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The International

System of

Units (SI)

NIST Special Publication 330

2001 Edition

United States Department of Commerce

National Institute of Standards and Technology

DERN

METRIC SYSTEM MO

TEM MODERN METRIC SYSTEM

ETRIC SYSTEM MODERN METRIC SY

STEM MODERN METRIC SYSTEM

YSTEM MODERN METRIC SYSTEM MODERN METR

RN METRIC SYSTEM MODERN M

TEM MODERN METRIC SYSTEM MODE

TRIC SYSTEM MODERN METRIC S

METRIC SYSTEM MODE

N METR

RN ME

YSTEM

RN ME

STEM

N MET

TEM M

METR

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R

Barry N. Taylor, Editor
National Institute of Standards and Technology

Technology Administration, U.S. Department of Commerce

NIST Special Publication 330

2001 Edition

The International

System of

Units (SI)

Barry N. Taylor, Editor
UNITED STATES OF AMERICA

DEPARTMENT OF COMMERCE

NIST SPECIAL PUBLICATION 330

2001 EDITION

THE INTERNATIONAL SYSTEM OF UNITS (SI)

Barry N. Taylor, Editor

Physics Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

United States version of the English text of the seventh

edition (1998) of the International Bureau

of Weights and Measures publication

Le Syste`me International d’Unite ́s (SI), including

Supple ́ment 2000: additions et corrections a` la 7 e e ́dition (1998)

(Supersedes NIST Special Publication

330 1991 Edition)

Issued July 2001

U.S. DEPARTMENT OF COMMERCE, Donald L. Evans, Secretary

TECHNOLOGY ADMINISTRATION, Karen H. Brown, Acting Under Secretary of Commerce for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Karen H. Brown, Acting Director
National Institute of Standards and Technology Special Publication 330, 2001 Edition

Natl. Inst. Stand. Technol. Spec. Publ. 330, 2001 Edition, 75 pages (July 2001)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2001

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402–9325
iii

Foreword

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 system used in science, the SI is

rapidly becoming the dominant measurement system used in international commerce. In recognition of this fact

and the increasing global nature of the marketplace, the Omnibus Trade and Competitiveness Act of 1988,

which 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 U.S. industry increase its competitiveness,

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

trade and commerce.”

The definitive international reference on the SI is a booklet published by the International Bureau of Weights and

Measures (BIPM, Bureau International des Poids et Mesures) and often referred to as the BIPM SI Brochure.

Entitled Le Syste`me International d’Unite ́s (SI), the booklet is in French followed by a text in English. This

2001 edition of NIST Special Publication (SP) 330 is the United States version of the English text of the seventh

edition of the Brochure (the most current). However, it also incorporates the contents of Supplement 2000:

addenda and corrigenda to the 7th edition (1998) [Supple ́ment 2000: additions et corrections a` la 7 e e ́dition

(1998)] published by the BIPM in June 2000. The 2001 edition of NIST SP 330 replaces its immediate

predecessor, the 1991 edition, which was based on the sixth edition of the BIPM SI Brochure published in 1991.

Like its 1991 predecessor, this edition of NIST SP 330 conforms with the English text in the BIPM SI Brochure

but contains a few minor differences to reflect the most recent interpretation of the SI for the United States by

the Secretary of Commerce, as published in the Federal Register of July 28, 1998, 63 FR 40334-40340. (The

Metric Conversion Act of 1975 gives the Secretary of Commerce the responsibility of interpreting or modifying

the SI for use in the United States.) These differences are as follows: (i) The spelling of English words is in

accordance with the United States Government Printing Office Style Manual, which follows Webster’s Third

New International Dictionary rather than the Oxford Dictionary. Thus the spellings “meter,” “liter,” and

“deca” are used rather than “metre,” “litre,” and “deka” as in the original BIPM English text; (ii) the name of

the unit with symbol t and defined according to 1 t = 103 kg is called “metric ton” rather than “tonne”; (iii) the

four units curie, roentgen, rad, and rem are included in Table 8; (iv) a number of “Editor’s notes” are added in

order to indicate such differences (except spelling differences) and to clarify the text; and (v) a few very minor

editorial changes are made in order to “Americanize” some phrases.

