British thermal unit (60 8F) (Btu). . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.054 68 E+03

calorieIT (calIT)

11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1868 E+00

calorieth (calth)

11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.184 E+00

calorie (mean) (cal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.190 02 E+00

calorie (15 8C) (cal15). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.185 80 E+00

calorie (20 8C) (cal20). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.181 90 E+00

calorieIT, kilogram (nutrition)12 . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1868 E+03

calorieth, kilogram (nutrition)12 . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.184 E+03

calorie (mean), kilogram (nutrition)12. . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.190 02 E+03

electronvolt (eV) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.602 177 E219

erg (erg). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E207

foot poundal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.214 011 E202

foot pound-force (ft ? lbf) . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.355 818 E+00

kilocalorieIT (kcalIT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1868 E+03

kilocalorieth (kcalth) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.184 E+03

kilocalorie (mean) (kcal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.190 02 E+03

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kilowatt hour (kW ? h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 E+06

kilowatt hour (kW ? h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . megajoule (MJ) ................................ 3.6 E+00

quad (1015 BtuIT)

11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.055 056 E+18

therm (EC)25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.055 06 E+08

therm (U.S.)25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.054 804 E+08

ton of TNT (energy equivalent)26 . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.184 E+09

watt hour (W ? h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 E+03

watt second (W ? s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+00

ENERGY DIVIDED BY AREA TIME

erg per square centimeter second

|1obrktl1ru|/(cm2 ? s)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2

)................. 1.0 E203

watt per square centimeter (W/cm2). . . . . . . . . . . . . . . . watt per square meter (W/m2)................. 1.0 E+04

watt per square inch (W/in2

) . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2)................. 1.550 003 E+03

FLOW (see MASS DIVIDED BY TIME or VOLUME DIVIDED BY TIME)

FORCE

dyne (dyn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 1.0 E205

kilogram-force (kgf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 9.806 65 E+00

kilopond (kilogram-force) (kp) . . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 9.806 65 E+00

kip (1 kip=1000 lbf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 4.448 222 E+03

kip (1 kip=1000 lbf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilonewton (kN) ............................... 4.448 222 E+00

ounce (avoirdupois)-force (ozf). . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 2.780 139 E201

poundal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 1.382 550 E201

pound-force (lbf)24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 4.448 222 E+00

pound-force per pound

(lbf/lb) (thrust to mass ratio) . . . . . . . . . . . . . . . . . . . . . newton per kilogram (N/kg)................... 9.806 65 E+00

ton-force (2000 lbf). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . newton (N) .................................... 8.896 443 E+03

ton-force (2000 lbf). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilonewton (kN) ............................... 8.896 443 E+00

FORCE DIVIDED BY AREA (see PRESSURE)

FORCE DIVIDED BY LENGTH

pound-force per foot (lbf/ft) . . . . . . . . . . . . . . . . . . . . . . . . newton per meter (N/m)....................... 1.459 390 E+01

pound-force per inch (lbf/in). . . . . . . . . . . . . . . . . . . . . . . . newton per meter (N/m)....................... 1.751 268 E+02

HEAT

Available Energy

British thermal unitIT per cubic foot

(BtuIT /ft3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per cubic meter (J/m3)................... 3.725 895 E+04

British thermal unitth per cubic foot

(Btuth /ft3

). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per cubic meter (J/m3)................... 3.723 403 E+04

British thermal unitIT per pound (BtuIT /lb). . . . . . . . . . joule per kilogram (J/kg) ...................... 2.326 E+03

British thermal unitth per pound (Btuth /lb) . . . . . . . . . . joule per kilogram (J/kg) ...................... 2.324 444 E+03

calorieIT per gram (calIT /g) . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram (J/kg) ...................... 4.1868 E+03

calorieth per gram (calth /g) . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram (J/kg) ...................... 4.184 E+03

Coefficient of Heat Transfer

British thermal unitIT per hour square foot degree Fahrenheit

[BtuIT /(h ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter kelvin

[W/(m2 ? K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.678 263 E+00

British thermal unitth per hour square foot degree Fahrenheit

[Btuth /(h ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter kelvin

[W/(m2 ? K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.674 466 E+00

British thermal unitIT per second square foot degree Fahrenheit

[BtuIT /(s ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter kelvin

[W/(m2 ? K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.044 175 E+04

British thermal unitth per second square foot degree Fahrenheit

[Btuth /(s ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter kelvin

[W/(m2 ? K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.042 808 E+04

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Density of Heat

British thermal unitIT per square foot

(BtuIT /ft2

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per square meter (J/m2).................. 1.135 653 E+04

British thermal unitth per square foot

(Btuth /ft2

). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per square meter (J/m2).................. 1.134 893 E+04

calorieth per square centimeter (calth /cm2

) . . . . . . . . . . joule per square meter (J/m2).................. 4.184 E+04

langley (calth /cm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per square meter (J/m2).................. 4.184 E+04

Density of Heat Flow Rate

British thermal unitIT per square foot hour

[BtuIT /(ft2 ? h)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2

)................. 3.154 591 E+00

British thermal unitth per square foot hour

[Btuth /(ft2 ? h)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2

)................. 3.152 481 E+00

British thermal unitth per square foot minute

[Btuth /(ft2 ? min)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2

)................. 1.891 489 E+02

British thermal unitIT per square foot second

[BtuIT /(ft2 ? s)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2

)................. 1.135 653 E+04

British thermal unitth per square foot second

[Btuth /(ft2 ? s)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2)................. 1.134 893 E+04

British thermal unitth per square inch second

[Btuth /(in2 ? s)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2)................. 1.634 246 E+06

calorieth per square centimeter minute

[calth /(cm2 ? min)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2)................. 6.973 333 E+02

calorieth per square centimeter second

[calth /(cm2 ? s)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per square meter (W/m2

)................. 4.184 E+04

Fuel Consumption

gallon (U.S.) per horsepower hour

[gal/(hp ? h)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter per joule (m3/J) . . . . . . . . . . . . . . . . . . . 1.410 089 E209

gallon (U.S.) per horsepower hour

[gal/(hp ? h)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . liter per joule (L/J) ............................ 1.410 089 E206

mile per gallon (U.S.) (mpg) (mi/gal)............... meter per cubic meter (m/m3)................. 4.251 437 E+05

mile per gallon (U.S.) (mpg) (mi/gal). . . . . . . . . . . . . . . kilometer per liter (km/L) ..................... 4.251 437 E201

mile per gallon (U.S.) (mpg) (mi/gal)22 ............. liter per 100 kilometer (L/100 km) . . . . . . . .divide 235.215 by number

of miles per gallon

pound per horsepower hour [lb/(hp ? h)] . . . . . . . . . . . . kilogram per joule (kg/J) ...................... 1.689 659 E207

Heat Capacity and Entropy

British thermal unitIT per degree Fahrenheit

(BtuIT /8F). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kelvin (J/k) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.899 101 E+03

British thermal unitth per degree Fahrenheit

(Btuth /8F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kelvin (J/k) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.897 830 E+03

