40334 Federal Register / Vol. 63, No. 144 /Tuesday, July 28, 1998 / Notices

DEPARTMENT OF COMMERCE

National Institute of Standards and

Technology

[Docket No. 980430113–8113–01]

Metric System of Measurement:

Interpretation of the International

System of Units for the United States

AGENCY: National Institute of Standards

and Technology, Commerce.

ACTION: Notice.

SUMMARY: This notice restates the

interpretation of the International

System of Units (SI) for the United

States by the Department of Commerce.

This interpretation was last published

by the Department of Commerce in the

Federal Register on December 20, 1990

(55 FR 52242–52245). Since the

publication of that notice, the

international bodies that are responsible

for the SI have made some changes to

it. It has therefore become necessary to

set forth a new interpretation of the SI

for the United States that reflects these

changes.

FOR FURTHER INFORMATION CONTACT: For

information regarding the International

System of Units, contact Dr. Barry N.

Taylor, Building 225, Room B161,

National Institute of Standards and

Technology, Gaithersburg, MD 20899–

0001, telephone number (301) 975–

4220. For information regarding the

Federal Government’s efforts to

coordinate the transition of the United

States to the International System of

Units, contact Mr. James B. McCracken,

Metric Program, Building 820, Room

306, National Institute of Standards and

Technology, Gaithersburg, MD 20899–

0001, telephone number (301) 975–

3690, email: metriclprg@nist.gov

SUPPLEMENTARY INFORMATION: Section

5164 of Public Law 100–418, the

Omnibus Trade and Competitiveness

Act of 1988, amended Public Law 94–

168, the Metric Conversion Act of 1975.

In particular, section 3 of the Metric

Conversion Act (codified as amended 15

U.S.C. 205b) reads as follows:

‘‘Sec. 3. It is therefore the declared

policy of the United States—

‘‘(1) to designate the metric system of

measurement as the preferred system of

weights and measures for United States

trade and commerce;

‘‘(2) to require that each Federal

agency, by a date certain and to the

extent economically feasible by the end

of the 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 to United States firms,

such as when foreign competitors are

producing competing products in nonmetric units;

‘‘(3) to seek out ways to increase

understanding of the metric system of

measurement through educational

information and guidance and in

Government publications; and

‘‘(4) to permit the continued use of

traditional systems of weights and

measures in nonbusiness activities.’’

In the Metric Conversion Act of 1975,

the ‘‘metric system of measurement’’ is

defined as the International System of

Units as established in 1960 by the

General Conference of Weights and

Measures (abbreviated CGPM after the

French Confe ́rence Ge ́ne ́ral des Poids et

Mesures) and interpreted or modified

for the United States by the Secretary of

Commerce (15 U.S.C. 205c). The

Secretary has delegated this authority to

the Director of the National Institute of

Standards and Technology. In

implementation of this authority, tables

and associated text were published in

the Federal Register of December 20,

1990 (55 FR 52242–52245), setting forth

the interpretation for the United States

of the International System of Units

(abbreviated SI in all languages after the

French Syste ́me International d’Unite ́s).

The CGPM is an intergovernmental

organization established by the Meter

Convention (Convention du Me ́tre),

which was signed by the United States

and 16 other countries in Paris in 1875

(nearly 50 countries are now members

of the Convention). One of the

responsibilities of the CGPM is to

ensure that the SI reflects the latest

advances in science and technology.

Since the publication of the 1990

Federal Register notice, the CGPM has

made two significant changes to the SI.

These are (1) the addition of four new

SI prefixes to form decimal multiples

and submultiples of SI units; and (2) the

elimination of the class of

supplementary units (the radian and the

steradian) as a separate class in the SI.

Further, the International Committee for

Weights and Measures (abbreviated

CIPM after the French Comite ́

International des Poids et Mesures),

which comes under the authority of the

CGPM, has made some new

recommendations regarding units not

part of the SI that may be used with the

SI. It is therefore necessary to issue new

tables and associated text that reflect

these changes and which set forth a new

interpretation of the SI for the United

States. Thus this Federal Register notice

supersedes the previous interpretation

published in the Federal Register on

December 20, 1990 (55 FR 52242–

52245).