Because of the importance of the SI to science, technology, and commerce, and because (i) NIST coordinates the

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

industry, (ii) NIST provides official U.S. representation in the various international bodies established by the

Meter Convention (see Appendix 3), and (iii) the Secretary of Commerce has delegated his authority to interpret

or modify the SI for use in the United States to the NIST Director, NIST provides a number of other sources of

information on the SI in addition to NIST SP 330. These include NIST Special Publication 811, Guide for

the Use of the International System of Units (SI), by Barry N. Taylor; and NIST Special Publication 814,

Interpretation of the SI for the United States and Metric Conversion Policy for Federal Agencies, Barry N. Taylor,

Editor. Further, NIST SP 330, NIST SP 811, the aforementioned 1998 Federal Register notice, the “essentials”

of the SI together with useful background information, and links to other organizations involved with the SI,

for example, the NIST Metric Program and the BIPM itself, are all available on the Web site entitled “NIST

Reference on Constants, Units, and Uncertainty” at physics.nist.gov/cuu. Users of this NIST publication are

encouraged to take advantage of these other sources of information.

I should like to thank James B. McCracken of the NIST Metric Program, NIST Guest Researcher Ralph P.

Hudson, and Ilse E. Putman of the NIST Electronic Typesetting Group for their highly capable assistance in the

preparation of this publication.

July, 2001

Barry N. Taylor
iv

Preface to the 7th edition

Since 1970, the Bureau International des Poids et Mesures (BIPM) has

now published seven editions of this document. It lists all Resolutions and

Recommendations of the Confe ́rence Ge ́ne ́rale des Poids et Mesures (CGPM)

and the Comite ́ International des Poids et Mesures (CIPM) relating to the

International System of Units. Formal reference to CIPM and CGPM decisions

are to be found in successive volumes of the Comptes Rendus of the CGPM

(CR) and Proce`s-Verbaux of the CIPM (PV); the most recent are also listed in

Metrologia. To simplify practical use of the SI, the text provides explanations

of these decisions and accompanies them with relevant extracts from the

international standards of the International Organization for Standardization

(ISO).

The Comite ́ Consultatif des Unite ́s (CCU) of the CIPM helped to draft the

document and approved the final text. This 7th edition is a revision of the 6th

edition (1991); it takes into consideration decisions made by the CGPM and the

CIPM since 1991. It also incorporates amendments made by the CCU.

Appendix 1 reproduces the decisions (Resolutions, Recommendations,

Declarations) promulgated since 1889 by the CGPM and the CIPM on units of

measurement and the International System of Units.

Appendix 2 outlines the measurements, consistent with the theoretical

definitions given in the principal text, which metrological laboratories can

make to realize physical units and to calibrate material standards of the highest

quality. In this edition, for the first time, the definition and hence the practical

realizations of both the meter and the second are considered in the context of

general relativity. Except where specified, uncertainties are quoted in the

form of combined standard uncertainties or as relative combined standard

uncertainties.
Preface to the 7th edition • v

For more than twenty-five years this document has been used as a work of

reference in many countries, organizations and scientific unions. To make its

contents accessible to a greater number of readers, the CIPM decided, in

1985, to include an English version of the text in the 5th edition; this double

presentation is continued in this 7th edition. For the first English version the

BIPM endeavoured to produce a faithful translation of the French original by

close collaboration with the National Physical Laboratory (Teddington,

United Kingdom) and the National Institute of Standards and Technology

(Gaithersburg, United States), at that time the National Bureau of Standards.

For the present edition the French and English versions were prepared by the

BIPM in close collaboration with the CCU. The CIPM decided in 1997 that in

the English text the decimal marker would be the dot on the line, treating this as

a translation of the comma, the French decimal marker. This has no implication

for the translation of the decimal marker into other languages. A point to note is

that slight spelling variations occur in the language of the English-speaking

countries (for instance, “metre” and “meter,” “litre” and “liter”). In this respect,

the English text presented here follows the International Standard ISO 31

(1992), Quantities and units. Readers should note that the official record

is always that of the French text. This must be used when an authoritative

reference is required or when there is doubt about the interpretation of the text.