British thermal unitIT per degree Rankine

(BtuIT /8R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kelvin (J/k) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.899 101 E+03

British thermal unitth per degree Rankine

(Btuth /8R). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kelvin (J/k) . . . . . . . . . . . . . . . . . . . . . . . . . . 1.897 830 E+03

Heat Flow Rate

British thermal unitIT per hour (BtuIT /h) . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.930 711 E201

British thermal unitth per hour (Btuth /h) . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.928 751 E201

British thermal unitth per minute (Btuth /min) . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.757 250 E+01

British thermal unitIT per second (BtuIT /s). . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.055 056 E+03

British thermal unitth per second (Btuth /s) . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.054 350 E+03

calorieth per minute (calth /min) . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.973 333 E202

calorieth per second (calth /s) . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.184 E+00

kilocalorieth per minute (kcalth /min) . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.973 333 E+01

kilocalorieth per second (kcalth /s) . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.184 E+03

ton of refrigeration (12 000 BtuIT /h). . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.516 853 E+03

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Specific Heat Capacity and Specific Entropy

British thermal unitIT per pound degree Fahrenheit

[BtuIT /(lb ? 8F)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)]. . . . . . . . . . 4.1868 E+03

British thermal unitth per pound degree Fahrenheit

[Btuth /(lb ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)]. . . . . . . . . . 4.184 E+03

British thermal unitIT per pound degree Rankine

[BtuIT /(lb ? 8R)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)]. . . . . . . . . . 4.1868 E+03

British thermal unitth per pound degree Rankine

[Btuth /(lb ? 8R)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)]. . . . . . . . . . 4.184 E+03

calorieIT per gram degree Celsius

[calIT /(g ? 8C)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)]. . . . . . . . . . 4.1868 E+03

calorieth per gram degree Celsius

[calth /(g ? 8C)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)]. . . . . . . . . . 4.184 E+03

calorieIT per gram kelvin [calIT /(g ? K)] . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)]. . . . . . . . . . 4.1868 E+03

calorieth per gram kelvin [calth /(g ? K)] . . . . . . . . . . . . . joule per kilogram kelvin [J/(kg ? K)]. . . . . . . . . . 4.184 E+03

Thermal Conductivity

Britsh thermal unitIT foot per hour square foot degree Fahrenheit

[BtuIT ? ft/(h ? ft2 ? 8F)].. . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m ? K)]. . . . . . . . . . . . . 1.730 735 E+00

Britsh thermal unitth foot per hour square foot degree Fahrenheit

[Btuth ? ft/(h ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m ? K)]. . . . . . . . . . . . . 1.729 577 E+00

Britsh thermal unitIT inch per hour square foot degree Fahrenheit

[BtuIT ? in/(h ? ft2 ? 8F)].. . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m ? K)]. . . . . . . . . . . . . 1.442 279 E201

Britsh thermal unitth inch per hour square foot degree Fahrenheit

[Btuth ? in/(h ? ft2 ? 8F)]. . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m ? K)]. . . . . . . . . . . . . 1.441 314 E201

Britsh thermal unitIT inch per second square foot degree Fahrenheit

[BtuIT ? in/(s ? ft2 ? 8F)]. . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m ? K)]. . . . . . . . . . . . . 5.192 204 E+02

Britsh thermal unitth inch per second square foot degree Fahrenheit

[Btuth ? in/(s ? ft2 ? 8F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m ? K)]. . . . . . . . . . . . . 5.188 732 E+02

calorieth per centimeter second degree Celsius

[calth /(cm ? s ? 8C)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m ? K)]. . . . . . . . . . . . . 4.184 E+02

Thermal Diffusivity

square foot per hour (ft2/h) . . . . . . . . . . . . . . . . . . . . . . . . . square meter per second (m2/s). . . . . . . . . . . . . . . . 2.580 64 E205

Thermal Insulance

clo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter kelvin per watt (m2 ? K/W) . . . . . . 1.55 E201

degree Fahrenheit hour square foot per British thermal unitIT

(8F ? h ? ft2/BtuIT). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter kelvin per watt (m2 ? K/W) . . . . . . 1.761 102 E201

degree Fahrenheit hour square foot per British thermal unitth

(8F ? h ? ft2/Btuth) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter kelvin per watt (m2 ? K/W) . . . . . . 1.762 280 E201

Thermal Resistance

degree Fahrenheit hour per British thermal unitIT

(8F ? h/BtuIT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin per watt (K/W) . . . . . . . . . . . . . . . . . . . . . . . . . 1.895 634 E+00

degree Fahrenheit hour per British thermal unitth

(8F ? h/Btuth) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin per watt (K /W). . . . . . . . . . . . . . . . . . . . . . . . . 1.896 903 E+00

degree Fahrenheit second per British thermal unitIT

(8F ? s/BtuIT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin per watt (K /W). . . . . . . . . . . . . . . . . . . . . . . . . 5.265 651 E204

degree Fahrenheit second per British thermal unitth

(8F ? s/Btuth). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin per watt (K/W) . . . . . . . . . . . . . . . . . . . . . . . . . 5.269 175 E204

Thermal Resistivity

degree Fahrenheit hour square foot per British thermal unitIT inch

[8F ? h ? ft2/(BtuIT ? in)] .......................... meter kelvin per watt (m ? K /W) . . . . . . . . . . . . . . 6.933 472 E+00

degree Fahrenheit hour square foot per British thermal unitth inch

[8F ? h ? ft2

/(Btuth ? in)]........................... meter kelvin per watt (m ? K/W) . . . . . . . . . . . . . . 6.938 112 E+04

61
Guide for the Use of the International System of Units (SI)

To convert from to Multiply by

LENGTH

ångstro ̈m (Å). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m)...................................... 1.0 E210

ångstro ̈m (Å). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nanometer (nm)................................ 1.0 E201

astronomical unit (AU).............................. meter (m)...................................... 1.495 979 E+11

chain (based on U.S. survey foot) (ch)9 ............. meter (m)...................................... 2.011 684 E+01

fathom (based on U.S. survey foot)9 ................ meter (m)...................................... 1.828 804 E+00

fermi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m)...................................... 1.0 E215

fermi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . femtometer (fm) ............................... 1.0 E+00

foot (ft)............................................. meter (m)...................................... 3.048 E201

foot (U.S. survey) (ft)9 .............................. meter (m)...................................... 3.048 006 E201

inch (in) ............................................ meter (m)...................................... 2.54 E202

inch (in) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . centimeter (cm)................................ 2.54 E+00

kayser (K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reciprocal meter (m21