Classes of SI Units

There are now only two classes of

units in the International System of

Units: base units and derived units. The

units of these two classes form a

coherent set of units and are designated

by the name ‘‘SI units.’’ Here, the term

coherent is used to mean a unit system

where all derived units are obtained

from the base units by the rules of

multiplication and division with no

numerical factor other than the number

1 ever occurring in the expressions for

the derived units in terms of the base

units. The SI also includes prefixes to

form decimal multiples and

submultiples of SI units. Because units

formed with SI prefixes are not coherent

with SI units, the units so formed are

designated by their complete name

‘‘decimal multiples and submultiples of

SI units’’ in order to make a distinction

between them and the coherent set of SI

units proper. The SI units and their

decimal multiples and submultiples

together are often called ‘‘units of the

SI.’’

SI Base Units

The SI is founded on seven SI base

units for seven base quantities assumed

to be mutually independent. These units

and quantities are given in Table 1.
Federal Register / Vol. 63, No. 144 /Tuesday, July 28, 1998 / Notices 40335

SI Derived Units

Other quantities, called derived

quantities, are defined in terms of these

seven base quantities through a system

of quantity equations. SI derived units

for these derived quantities are obtained

from this system of equations and the

seven SI base units in a coherent

manner, which means, in keeping with

the above discussion of the term

coherent, that they are formed as

products of powers (both positive and

negative) of the SI base units

corresponding to the base quantities

concerned without numerical factors.

Table 2 gives some examples of SI

derived units.

Quantities of Dimension 1

The last entry of Table 2, mass

fraction, is an example of certain

derived quantities that are defined as

the ratio of two mutually comparable

quantities, that is, two quantities of the

same kind. Since the coherent SI

derived unit of such a derived quantity

is the ratio of two identical SI units, that

unit may also be expressed by the

number one, symbol 1. Such quantities

are called quantities of dimension 1, or

dimensionless quantities, and the SI

unit of all such quantities is the number

1. Examples of other derived quantities

of dimension 1, and thus with a

coherent SI derived unit that may be

expressed by the number 1, are relative

permeability, dynamic friction factor,

refractive index, characteristic numbers

such as the Mach number, and numbers

that represent a count, such as a number

of molecules. However, the number 1 is

generally not explicitly shown in the

expression for the value of a quantity of

dimension 1. For example, the value of

the refractive index of a given medium

is expressed as n = 1.51 rather than as

n = 1.51 × 1. In a few cases a special

name and symbol are given to the

number 1 to aid understanding. The

radian, unit symbol rad, and steradian,

unit symbol sr, which are given in Table

3 and are discussed in connection with

Table 4, are two such examples.

SI Derived Units With Special Names

and Symbols

For ease of understanding and

convenience, 21 SI derived units have

been given special names and symbols.

These are listed in Table 3, where it

should be noted that the last three units

of Table 3, the becquerel, unit symbol

Bq, the gray, unit symbol Gy, and the

sievert, unit symbol Sv, were

specifically introduced by the CGPM

with a view to safeguarding human

health.
40336 Federal Register / Vol. 63, No. 144 /Tuesday, July 28, 1998 / Notices

Degree Celsius

The derived unit in Table 3 with

special name degree Celsius and special

symbol °C deserves comment. Because

of the way temperature scales used to be

defined, it remains common practice to

express a thermodynamic temperature,

symbol T, in terms of its difference from

the reference temperature T0 = 273.15 K,

the ice point. This temperature

difference is called Celsius temperature,

symbol t, and is defined by the quantity

equation t = T¥T0. The unit of Celsius

temperature is the degree Celsius,

symbol °C. The numerical value of a

Celsius temperature t expressed in

degrees Celsius is given by

t T

° = − C K

27315 . .

It follows from the definition of t that

the degree Celsius is equal in magnitude

to the kelvin, which in turn implies that

the numerical value of a given

temperature difference or temperature

interval whose value is expressed in the

unit degree Celsius (°C) is equal to the

numerical value of the same difference

or interval when its value is expressed

in the unit kelvin (K). Thus temperature

differences or temperature intervals may

be expressed in either the degree Celsius

or the kelvin using the same numerical

value. For example, the Celsius

temperature difference ∆t and the

thermodynamic temperature difference

∆T between the melting point of gallium

and the triple point of water may be

written as ∆t = 29.7546 °C = ∆T =

29.7546 K. (Note that the centigrade

temperature scale is obsolete; the unit

name degree centigrade should no

longer be used.)