November 1997

T. J. QUINN I. M. MILLS

Director, BIPM President, CCU
vi

Note on the use of the English text

To make its work more widely accessible, the Comite ́ International

des Poids et Mesures has decided to publish an English version

of its reports. Readers should note that the official record is always

that of the French text. This must be used when an authoritative reference

is required or when there is doubt about the interpretation of the text.

Translations, complete or partial, of this brochure (or of its earlier editions) have

been published in various languages, notably in Bulgarian,

Chinese, Czech, English, German, Japanese, Korean, Portuguese,

Romanian and Spanish. The ISO and numerous countries have also

published standards and guides to the use of SI units.
vii

The International System of Units

Contents

Page

Foreword. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Preface to the 7th edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

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

1.1 Historical note ..................................................... 1

1.2 Two classes of SI units .............................................. 3

1.3 The SI prefixes..................................................... 3

1.4 System of quantities................................................. 4

1.5 SI units in the framework of general relativity............................ 4

1.6 Legislation on units ................................................. 4

2 SI units............................................................... 5

2.1 SI base units....................................................... 5

2.1.1 Definitions ................................................... 5

2.1.1.1 Unit of length (meter) ................................... 5

2.1.1.2 Unit of mass (kilogram) ................................. 5

2.1.1.3 Unit of time (second).................................... 6

2.1.1.4 Unit of electric current (ampere)........................... 6

2.1.1.5 Unit of thermodynamic temperature (kelvin) ................. 7

2.1.1.6 Unit of amount of substance (mole) ........................ 8

2.1.1.7 Unit of luminous intensity (candela)........................ 8

2.1.2 Symbols for base units ......................................... 9

2.2 SI derived units .................................................... 9

2.2.1 Units expressed in terms of base units............................. 9

2.2.2 Units with special names and symbols; units which

incorporate units with special names and symbols . . . . . . . . . . . . . . . . . . . 10

2.2.3 Units for dimensionless quantities, quantities of

dimension one . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 Decimal multiples and submultiples of SI units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1 SI prefixes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 The kilogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4 Units outside the SI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.1 Units used with the SI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.2 Other non-SI units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
viii

5 The writing of SI unit names and symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.1 General principles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.2 SI unit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.3 Algebra of SI unit symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.4 Rules for using SI prefixes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Appendix 1. Decisions of the CGPM and the CIPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1 Decisions relating to the establishment of the International System

of Units, SI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.1 Practical system of units: establishment of the SI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.2 The SI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2 Decisions relating to base units of the International System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.1 Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.2 Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.3 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4 Electric current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.5 Thermodynamic temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.6 Amount of substance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.7 Luminous intensity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3 Decisions relating to SI derived and supplementary units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1 SI derived units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2 SI supplementary units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4 Decisions concerning terminology and the acceptance

of units for use with the SI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.1 SI prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2 Unit symbols and numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.3 Unit names. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.4 Units accepted for use with the SI; an example:

the liter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Appendix 2. Practical realization of the definitions

of some important units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

1 Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2 Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.1 Unit of time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.2 Clock comparisons, time scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.3 Legal time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4 Electrical quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

6 Amount of substance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

7 Photometric quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Appendix 3. The BIPM and the Meter Convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
1

1 Introduction

1.1 Historical note

The 9th CGPM† (1948, Resolution 6; CR, 64), instructed the CIPM:

• to study the establishment of a complete set of rules for units of

measurement;

• to find out for this purpose, by official inquiry, the opinion prevailing in

scientific, technical and educational circles in all countries;

• to make recommendations on the establishment of a practical system of units

of measurement suitable for adoption by all signatories to the Meter

Convention.

It also laid down, in Resolution 7 (CR, 70), general principles for the writing of

unit symbols and listed units which have been assigned special names.

The 10th CGPM (1954, Resolution 6; CR, 80), and the 14th CGPM (1971,

Resolution 3; CR, 78 and Metrologia, 1972, 8, 36), adopted as base units of this

practical system of units, the units of the following seven quantities: length,

mass, time, electric current, thermodynamic temperature, amount of substance,

and luminous intensity.