) ........................ 1 E+02

light year (l.y.)19 .................................... meter (m)...................................... 9.460 73 E+15

microinch ........................................... meter (m)...................................... 2.54 E208

microinch ........................................... micrometer (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.54 E202

micron (m) .......................................... meter (m)...................................... 1.0 E206

micron (m) .......................................... micrometer (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+00

mil (0.001 in)....................................... meter (m)...................................... 2.54 E205

mil (0.001 in)....................................... millimeter (mm) ............................... 2.54 E202

mile (mi)............................................ meter (m)...................................... 1.609 344 E+03

mile (mi). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilometer (km)................................. 1.609 344 E+00

mile (based on U.S. survey foot) (mi)9 .............. meter (m)...................................... 1.609 347 E+03

mile (based on U.S. survey foot) (mi)9 . . . . . . . . . . . . . . kilometer (km)................................. 1.609 347 E+00

mile, nautical 21 ..................................... meter (m)...................................... 1.852 E+03

parsec (pc) .......................................... meter (m)...................................... 3.085 678 E+16

pica (computer) (1/6 in)............................ meter (m)...................................... 4.233 333 E203

pica (computer) (1/6 in)............................ millimeter (mm) ............................... 4.233 333 E+00

pica (printer’s) ...................................... meter (m)...................................... 4.217 518 E203

pica (printer’s) ...................................... millimeter (mm) ............................... 4.217 518 E+00

point (computer) (1/72 in).......................... meter (m)...................................... 3.527 778 E204

point (computer) (1/72 in).......................... millimeter (mm) ............................... 3.527 778 E201

point (printer’s) ..................................... meter (m)...................................... 3.514 598 E204

point (printer’s) ..................................... millimeter (mm) ............................... 3.514 598 E201

rod (based on U.S. survey foot) (rd)9................ meter (m)...................................... 5.029 210 E+00

yard (yd)............................................ meter (m)...................................... 9.144 E201

LIGHT

candela per square inch (cd/in2) . . . . . . . . . . . . . . . . . . . . candela per square meter (cd/m2).............. 1.550 003 E+03

footcandle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lux (lx) ........................................ 1.076 391 E+01

footlambert. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . candela per square meter (cd/m2).............. 3.426 259 E+00

lambert18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . candela per square meter (cd/m2

).............. 3.183 099 E+03

lumen per square foot (lm/ft2) . . . . . . . . . . . . . . . . . . . . . . lux (lx) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.076 391 E+01

phot (ph) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lux (lx) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+04

stilb (sb). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . candela per square meter (cd/m2).............. 1.0 E+04

MASS and MOMENT OF INERTIA

carat, metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 2.0 E204

carat, metric ........................................ gram (g) ....................................... 2.0 E201

grain (gr). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 6.479 891 E205

grain (gr)............................................ milligram (mg) ................................ 6.479 891 E+01

hundredweight (long, 112 lb) . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 5.080 235 E+01

hundredweight (short, 100 lb). . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 4.535 924 E+01

62
Guide for the Use of the International System of Units (SI)

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kilogram-force second squared per meter

(kgf ? s

2

/m). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 9.806 65 E+00

ounce (avoirdupois) (oz). . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 2.834 952 E202

ounce (avoirdupois) (oz)............................ gram (g) ....................................... 2.834 952 E+01

ounce (troy or apothecary) (oz). . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 3.110 348 E202

ounce (troy or apothecary) (oz)..................... gram (g) ....................................... 3.110 348 E+01

pennyweight (dwt). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 1.555 174 E203

pennyweight (dwt).................................. gram (g) ....................................... 1.555 174 E+00

pound (avoirdupois) (lb)23. . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 4.535 924 E201

pound (troy or apothecary) (lb) . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 3.732 417 E201

pound foot squared (lb ? ft2

). . . . . . . . . . . . . . . . . . . . . . . . . kilogram meter squared (kg ? m2).............. 4.214 011 E202

pound inch squared (lb ? in2) . . . . . . . . . . . . . . . . . . . . . . . . kilogram meter squared (kg ? m2).............. 2.926 397 E204

slug (slug). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 1.459 390 E+01

ton, assay (AT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 2.916 667 E202

ton, assay (AT) ...................................... gram (g) ....................................... 2.916 667 E+01

ton, long (2240 lb) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 1.016 047 E+03

ton, metric (t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 1.0 E+03

tonne (called ‘‘metric ton’’ in U.S.) (t). . . . . . . . . . . . . kilogram (kg) .................................. 1.0 E+03

ton, short (2000 lb) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram (kg) .................................. 9.071 847 E+02

MASS DENSITY (see MASS DIVIDED BY VOLUME)

MASS DIVIDED BY AREA

ounce (avoirdupois) per square foot (oz/ft2). . . . . . . . . kilogram per square meter (kg/m2)............ 3.051 517 E201

ounce (avoirdupois) per square inch (oz/in2) . . . . . . . . kilogram per square meter (kg/m2)............ 4.394 185 E+01

ounce (avoirdupois) per square yard (oz/yd2

). . . . . . . . kilogram per square meter (kg/m2)............ 3.390 575 E202

pound per square foot (lb/ft2

) . . . . . . . . . . . . . . . . . . . . . . . kilogram per square meter (kg/m2)............ 4.882 428 E+00

pound per square inch (not pound force)

(lb/in2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per square meter (kg/m2)............ 7.030 696 E+02

MASS DIVIDED BY CAPACITY (see MASS DIVIDED BY VOLUME)

MASS DIVIDED BY LENGTH

denier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) .................... 1.111 111 E207

denier ............................................... gram per meter (g/m) ......................... 1.111 111 E204

pound per foot (lb/ft) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) .................... 1.488 164 E+00

pound per inch (lb/in). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) .................... 1.785 797 E+01

pound per yard (lb/yd) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) .................... 4.960 546 E201

tex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per meter (kg/m) .................... 1.0 E206

MASS DIVIDED BY TIME (includes FLOW)

pound per hour (lb/h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per second (kg/s) .................... 1.259 979 E204

pound per minute (lb/min). . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per second (kg/s) .................... 7.559 873 E203

pound per second (lb/s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per second (kg/s) .................... 4.535 924 E201

ton, short, per hour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per second (kg/s) .................... 2.519 958 E201

MASS DIVIDED BY VOLUME (includes MASS DENSITY and MASS CONCENTRATION)

grain per gallon (U.S.) (gr/gal). . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 1.711 806 E202

grain per gallon (U.S.) (gr/gal)...................... milligram per liter (mg/L)..................... 1.711 806 E+01

gram per cubic centimeter (g/cm3) . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 1.0 E+03

ounce (avoirdupois) per cubic inch (oz/in3

) . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 1.729 994 E+03

ounce (avoirdupois) per gallon [Canadian and

U.K. (Imperial)] (oz/gal). . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3

) ............. 6.236 023 E+00

ounce (avoirdupois) per gallon [Canadian and

U.K. (Imperial)] (oz/gal)......................... gram per liter (g/L) ........................... 6.236 023 E+00

ounce (avoirdupois) per gallon (U.S.) (oz/gal) . . . . . . . kilogram per cubic meter (kg/m3) ............. 7.489 152 E+00

ounce (avoirdupois) per gallon (U.S.) (oz/gal) ....... gram per liter (g/L) ........................... 7.489 152 E+00