Use of SI Derived Units With Special

Names and Symbols

The special names and symbols of the

21 SI derived units with special names

and symbols given in Table 3 may

themselves be included in the names

and symbols of other SI derived units.

This use is shown in Table 4. All of the

SI derived units in Table 4, like those

in Table 3, have been obtained from the

SI base units in the same coherent

manner discussed above.
Federal Register / Vol. 63, No. 144 /Tuesday, July 28, 1998 / Notices 40337

Radian and Steradian

As indicated in Table 3, the radian,

unit symbol rad, and steradian, unit

symbol sr, are the special names and

symbols for the derived units of plane

angle and solid angle, respectively.

These units may be used or not in

expressions for derived units as is

convenient in order to distinguish

between derived quantities that are not

of the same kind but are of the same

dimension (that is, derived quantities

whose units when expressed in SI base

units are the same). Table 4 includes

some examples of derived units that use

the radian and steradian.

SI Prefixes

Table 5 gives the 20 SI prefixes used

to form decimal multiples and

submultiples of SI units. It is important

to note that the kilogram is the only SI

unit with a prefix as part of its name and

symbol. Because multiple prefixes may

not be used, in the case of the kilogram

the prefix names of Table 5 are used

with the unit name ‘‘gram’’ and the

prefix symbols are used with the unit

symbol ‘‘g.’’ With this exception, any SI

prefix may be used with any SI unit,

including the degree Celsius and its

symbol °C.
40338 Federal Register / Vol. 63, No. 144 /Tuesday, July 28, 1998 / Notices

Because the SI prefixes strictly

represent powers of 10, it is

inappropriate to use them to represent

powers of 2. Thus 1 kbit = 103 bit =

1000 bit and not 210 = 1024 bit, where

1 kbit is one kilobit.

Units Outside the SI

Certain units are not part of the

International System of Units, that is,

they are outside the SI, but are

important and widely used. Consistent

with the recommendations of the CIPM,

the units in this category that are

accepted for use in the United States

with the SI are given in Tables 6 and 7.

Liter and Metric Ton

The units liter and metric ton in Table

6 deserve comment. The liter and its

symbol l were adopted by the CIPM in

1879. The alternative symbol for the

liter, L, was adopted by the CGPM in

1979 in order to avoid the risk of

confusion between the letter l and the

number 1. Thus, although both l and L

are internationally accepted symbols for

the liter, to avoid this risk the preferred

symbol for use in the United States is L.

Neither a lowercase script letter l nor an

uppercase script letter l are approved

symbols for the liter. With regard to the

metric ton, this is the name to be used

in the United States for the unit with

symbol t and defined according to 1 t =

103 kg. (The name ‘‘metric ton’’ is also

used in some other English speaking

countries, but the name ‘‘tonne’’ is used

in many countries.)
Federal Register / Vol. 63, No. 144 /Tuesday, July 28, 1998 / Notices 40339

Other Units Outside the SI

Other units outside the SI that are

currently accepted for use with the SI in

the United States are given in Table 8.

These units, which are subject to future

review by the NIST Director on behalf

of the Secretary of Commerce, should be

defined in relation to the SI in every

document in which they are used; their

continued use is not encouraged. The

CIPM currently accepts the use of all of

the units given in Table 8 with the SI

except for the curie, roentgen, rad, and

rem. Because of the continued wide use

of these units in the United States,

especially in regulatory documents

dealing with health and safety, this

interpretation of the SI for the United

States accepts their use with the SI.

Nevertheless, use of the corresponding

SI units is encouraged whenever

possible, with values given in terms of

the older units in parentheses if

necessary.

Use of SI Prefixes With Units Outside

the SI

Some SI prefixes are used with some

of the units given in Tables 6, 7, and 8.

For example, prefixes for both positive

and negative powers of ten are used

with the liter, the electronvolt, the

unified atomic mass unit, the bar, and

the barn. Prefixes for positive powers of

ten are used with the metric ton, and

prefixes for negative powers of ten are

used with the neper and the bel,

although the bel is most commonly

used in the form of the decibel:

1 dB = 0.1 B.