The 11th CGPM (1960, Resolution 12; CR, 87), adopted the name Syste`me

International d’Unite ́s (International System of Units), with the international

abbreviation SI, for this practical system of units and laid down rules for

prefixes, derived units and the former supplementary units, and other matters; it

thus established a comprehensive specification for units of measurement. Since

then, successive meetings of the CGPM and CIPM have added to, and modified

as necessary, the original structure of the SI to take account of advances in

science and the needs of users.

The main historical steps which led to these important CGPM decisions may be

summarized as follows.

• The creation of the Decimal Metric System at the time of the French

Revolution and the subsequent deposition of two platinum standards

representing the meter and the kilogram, on 22 June 1799, in the Archives de

la Re ́publique in Paris can be seen as the first step in the development of the

present International System of Units.

• In 1832, Gauss strongly promoted the application of this Metric System,

together with the second defined in astronomy, as a coherent system of

units for the physical sciences. Gauss was the first to make absolute

measurements of the Earth’s magnetic field in terms of a decimal system

based on the three mechanical units millimeter, gram and second for,

respectively, the quantities length, mass and time. In later years Gauss and

Weber extended these measurements to include electrical phenomena.

† Editor’s note: Throughout, CGPM means General Conference on Weights and Measures (Confe ́rence

Ge ́ne ́rale des Poids et Mesures), CIPM means International Committee for Weights and Measures

(Comite ́ International des Poids et Mesures), and BIPM means International Bureau of Weights and

Measures (Bureau International des Poids et Mesures). See Appendix 3, p. 63, for a discussion of the

Meter Convention (Convention du Me`tre ), often called the Treaty of the Meter in the United States, and

of the CGPM, CIPM, and BIPM which were established by the Convention.

Decisions of the

CGPM are recorded in

the Comptes Rendus

des Se ́ances de la

Confere ́nce Ge ́ne ́rale

des Poids et Mesures

and are here identified

by the letters CR.
2 • Introduction

• These applications in the field of electricity and magnetism were further

developed in the 1860s under the active leadership of Maxwell and Thomson

through the British Association for the Advancement of Science (BAAS).

They formulated the requirement for a coherent system of units with base

units and derived units. In 1874 the BAAS introduced the CGS system, a

three-dimensional coherent unit system based on the three mechanical units

centimeter, gram, and second, using prefixes ranging from micro to mega to

express decimal submultiples and multiples. The following development of

physics as an experimental science was largely based on this system.

• The sizes of the coherent CGS units in the fields of electricity and

magnetism proved to be inconvenient so, in the 1880s, the BAAS and

the International Electrical Congress, predecessor of the International

Electrotechnical Commission (IEC), approved a mutually coherent set of

practical units. Among them were the ohm for electrical resistance, the

volt for electromotive force, and the ampere for electric current.

• After the establishment of the Meter Convention on 20 May 1875 the CIPM

concentrated on the construction of new prototypes taking the meter and

kilogram as the base units of length and mass. In 1889 the 1st CGPM

sanctioned the international prototypes for the meter and the kilogram.

Together with the astronomical second as unit of time, these units

constituted a three-dimensional mechanical unit system similar to the CGS

system, but with the base units meter, kilogram, and second, the MKS

system.

• In 1901 Giorgi showed that it is possible to combine the mechanical units of

this meter-kilogram-second system with the practical electric units to form a

single coherent four-dimensional system by adding to the three base units

a fourth unit of an electrical nature, such as the ampere or the ohm, and

rewriting the equations occurring in electromagnetism in the so-called

rationalized form. Giorgi’s proposal opened the path to a number of new

developments.

• After the revision of the Meter Convention by the 6th CGPM in 1921, which

extended the scope and responsibilities of the BIPM to other fields in

physics, and the subsequent creation of the CCE† by the 7th CGPM in 1927,

the Giorgi proposal was thoroughly discussed by the IEC, the IUPAP‡ and

other international organizations. This led the CCE to propose, in 1939, the

adoption of a four-dimensional system based on the meter, kilogram, second,

and ampere, the MKSA system, a proposal approved by the ClPM in 1946.