63
Guide for the Use of the International System of Units (SI)

To convert from to Multiply by

pound per cubic foot (lb/ft3) . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 1.601 846 E+01

pound per cubic inch (lb/in3

) . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 2.767 990 E+04

pound per cubic yard (lb/yd3

) . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3)............. 5.932 764 E201

pound per gallon [Canadian and

U.K. (Imperial)] (lb/gal) . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 9.977 637 E+01

pound per gallon [Canadian and

U.K. (Imperial)] (lb/gal) . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per liter (kg/L) ...................... 9.977 637 E202

pound per gallon (U.S.) (lb/gal). . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3

) ............. 1.198 264 E+02

pound per gallon (U.S.) (lb/gal). . . . . . . . . . . . . . . . . . . . . kilogram per liter (kg/L) ...................... 1.198 264 E201

slug per cubic foot (slug/ft3) . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 5.153 788 E+02

ton, long, per cubic yard . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3

) ............. 1.328 939 E+03

ton, short, per cubic yard . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per cubic meter (kg/m3) ............. 1.186 553 E+03

MOMENT OF FORCE or TORQUE

dyne centimeter (dyn ? cm) . . . . . . . . . . . . . . . . . . . . . . . . . newton meter (N ? m). . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E207

kilogram-force meter (kgf ? m). . . . . . . . . . . . . . . . . . . . . . newton meter (N ? m). . . . . . . . . . . . . . . . . . . . . . . . . . 9.806 65 E+00

ounce (avoirdupois)-force inch (ozf ? in) . . . . . . . . . . . . newton meter (N ? m). . . . . . . . . . . . . . . . . . . . . . . . . . 7.061 552 E203

ounce (avoirdupois)-force inch (ozf ? in) . . . . . . . . . . . . millinewton meter (mN ? m) . . . . . . . . . . . . . . . . . . . 7.061 552 E+00

pound-force foot (lbf ? ft) . . . . . . . . . . . . . . . . . . . . . . . . . . . newton meter (N ? m). . . . . . . . . . . . . . . . . . . . . . . . . . 1.355 818 E+00

pound-force inch (lbf ? in). . . . . . . . . . . . . . . . . . . . . . . . . . . newton meter (N ? m). . . . . . . . . . . . . . . . . . . . . . . . . . 1.129 848 E201

MOMENT OF FORCE or TORQUE, DIVIDED BY LENGTH

pound-force foot per inch (lbf ? ft/in) . . . . . . . . . . . . . . . newton meter per meter (N ? m/m) . . . . . . . . . . . . 5.337 866 E+01

pound-force inch per inch (lbf ? in/in) . . . . . . . . . . . . . . newton meter per meter (N ? m/m) . . . . . . . . . . . . 4.448 222 E+00

PERMEABILITY

darcy15.............................................. meter squared (m2)............................ 9.869 233 E213

perm (0 8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per pascal second square meter

[kg/(Pa ? s ? m2)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.721 35 E211

perm (23 8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per pascal second square meter

[kg/(Pa ? s ? m2

)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.745 25 E211

perm inch (0 8C). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per pascal second meter

[kg/(Pa ? s ? m)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.453 22 E212

perm inch (23 8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilogram per pascal second meter

[kg/(Pa ? s ? m)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.459 29 E212

POWER

erg per second (erg/s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E207

foot pound-force per hour (ft ? lbf/h). . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.766 161 E204

foot pound-force per minute (ft ? lbf/min) . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.259 697 E202

foot pound-force per second (ft ? lbf/s) . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.355 818 E+00

horsepower (550 ft ? lbf/s) . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.456 999 E+02

horsepower (boiler) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.809 50 E+03

horsepower (electric). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.46 E+02

horsepower (metric). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.354 988 E+02

horsepower (U.K.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4570 E+02

horsepower (water). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . watt (W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.460 43 E+02

PRESSURE or STRESS (FORCE DIVIDED BY AREA)

atmosphere, standard (atm) ......................... pascal (Pa)..................................... 1.013 25 E+05

atmosphere, standard (atm) . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 1.013 25 E+02

atmosphere, technical (at)10......................... pascal (Pa)..................................... 9.806 65 E+04

atmosphere, technical (at)10. . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 9.806 65 E+01

bar (bar)............................................. pascal (Pa)..................................... 1.0 E+05

bar (bar). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 1.0 E+02

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centimeter of mercury (0 8C)13 ...................... pascal (Pa)..................................... 1.333 22 E+03

centimeter of mercury (0 8C)13 . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 1.333 22 E+00

centimeter of mercury, conventional (cmHg)13 ....... pascal (Pa)..................................... 1.333 224 E+03

centimeter of mercury, conventional (cmHg)13 . . . . . . . kilopascal (kPa)................................ 1.333 224 E+00

centimeter of water (4 8C)13 ......................... pascal (Pa)..................................... 9.806 38 E+01

centimeter of water, conventional (cmH2O)13 ....... pascal (Pa)..................................... 9.806 65 E+01

dyne per square centimeter (dyn/cm2) .............. pascal (Pa)..................................... 1.0 E201

foot of mercury, conventional (ftHg)13 .............. pascal (Pa)..................................... 4.063 666 E+04

foot of mercury, conventional (ftHg)13 . . . . . . . . . . . . . . kilopascal (kPa)................................ 4.063 666 E+01

foot of water (39.2 8F)13 ............................ pascal (Pa)..................................... 2.988 98 E+03

foot of water (39.2 8F)13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 2.988 98 E+00

foot of water, conventional (ftH2O)13 ............... pascal (Pa)..................................... 2.989 067 E+03

foot of water, conventional (ftH2O)13 . . . . . . . . . . . . . . . kilopascal (kPa)................................ 2.989 067 E+00

gram-force per square centimeter (gf/cm2) ......... pascal (Pa)..................................... 9.806 65 E+01

inch of mercury (32 8F)13 ........................... pascal (Pa)..................................... 3.386 38 E+03

inch of mercury (32 8F)13 . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 3.386 38 E+00

inch of mercury (60 8F)13 ........................... pascal (Pa)..................................... 3.376 85 E+03

inch of mercury (60 8F)13 . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 3.376 85 E+00

inch of mercury, conventional (inHg)13 ............. pascal (Pa)..................................... 3.386 389 E+03

inch of mercury, conventional (inHg)13 . . . . . . . . . . . . . kilopascal (kPa)................................ 3.386 389 E+00

inch of water (39.2 8F)13 ............................ pascal (Pa)..................................... 2.490 82 E+02

inch of water (60 8F)13 .............................. pascal (Pa)..................................... 2.4884 E+02

inch of water, conventional (inH2O)13 .............. pascal (Pa)..................................... 2.490 889 E+02

kilogram-force per square

centimeter (kgf/cm2

) ............................. pascal (Pa)..................................... 9.806 65 E+04

kilogram-force per square

centimeter (kgf/cm2

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 9.806 65 E+01

kilogram-force per square meter (kgf/m2)........... pascal (Pa)..................................... 9.806 65 E+00

kilogram-force per square

millimeter (kgf/mm2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa)..................................... 9.806 65 E+06

kilogram-force per square

millimeter (kgf/mm2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . megapascal (MPa) ............................. 9.806 65 E+00