Rules and Style Conventions

A number of rules and style

conventions have been adopted

internationally for the use of the SI to

ensure that scientific and technical

communication is not hindered by

ambiguity. The most important of these

are as follows:

1. Unit symbols are printed in roman

(upright) type regardless of the type

used in the surrounding text.

2. Unit symbols are printed in lowercase 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 preferred symbol for the liter

in the United States is L.

3. When the name of a unit is spelled

out, it is always written with a lowercase initial letter unless it begins a

sentence.

4. Unit symbols are unaltered in the

plural.

5. Unit symbols are not followed by

a period unless at the end of a sentence.

6. Symbols for units formed from

other units by multiplication are

indicated by means of a half-high (that

is, centered) dot or space.
40340 Federal Register / Vol. 63, No. 144 /Tuesday, July 28, 1998 / Notices

Example: N•m or N m

7. 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 or m s /s, m

s , ⋅ −1

However, to avoid ambiguity, the

solidus must not be repeated on the

same line unless parentheses are used.

Examples:

m/s2 or m•s¥2 but not: m/s/s

m•kg/(s3•A) or m•kg•s¥3•A¥1 but

not: m•kg/s3/A

Negative exponents should be used in

complicated cases.

8. 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 prefix names attached to unit

names.

Examples:

1 mL (one milliliter)

1 pm (one picometer)

1 GΩ (one gigaohm)

1 THz (one terahertz)

9. The dgrouping formed by a prefix

symbol attached to a unit sybmbol

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 (10¥2 m)3

= 2.3×10¥6 m3

1 cm¥1 = 1 (cm)¥1 = 1 (10¥2 m)¥1

= 102 m¥1

5000 μs¥1 = 5000 (μs)¥1

= 5000 (10¥6 s)¥1

= 5000×106 s¥1 = 5×109 s¥1

Prefix names are also inseparable

form the unit names to which they are

attached. Thus, for example, millimeter,

micropascal, and meganewton are single

words.

10. 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 prefix names.

Example: 1 nm (one nanometer) but not:

1 mμm (one millimicrometer)

11. An SI prefix symbol (and name)

cannot stand alone, but must always be

attached to a unit symbol (or name).

Example: 5×106/m3 but not: 5M/m3

12. 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: °, ′, and ′′, respectively (see Table

6), in which case no space is left

between the numerical value and the

unit symbol.

Example: α = 30°22′8′′

This rule means that:

(a) The symbol °C for the degree

Celsius is preceded by a space when one

expresses the values of Celsius

temperatures.

Example: t = 30.2 °C but not: t = 30.2°C

or t = 30.2° 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.)

Examples:

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

gage

a 10 kΩ resistance but not: a 10-kΩ

resistance

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, ’’ or ‘‘the

samples were placed in 22 vials of

volume 1 mL,’’ whichever was meant.

Note: When unit names are spelled out as

is often the case in nontechnical writing, the

normal rules of English apply. Thus, for

example, ‘‘a roll of 35-millimeter film’’ is

acceptable.

Obsolete Units

As stated in the 1990 Federal Register

notice, metric units, symbols, and terms

that are not in accordance with the

foregoing interpretation are not accepted

for continued use in the United States

with the International System of Units.

Accordingly, the following units and

terms listed in the table of metric units

in section 2 of the Act of July 28, 1866

(15 U.S.C. 205) that legalized the metric

system of weights and measures in the

United States are not accepted for use in

the United States:

myriameter

stere

millier or tonneau

quintal

myriagram

kilo (for kilogram).

Additional Information on the SI

Additional information on the SI may

be found in NIST Special Publication

(SP) 811, Guide for the Use of the

International System of Units (SI), by

Barry N. Taylor. This publication is for

sale by the Superintendent of

Documents, but is also available online

(as will be this notice) at URL http://

physics.nist.gov/cuu. (Although the

1995 edition of SP 811 is the edition

currently available in print and online,

a new edition that fully reflects the

contents of this notice is under

preparation and will replace the 1995

edition.)

Although there is no formal comment

period, public comments are welcome

on a continuing basis. Comments should

be submitted to Dr. Barry N. Taylor at

the above address.

Dated: June 19, 1998.

Robert E. Hebner,

Acting Deputy Director.

[FR Doc. 98–16965 Filed 7–27–98; 8:45 am]

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