• Following an international inquiry by the BIPM, which began in 1948,

the 10th CGPM, in 1954, approved the introduction of the ampere, the

kelvin and the candela as base units, respectively, for electric current,

thermodynamic temperature and luminous intensity. The name Syste`me

International d’Unite ́s (SI) was given to the system by the 11th CGPM

in 1960. At the 14th CGPM in 1971 the current version of the SI was

completed by adding the mole as the base unit for amount of substance,

bringing the total number of base units to seven.

† Editor’s note: CCE—Consultative Committee for Electricity; see Appendix 3.

‡ Editor’s note: IUPAP—International Union of Pure and Applied Physics.
Introduction • 3

1.2 Two classes of SI units

SI units are divided into two classes:

• base units;

• derived units.

From the scientific point of view, the division of SI units into these two classes

is to a certain extent arbitrary, because it is not essential to the physics of

the subject. Nevertheless, the CGPM, considering the advantages of a single,

practical, world-wide system of units for international relations, for teaching,

and for scientific work, decided to base the International System on a choice of

seven well-defined units which by convention are regarded as dimensionally

independent: the meter, the kilogram, the second, the ampere, the kelvin, the

mole, and the candela (see 2.1, p. 5). These SI units are called base units.

The second class of SI units is that of derived units. These are units that are

formed as products of powers of the base units according to the algebraic

relations linking the quantities concerned. The names and symbols of some

units thus formed in terms of base units may be replaced by special names and

symbols which can themselves be used to form expressions and symbols for

other derived units (see 2.2, p. 9).

The SI units of these two classes form a coherent set of units, where coherent is

used in the specialist sense of a system whose units are mutually related by rules

of multiplication and division with no numerical factor other than 1. Following

CIPM Recommendation 1 (1969; PV, 37, 30-31 and Metrologia, 1970, 6, 66),

the units of this coherent set of units are designated by the name SI units.

It is important to emphasize that each physical quantity has only one SI unit,

even if this unit can be expressed in different forms. The inverse, however, is not

true; in some cases the same SI unit can be used to express the values of several

different quantities (see p. 12).

1.3 The SI prefixes

The CGPM adopted a series of prefixes for use in forming the decimal

multiples and submultiples of SI units (see 3.1 and 3.2, p. 14). Following CIPM

Recommendation 1 (1969) mentioned above, these are designated by the name

SI prefixes.

The SI units, that is to say the base and derived units of the SI, form a coherent

set, the set of SI units. The multiples and submultiples of the SI units formed by

using the SI units combined with SI prefixes are designated by their complete

name, decimal multiples and submultiples of SI units. These decimal multiples

and submultiples of SI units are not coherent with the SI units themselves.

As an exception, the multiples and submultiples of the kilogram are formed by

attaching prefix names to the unit name “gram,” and prefix symbols to the unit

symbol “g.”

The radian and steradian,

units of plane and solid

angle, were admitted

to the SI as a separate

class of units, called

supplementary units, by

the 11th CGPM (1960,

Resolution 12; CR, 87).

The 20th CGPM (1995,

Resolution 8; CR, 223

and Metrologia, 1996,

33, 83) eliminated the

supplementary units as a

separate class within

the SI and included the

radian and steradian in

the class of derived units.

Recommendations

of the CIPM are recorded

in the Proce`s-Verbaux

des Se ́ances du Comite ́

International des Poids et

Mesures and are here

identified by the letters

PV.
4 • Introduction

1.4 System of quantities

The system of quantities used with the SI units is dealt with by Technical

Committee 12 of the International Organization for Standardization (ISO/TC

12) and is not treated here. Since 1955, the ISO/TC 12 has published a series

of International Standards on quantities and their units which strongly

recommends the use of the International System of Units.

In these International Standards, the ISO has adopted a system of physical

quantities based on the seven base quantities corresponding to the seven base

units of the SI, namely: length, mass, time, electric current, thermodynamic

temperature, amount of substance, and luminous intensity. Other quantities,

called derived quantities, are defined in terms of these seven base quantities; the

relationships between derived quantities and base quantities are expressed by a

system of equations. It is this system of quantities and equations that is properly

used with the SI units.