kip per square inch (ksi) (kip/in2)................... pascal (Pa)..................................... 6.894 757 E+06

kip per square inch (ksi) (kip/in2

). . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 6.894 757 E+03

millibar (mbar)...................................... pascal (Pa)..................................... 1.0 E+02

millibar (mbar). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa)................................ 1.0 E201

millimeter of mercury, conventional (mmHg)13 ....... pascal (Pa)..................................... 1.333 224 E+02

millimeter of water, conventional (mmH2O)13 ........ pascal (Pa)..................................... 9.806 65 E+00

poundal per square foot ............................. pascal (Pa)..................................... 1.488 164 E+00

pound-force per square foot (lbf/ft2) ................ pascal (Pa)..................................... 4.788 026 E+01

pound-force per square inch (psi) (lbf/in2

).......... pascal (Pa)..................................... 6.894 757 E+03

pound-force per square inch (psi) (lbf/in2) . . . . . . . . . . kilopascal (kPa)................................ 6.894 757 E+00

psi (pound-force per square inch) (lbf/in2) ......... pascal (Pa)..................................... 6.894 757 E+03

psi (pound-force per square inch) (lbf/in2) . . . . . . . . . kilopascal (kPa)................................ 6.894 757 E+00

torr (Torr) ........................................... pascal (Pa)..................................... 1.333 224 E+02

RADIOLOGY

curie (Ci) ........................................... becquerel (Bq)................................. 3.7 E+10

rad (absorbed dose) (rad) . . . . . . . . . . . . . . . . . . . . . . . . . . . gray (Gy) ...................................... 1.0 E202

rem (rem) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sievert (Sv) .................................... 1.0 E202

roentgen (R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb per kilogram (C/kg).................. 2.58 E204

SPEED (see VELOCITY)

STRESS (see PRESSURE)

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TEMPERATURE

degree Celsius (8C). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T/ K = t/ 8C + 273.15

degree centigrade16 ................................. degree Celsius (8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .t/ 8C ≈ t /deg. cent.

degree Fahrenheit (8F). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . degree Celsius (8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . t/ 8C=(t/ 8F 2 32)/1.8

degree Fahrenheit (8F). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T/ K=(t/ 8F + 459.67)/1.8

degree Rankine (8R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T/ K=(T/ 8R)/1.8

kelvin (K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . degree Celsius (8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . t /8C = T/ K 2 273.15

TEMPERATURE INTERVAL

degree Celsius (8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+00

degree centigrade16 ................................. degree Celsius (8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E+00

degree Fahrenheit (8F). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . degree Celsius (8C) . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.555 556 E201

degree Fahrenheit (8F). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.555 556 E201

degree Rankine (8R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kelvin (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.555 556 E201

TIME

day (d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s)..................................... 8.64 E+04

day (sidereal)........................................ second (s)..................................... 8.616 409 E+04

hour (h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . second (s)..................................... 3.6 E+03

hour (sidereal) ...................................... second (s)..................................... 3.590 170 E+03

minute (min) ....................................... second (s)..................................... 6.0 E+01

minute (sidereal) .................................... second (s)..................................... 5.983 617 E+01

second (sidereal) .................................... second (s)..................................... 9.972 696 E201

shake................................................ second (s)..................................... 1.0 E208

shake................................................ nanosecond (ns) .............................. 1.0 E+01

year (365 days)...................................... second (s)..................................... 3.1536 E+07

year (sidereal)....................................... second (s)..................................... 3.155 815 E+07

year (tropical)....................................... second (s)..................................... 3.155 693 E+07

TORQUE (see MOMENT OF FORCE)

VELOCITY (includes SPEED)

foot per hour (ft/h). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) ....................... 8.466 667 E205

foot per minute (ft/min)............................ meter per second (m/s) ....................... 5.08 E203

foot per second (ft/s) ............................... meter per second (m/s) ....................... 3.048 E201

inch per second (in/s) .............................. meter per second (m/s) ....................... 2.54 E202

kilometer per hour (km/h) . . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) ....................... 2.777 778 E201

knot (nautical mile per hour)........................ meter per second (m/s) ....................... 5.144 444 E201

mile per hour (mi/h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter per second (m/s) ....................... 4.4704 E201

mile per hour (mi/h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilometer per hour (km/h).................... 1.609 344 E+00

mile per minute (mi/min)........................... meter per second (m/s) ....................... 2.682 24 E+01

mile per second (mi/s) .............................. meter per second (m/s) ....................... 1.609 344 E+03

revolution per minute (rpm) (r/min)................. radian per second (rad/s) ..................... 1.047 198 E201

rpm (revolution per minute) (r/min)................. radian per second (rad/s) ..................... 1.047 198 E201

VISCOSITY, DYNAMIC

centipoise (cP)...................................... pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E203

poise (P). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 E201

poundal second per square foot ..................... pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . 1.488 164 E+00

pound-force second per square foot

(lbf ? s/ft2

)........................................ pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . 4.788 026 E+01

pound-force second per square inch

(lbf ? s/in2) ....................................... pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . 6.894 757 E+03

pound per foot hour [lb/(ft ? h)] . . . . . . . . . . . . . . . . . . . . pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . 4.133 789 E204

pound per foot second [lb/(ft ? s)] . . . . . . . . . . . . . . . . . . pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . 1.488 164 E+00

rhe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reciprocal pascal second [(Pa ? s)21

].......... 1.0 E+01

slug per foot second [slug/(ft ? s)] . . . . . . . . . . . . . . . . . . pascal second (Pa ? s) . . . . . . . . . . . . . . . . . . . . . . . . . 4.788 026 E+01

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VISCOSITY, KINEMATIC

centistokes (cSt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter squared per second (m2/s). . . . . . . . . . . . . . . 1.0 E206

square foot per second (ft2

/s) . . . . . . . . . . . . . . . . . . . . . . . meter squared per second (m2/s). . . . . . . . . . . . . . . 9.290 304 E202

stokes (St) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter squared per second (m2

/s). . . . . . . . . . . . . . . 1.0 E204

VOLUME (includes CAPACITY)

acre-foot (based on U.S. survey foot)9 .............. cubic meter (m3)............................... 1.233 489 E+03

barrel [for petroleum, 42 gallons (U.S.)](bbl) ....... cubic meter (m3)............................... 1.589 873 E201

barrel [for petroleum, 42 gallons (U.S.)](bbl) ....... liter (L) ........................................ 1.589 873 E+02

bushel (U.S.) (bu)................................... cubic meter (m3

)............................... 3.523 907 E202

bushel (U.S.) (bu)................................... liter (L) ........................................ 3.523 907 E+01

cord (128 ft3

)....................................... cubic meter (m3)............................... 3.624 556 E+00

cubic foot (ft3

)...................................... cubic meter (m3)............................... 2.831 685 E202

cubic inch (in3 )

14................................... cubic meter (m3

)............................... 1.638 706 E205

cubic mile (mi3)..................................... cubic meter (m3)............................... 4.168 182 E+09

cubic yard (yd3)..................................... cubic meter (m3)............................... 7.645 549 E201

cup (U.S.) .......................................... cubic meter (m3)............................... 2.365 882 E204

cup (U.S.) .......................................... liter (L) ........................................ 2.365 882 E201

cup (U.S.) .......................................... milliliter (mL) ................................. 2.365 882 E+02

fluid ounce (U.S.) (fl oz) ........................... cubic meter (m3)............................... 2.957 353 E205

fluid ounce (U.S.) (fl oz) ........................... milliliter (mL) ................................. 2.957 353 E+01

gallon [Canadian and U.K. (Imperial)] (gal) ........ cubic meter (m3

)............................... 4.546 09 E203

gallon [Canadian and U.K. (Imperial)] (gal) ........ liter (L) ........................................ 4.546 09 E+00

gallon (U.S.) (gal)................................... cubic meter (m3)............................... 3.785 412 E203

gallon (U.S.) (gal)................................... liter (L) ........................................ 3.785 412 E+00

gill [Canadian and U.K. (Imperial)] (gi) ............ cubic meter (m3)............................... 1.420 653 E204

gill [Canadian and U.K. (Imperial)] (gi) ............ liter (L) ........................................ 1.420 653 E201

gill (U.S.) (gi)....................................... cubic meter (m3

)............................... 1.182 941 E204

gill (U.S.) (gi)....................................... liter (L) ........................................ 1.182 941 E201

liter (L)20 ........................................... cubic meter (m3)............................... 1.0 E203

ounce [Canadian and U.K. fluid (Imperial)]

(fl oz) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cubic meter (m3

)............................... 2.841 306 E205

ounce [Canadian and U.K. fluid (Imperial)]

(fl oz) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . milliliter (mL) ................................. 2.841 306 E+01

ounce (U.S. fluid) (fl oz) ........................... cubic meter (m3

)............................... 2.957 353 E205

ounce (U.S. fluid) (fl oz) ........................... milliliter (mL) ................................. 2.957 353 E+01

peck (U.S.) (pk) .................................... cubic meter (m3)............................... 8.809 768 E203

peck (U.S.) (pk) .................................... liter (L) ........................................ 8.809 768 E+00

pint (U.S. dry) (dry pt).............................. cubic meter (m3)............................... 5.506 105 E204

pint (U.S. dry) (dry pt).............................. liter (L) ........................................ 5.506 105 E201

pint (U.S. liquid) (liq pt) ............................ cubic meter (m3

)............................... 4.731 765 E204

pint (U.S. liquid) (liq pt) ............................ liter (L) ........................................ 4.731 765 E201

quart (U.S. dry) (dry qt) ............................ cubic meter (m3

)............................... 1.101 221 E203

quart (U.S. dry) (dry qt) ............................ liter (L) ........................................ 1.101 221 E+00

quart (U.S. liquid) (liq qt)........................... cubic meter (m3

)............................... 9.463 529 E204

quart (U.S. liquid) (liq qt)........................... liter (L) ........................................ 9.463 529 E201

stere (st)............................................. cubic meter (m3

)............................... 1.0 E+00

tablespoon........................................... cubic meter (m3)............................... 1.478 676 E205

tablespoon........................................... milliliter (mL) ................................. 1.478 676 E+01

teaspoon ............................................ cubic meter (m3)............................... 4.928 922 E206

teaspoon ............................................ milliliter (mL) ................................. 4.928 922 E+00

ton, register ......................................... cubic meter (m3

)............................... 2.831 685 E+00

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VOLUME DIVIDED BY TIME (includes FLOW)

cubic foot per minute (ft3/min) ..................... cubic meter per second (m3/s) . . . . . . . . . . . . . . . . . 4.719 474 E204

cubic foot per minute (ft3

/min) ..................... liter per second (L/s) .......................... 4.719 474 E201

cubic foot per second (ft3

/s) . . . . . . . . . . . . . . . . . . . . . . . . cubic meter per second (m3/s) . . . . . . . . . . . . . . . . . 2.831 685 E202

cubic inch per minute (in3

/min)..................... cubic meter per second (m3/s) . . . . . . . . . . . . . . . . . 2.731 177 E207

cubic yard per minute (yd3

/min) .................... cubic meter per second (m3/s) . . . . . . . . . . . . . . . . . 1.274 258 E202

gallon (U.S.) per day (gal/d) ........................ cubic meter per second (m3/s) . . . . . . . . . . . . . . . . . 4.381 264 E208

gallon (U.S.) per day (gal/d) ........................ liter per second (L/s) .......................... 4.381 264 E205

gallon (U.S.) per minute (gpm) (gal/min)........... cubic meter per second (m3

/s) . . . . . . . . . . . . . . . . . 6.309 020 E205

gallon (U.S.) per minute (gpm) (gal/min)........... liter per second (L/s).......................... 6.309 020 E202

WORK (see ENERGY)

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Guide for the Use of the International System of Units (SI)

Appendix C. Comments on the References of Appendix D — Bibliography

C.1 Official interpretation of the SI for the United States: 55 FR 52242-52245

The official interpretation of the International System of Units for the United States, which is

the responsibility of the United States Department of Commerce, is stated in the Federal Register,

Vol. 55, No. 245, p. 52242, December 20, 1990 [15]. This Federal Register Notice is reprinted in

NIST Special Publication 814 [1], together with the Federal Register Notice that states the metric

conversion policy for Federal agencies [16] and the Executive Order on metric usage in Federal

Government programs [17].

C.2 Defining document for the SI: BIPM SI Brochure

The defining document for the International System of Units is the Brochure published by the

International Bureau of Weights and Measures (BIPM) in French, followed by an English translation

[2]. This document is revised from time to time in accordance with the decisions of the General

Conference on Weights and Measures (CGPM).

C.3 United States version of defining document for the SI: NIST SP 330

The United States edition of the English translation in the BIPM SI Brochure (see Sec. C.2) is

published by the National Institute of Standards and Technology as NIST Special Publication 330 [3];

it differs from the translation in the BIPM publication in the following details:

— the dot is used as the decimal marker, in keeping with recommended United States practice (see

Secs. C.1 and C.7);

— the spelling of English-language words — for example, ‘‘meter,’’ ‘‘liter,’’ and ‘‘deka’’ are

used instead of ‘‘metre,’’ ‘‘litre,’’ and ‘‘deca’’ — is in accordance with the United States

Government Printing Office Style Manual [4], which follows Webster’s Third New International

Dictionary rather than the Oxford Dictionary used in many English-speaking countries. This

spelling also reflects recommended United States practice (see Secs. C.1 and C.7);

— editorial notes regarding the use of the SI in the United States are added;

— the index is moderately expanded.

Inasmuch as NIST Special Publication 330 is consistent with Ref. [1] (see Sec. C.1),

SP 330 is the authoritative source document on the SI for the purposes of this Guide .

C.4 ISO 1000

ISO 1000:1992 [5] is an international consensus standard published by the International

Organization for Standardization (ISO) to promote international uniformity in the technical interpretation of the actions of the CGPM as they are published by the BIPM in Ref. [2] (see Sec. C.2).