1.5 SI units in the framework of general relativity

The definitions of the base units of the SI were agreed to in a context which

takes no account of relativistic effects. When such account is taken, it is clear

that the definitions apply only in a small spatial domain which shares the

motion of the standards that realize them. These units are therefore proper

units; they are realized from local experiments in which the relativistic effects

that need to be taken into account are those of special relativity. The constants of

physics are local quantities with their values expressed in proper units.

Realizations of a unit using different standards are usually compared locally. For

frequency standards, however, it is possible to make such comparisons at a

distance by means of electromagnetic signals. To interpret the results, the

theory of general relativity is required since it predicts, among other things, a

frequency shift between standards of about 1 part in 1016 per meter of altitude

difference at the surface of the Earth. Effects of this magnitude can be

comparable with the uncertainty of realization of the meter or the second based

on a periodic signal of given frequency (see Appendix 2, p. 45).

1.6 Legislation on units

By legislation, individual countries have established rules concerning the use of

units on a national basis, either for general use or for specific areas such as

commerce, health, public safety and education. In almost all countries this

legislation is based on the use of the International System of Units.

The International Organization of Legal Metrology (OIML, Organisation

Internationale de Me ́trologie Le ́gale ), founded in 1955, is charged with the

international harmonization of this legislation.

For a detailed

exposition of the

system of quantities

used with the

SI units see ISO 31,

Quantities and

units (ISO Standards

Handbook,

3rd edition, ISO,

Geneva, 1993).

The question

of proper units is

addressed in

Resolution A4

adopted by the XXIst

General Assembly

of the International

Astronomical Union

(IAU) in 1991 and by

the report of the

CCDS working group

on the application

of general relativity

to metrology

(Metrologia, 1997,

34, 261-290).
5

2 SI units

2.1 SI base units

Formal definitions of all SI base units are approved by the CGPM. The

first such definition was approved in 1889 and the most recent in 1983. These

definitions are modified from time to time as techniques of measurement evolve

in order to allow more accurate realizations of the base units.

2.1.1 Definitions

Current definitions of the base units, as taken from the Comptes Rendus (CR) of

the corresponding CGPM, are here shown indented and in a heavy font. Related

decisions which clarify these definitions but are not formally part of them, as

taken from the Comptes Rendus (CR) of the corresponding CGPM or the

Proce`s-Verbaux (PV) of the CIPM, are also shown indented but in a font of

normal weight. For recent decisions, the appropriate article in Metrologia is also

cited. The associated text provides historical notes and explanations but is not

part of the definitions themselves.

2.1.1.1 Unit of length (meter)

The 1889 definition of the meter, based upon the international prototype of

platinum-iridium, was replaced by the 11th CGPM (1960) using a definition

based upon a wavelength of krypton 86 radiation. This definition was adopted in

order to improve the accuracy with which the meter may be realized. This was

replaced in 1983 by the 17th CGPM (Resolution 1; CR, 97 and Metrologia,

1984, 20, 25):

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.

Note that the effect of this definition is to fix the speed of light at exactly†

299 792 458 m  s–1. The original international prototype of the meter, which

was sanctioned by the 1st CGPM in 1889 (CR, 34-38), is still kept at the BIPM

under conditions specified in 1889.

2.1.1.2 Unit of mass (kilogram)

The international prototype of the kilogram, made of platinum-iridium, is kept

at the BIPM under conditions specified by the 1st CGPM in 1889 (CR, 34-38)

when it sanctioned the prototype and declared:

This prototype shall henceforth be considered to be the unit of mass.

† Editor’s note: Hence formally we have c0 = 299 792 458 m  s

–1 exactly, where c0 is the quantity symbol for

the speed of light in vacuum.
6 • SI Units

The 3rd CGPM (1901; CR, 70), in a declaration intended to end the ambiguity

in popular usage concerning the word “weight” confirmed that:

The kilogram is the unit of mass; it is equal to the mass of the

international prototype of the kilogram.

The complete declaration appears on page 29.