C.5 ISO 31

ISO 31-0:1992—ISO 31-13:1992 [6] constitute a series of international consensus standards

published by ISO to promote international uniformity in the practical use of the SI in various fields

of science and technology, and in particular to standardize the symbols for various quantities and the

units in which the values of these quantities are expressed. These standards are compatible with

Ref. [2] published by the BIPM (see Sec. C.2).

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C.6 IEC 27

IEC 27-1—IEC 27-4 [7] constitute a series of international consensus standards published by the International Electrotechnical Commission (IEC) to promote international

uniformity in the practical use of the SI in electrical technology, and in particular to

standardize the symbols for various quantities used in electrotechnology and the units in which the

values of these quantities are expressed. These IEC standards are also compatible with Ref. [2] published by the BIPM (see Sec. C.2), and they are coordinated with the ISO standards cited in Sec. C.5

(Ref. [6]). The IEC standards should be regarded as more authoritative than the corresponding ISO

standards only in connection with electrical technology.

C.7 ANSI/IEEE Std 268

ANSI/IEEE Std 268-1992 [8] is an American National Standard for Metric Practice; it is based

on the International System of Units as interpreted for use in the United States (see Secs. C.1 and

C.3). It has been approved by a consensus of providers and consumers that includes interests in

industrial organizations, government agencies, and scientific associations. This standard was developed by the Institute of Electrical and Electronics Engineers (IEEE), and approved as an American

National Standard by the American National Standards Institute (ANSI).27 ANSI/IEEE Std 268-1992

has been adopted for use by the United States Department of Defense (DoD) and serves as the basis

of Ref. [18] (see Sec. C.9); it is recommended as a comprehensive source of authoritative information

for the practical use of the SI in the United States. (Similar documents have also been developed by

other United States technical organizations; see Ref. [8], note 2.)

C.8 Federal Register notices

Important details concerning United States customary units of measurement and the interpretation of the SI for the United States are published from time to time in the Federal Register; these

notices have the status of official United States Government policy.

A Federal Register notice of July 1, 1959 [9] states the values of conversion factors to be used

in technical and scientific fields to obtain the values of the United States yard and pound from the SI

base units for length and mass, the meter and the kilogram. These conversion factors were adopted

on the basis of an agreement of English-speaking countries to reconcile small differences in the

values of the inch-pound units as they were used in different parts of the world. This action did not

affect the value of the yard or foot used for geodetic surveys in the United States. Thus, at that time,

it became necessary to recognize on a temporary basis a small difference between United States customary units of length for ‘‘international measure’’ and ‘‘survey measure.’’ A Federal Register

notice of July 19, 1988 [10] announced a tentative decision not to adopt the international foot of

0.3048 meters for surveying and mapping activities in the United States. A final decision to continue

the use of the survey foot indefinitely is pending the completion of an analysis of public comments

on the tentative decision; this decision will also be announced in the Federal register.

Even if a final decision affirms the continued use of the survey foot in surveying and mapping

services of the United States, it is significant to note that the Office of Charting and Geodetic

Services of the National Ocean Service in the National Oceanic and Atmospheric Administration

uses the meter exclusively for the North American Datum [11]. The North American Datum of 1983,

the most recent definition and adjustment of this information, was announced in a Federal Register

notice of June 14, 1989 [12].

27 The American National Standards Institute, Inc. (11 West 42nd Street, New York, NY 10036) is a private sector organization that serves as a standards coordinating body, accredits standards developers that follow procedures sanctioned by ANSI,

designates as American National Standards those standards submitted for and receiving approval, serves as the Untied States

Member Body of the International Organization for Standardization (ISO), and functions as the administrator of the United

States National Committee for the International Electrotechnical Commission (IEC).

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The definitions of the international foot and yard and the corresponding survey units are also

addressed in a Federal Register Notice published on February 3, 1975 [13].

A Federal Register notice of July 27, 1968 [14] provides a list of the common customary

measurement units used in commerce throughout the United States, together with the conversion

factors that link them with the meter and the kilogram.

A recent Federal Register notice concerning the SI [15] is a restatement of the interpretation of

the International System for use in the United States, and it updates the corresponding information

published in earlier notices.

A Federal Register notice of January 2, 1991 [16] removes the voluntary aspect of the conversion

to the SI for Federal agencies and provides policy direction to assist Federal agencies in their

transition to the use of the metric system of measurement.

A Federal Register notice of July 29, 1991 [17] provides Presidential authority and

direction for the use of the metric system of measurement by Federal departments and

agencies in their programs.

C.9 Federal Standard 376B

Federal Standard 376B [18] was developed by the Standards and Metric Practices

Subcommittee of the Metrication Operating Committee, which operates under the Interagency

Council on Metric Policy. Specified in the Federal Standardization Handbook and

issued by, and available from, the General Services Administration, Washington, DC, 20406, it is the

basic Federal standard that lists preferred metric units for use throughout the Federal Government.

It gives guidance on the selection of metric units required to comply with PL 94-168 (see Preface)

as amended by PL 100-418 (see Preface), and with Executive Order 12770 [17] (see Sec. C.8). The

basis of Fed. Std. 376B is ANSI/IEEE Std. 268-1992 [8] (see Sec. C.7).

C.10 1986 CODATA values of the fundamental constants

The set of self-consistent recommended values of the fundamental physical constants resulting

from the 1986 Committee on Data for Science and Technology (CODATA) least-squares adjustment

of the constants, the most up-to-date set currently available, is given in Ref. [20]. The next CODATA

adjustment of the constants is planned for completion in 1996; some of the considerations relevant to

that adjustment may be found in B. N. Taylor and E. R. Cohen, Recommended Values of the Fundamental Physical Constants: A Status Report, J. Res. Natl. Inst. Stand. Technol., Vol. 95, No. 5, p. 497

(September-October 1990).

C.11 Uncertainty in measurement

Reference [21] cites two publications that describe the evaluation and expression of uncertainty

in measurement based on the approach recommended by the CIPM in 1981 and which is currently

being adopted worldwide.

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Guide for the Use of the International System of Units (SI)

Appendix D. Bibliography

[1] Interpretation of the SI for the United States and Metric Conversion Policy for Federal

Agencies, Ed. by B. N. Taylor, Natl. Inst. Stand. Technol. Spec. Publ. 814 (U.S. Government

Printing Office, Washington, DC, October 1991).

[2] Le Syste`me International d’Unite ́s (SI), The International System of Units (SI), 6th Edition

(Bur. Intl. Poids et Mesures, Se`vres, France, 1991).

Note: This publication, which is commonly called the SI Brochure, consists of the

official French text followed by an English translation.

[3] The International System of Units (SI), Ed. by B. N. Taylor, Natl. Inst. Stand. Technol. Spec.

Publ. 330, 1991 Edition (U.S. Government Printing Office, Washington, DC, August 1991).

Note: This publication is the United States edition of the English translation in

Ref. [2].

[4] United States Government Printing Office Style Manual (U.S. Government Printing

Office, Washington, DC, 1984).

[5] SI units and recommendations for the use of their multiples and of certain other units, ISO

1000:1992 (International Organization for Standardization, Geneva, Switzerland, 1992).

Notes:

1 ISO publications are available in the United States from the sales department of

the American National Standards Institute (ANSI), 105-111 South State Street,

Hackensack, NJ 07601.

2 See the note at the end of Ref. [6].

[6] The following 14 Standards, which are cited in the text in the form [6: ISO 31- . . . ], are published by the International Organization for Standardization (ISO) Geneva, Switzerland:

Quantities and units — Part 0: General principles, ISO 31-0:1992.

Quantities and units — Part 1: Space and time, ISO 31-1:1992.

Quantities and units — Part 2: Periodic and related phenomena, ISO 31-2:1992.

Quantities and units — Part 3: Mechanics, ISO 31-3:1992.

Quantities and units — Part 4: Heat, ISO 31-4:1992.

Quantities and units — Part 5: Electricity and magnetism, ISO 31-5:1992.

Quantities and units — Part 6: Light and related electromagnetic radiations, ISO

31-6:1992.

Quantities and units — Part 7: Acoustics, ISO 31-7:1992.

Quantities and units — Part 8: Physical chemistry and molecular physics, ISO

31-8:1992.

Quantities and units — Part 9: Atomic and nuclear physics, ISO 31-9:1992.

Quantities and units — Part 10: Nuclear reactions and ionizing radiations, ISO

31-10:1992.

Quantities and units — Part 11: Mathematical signs and symbols for use in physical

sciences and technology, ISO 31-11:1992.

Quantities and units — Part 12: Characteristic numbers, ISO 31-12:1992.

Quantities and units — Part 13: Solid state physics, ISO 31-13:1992.

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Guide for the Use of the International System of Units (SI)

Note: ISO 31-0:1992 — ISO 31-13:1992 and ISO 1000:1992 are reprinted in the ISO

Standards Handbook Quantities and units (International Organization for

Standardization, Geneva, Switzerland, 1993). (The availability of ISO publications in the United States is discussed in Ref. [5], note 1.)

[7] The following four standards, which are cited in the text in the form [7: IEC 27- . . . ], are published by the International Electrotechnical Commission (IEC), Geneva, Switzerland.

Note: IEC publications are available in the United States from the American

National Standards Institute — see Ref. [5], note 1.

Letter symbols to be used in electrical technology, Part 1: General, IEC 27-1 (1991).

Letter symbols to be used in electrical technology, Part 2: Telecommunications and electronics,

IEC 27-2 (1972) [including IEC 27-2A (1975) and IEC 27-2B (1980), first and second supplements to IEC 27-2 (1972)].

Letter symbols to be used in electrical technology, Part 3: Logarithmic quantities and units,

IEC 27-3 (1989).

Letter symbols to be used in electrical technology, Part 4: Symbols for quantities to be used for

rotating electrical machines, IEC 27-4 (1985).

[8] American National Standard for Metric Practice, ANSI/IEEE Std 268-1992 (Institute of

Electrical and Electronics Engineers, New York, NY, October 1992).

Notes:

1 IEEE publications are available from the Institute of Electrical and Electronics

Engineers, Service Center, 445 Hoes Lane, P.O. Box 1331 Piscataway, NJ 08855-1331.

2 A number of similar standards for metric practice are published by United States

technical organizations. They include:

Standard Practice for Use of the International System of Units (SI) (The Modernized Metric System), E 380-93 (American Society for Testing and Materials,

Philadelphia, PA, 1993).

Note: ASTM publications are available from the Customer Service

Department, American Society for Testing and Materials, 1916

Race Street, Philadelphia, PA 19103.

Rules for SAE Use of SI (Metric) Units, SAE J916 MAY 91 (Society of

Automotive Engineers, Warrendale, PA, May 1991).

Note: SAE publications are available from the Society of Automotive

Engineers, 400 Commonwealth Drive, Warrendale, PA 15096.

3 The Canadian Standards Association, 178 Rexdale Boulevard, Rexdale (Toronto),

Ontario, Canada, M9W 1R3, publishes CAN/CSA-Z234.1-89, Canadian Metric

Practice Guide, a Canadian National Standard. It is similar in scope to ANSI/IEEE

Std 268-1992 (Ref. [8]).

4 A joint ASTM-IEEE effort is currently underway to consolidate ANSI/IEEE Std. 268-

1992 and ASTM E 380-93 into a single ANSI standard.

5 The application of the SI to physical chemistry is discussed in Quantities, Units and

Symbols in Physical Chemistry, prepared by I. Mills, T. Cvitasˇ, K. Homann, N. Kallay,

and K. Kuchitsu, Second Edition (International Union of Pure and Applied Chemistry,

Blackwell Scientific Publications, Oxford, 1993).

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Guide for the Use of the International System of Units (SI)

[9] Federal Register, Vol. 24, No. 128, p. 5348, July 1, 1959.

[10] Federal Register, Vol. 53, No. 138, p. 27213, July 19, 1988.

[11] Federal Register, Vol. 42, No. 57, p. 8847, March 24, 1977.

[12] Federal Register, Vol. 54, No. 113, p. 25318, June 14, 1989.

[13] Federal Register, Vol. 40, No. 23, p. 5954, February 3, 1975.

[14] Federal Register, Vol. 33, No. 146, p. 10755, July 27, 1968.

[15] Federal Register, Vol. 55, No. 245, p. 52242, December 20, 1990.

[16] Federal Register, Vol. 56, No. 1, p. 160, January 2, 1991.

[17] Federal Register, Vol. 56, No. 145, p. 35801, July 29, 1991.

[18] Preferred Metric Units for General Use by the Federal Government, Federal Standard 376B

(General Services Administration, Washington, DC, 1993).

[19] Radiation Quantities and Units, ICRU Report 33, 1980; and Quantities and Units in

Radiation Protection and Dosimetry, ICRU Report 51, 1993 (International Commission on

Radiation Units and Measurements, 7910 Woodmont Avenue, Bethesda, MD, 20814).

[20] E. R. Cohen and B. N. Taylor, The 1986 adjustment of the fundamental physical constants,

Rev. Mod. Phys., Vol. 59, No. 4, p. 1121 (October, 1987).

[21] The term combined standard uncertainty used in the footnotes to Table 7 of this Guide, and the

related terms expanded uncertainty and relative expanded uncertainty used in some of the

examples of Sec. 7.10.3, are discussed in ISO, Guide to the Expression of Uncertainty in

Measurement (International Organization for Standardization, Geneva, Switzerland, 1993); and

in B. N. Taylor and C. E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of

NIST Measurement Results, Natl. Inst. Stand. Technol. Spec. Publ. 1297, 1994 Edition (U.S.

Government Printing Office, Washington, DC, September 1994).

[22] A. J. Thor, Secretary, International Organization for Standardization (ISO) Technical

Committee (TC) 12, Quantities, units, symbols, conversion factors (private communication,

1993). ISO/TC 12 is responsible for the ISO International Standards cited in Refs. [5] and [6].

74