2.1.1.3 Unit of time (second)

The unit of time, the second, was at one time considered to be the fraction

1/86 400 of the mean solar day. The exact definition of “mean solar day”

was based on astronomical theories. However, measurement showed that

irregularities in the rotation of the Earth could not be taken into account by the

theory and have the effect that this definition does not allow the required

accuracy to be achieved. In order to define the unit of time more precisely, the

11th CGPM (1960; CR, 86) adopted a definition given by the International

Astronomical Union which was based on the tropical year. Experimental work,

however, had already shown that an atomic standard of time interval, based on a

transition between two energy levels of an atom or a molecule, could be realized

and reproduced much more precisely. Considering that a very precise definition

of the unit of time is indispensable for the International System, the 13th CGPM

(1967-1968, Resolution 1; CR, 103 and Metrologia, 1968, 4, 43) replaced the

definition of the second with the following:

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.

At its 1997 meeting, the CIPM affirmed that:

This definition refers to a cesium atom at rest at a temperature of 0 K.†

This note was intended to make it clear that the definition of the SI second

is based on a Cs atom unperturbed by black-body radiation, that is, in an

environment whose temperature is 0 K, and that the frequencies of primary

frequency standards should therefore be corrected for the shift due to ambient

radiation, as stated at the meeting of the CCTF in 1999.

2.1.1.4 Unit of electric current (ampere)

Electric units, called “international,” for current and resistance were introduced

by the International Electrical Congress held in Chicago in 1893, and

definitions of the “international” ampere and the “international” ohm were

confirmed by the International Conference of London in 1908.

† Editor’s note: This wording of the CIPM affirmation and the subsequent paragraph are given in Supplement

2000: addenda and corrigenda to the 7th edition (1998); June 2000. For the meaning of CCTF see Appendix

3, p. 65.
SI Units • 7

Although it was already obvious on the occasion of the 8th CGPM (1933) that

there was a unanimous desire to replace those “international” units by so-called

“absolute” units, the official decision to abolish them was only taken by the 9th

CGPM (1948), which adopted the ampere for the unit of electric current,

following a definition proposed by the CIPM (1946, Resolution 2; PV, 20,

129-137):

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 210–7 newton per meter

of length.

The expression “MKS unit of force” which occurs in the original text of 1946

has been replaced here by “newton,” a name adopted for this unit by the 9th

CGPM (1948, Resolution 7; CR, 70). Note that the effect of this definition is to

fix the permeability of vacuum at exactly† 410–7 H  m–1.

2.1.1.5 Unit of thermodynamic temperature (kelvin)

The definition of the unit of thermodynamic temperature was given in

substance by the 10th CGPM (1954, Resolution 3; CR, 79) which selected

the triple point of water as the fundamental fixed point and assigned to it

the temperature 273.16 K so defining the unit. The 13th CGPM (1967-1968,

Resolution 3; CR, 104 and Metrologia, 1968, 4, 43) adopted the name kelvin

(symbol K) instead of “degree Kelvin” (symbol K) and defined the unit of

thermodynamic temperature as follows (Resolution 4; CR, 104 and Metrologia,

1968, 4, 43):

The kelvin, unit of thermodynamic temperature, is the fraction

1/273.16 of the thermodynamic temperature of the triple point of

water.

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 the 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, which

is by definition equal in magnitude to the kelvin. A difference or interval of

temperature may be expressed in kelvins or in degrees Celsius (13th CGPM,

1967-1968, Resolution 3, mentioned above). The numerical value of a Celsius

temperature t expressed in degrees Celsius is given by

t/ C = T /K – 273.15 .

The kelvin and the degree Celsius are also the units of the International

Temperature Scale of 1990 (ITS-90) adopted by the CIPM in 1989 in its

Recommendation 5 (CI-1989) (PV, 57, 115 and Metrologia, 1990, 27, 13).

† Editor’s note: Hence formally we have 0 = 410–7 H  m–1 exactly, where 0 is the quantity symbol for

the magnetic constant, which is also called the permeability of vacuum.
8 • SI Units

2.1.1.6 Unit of amount of substance (mole)

Following the discovery of the fundamental laws of chemistry, units called, for

example, “gram-atom” and “gram-molecule,” were used to specify amounts of

chemical elements or compounds. These units had a direct connection with

“atomic weights” and “molecular weights,” which are in fact relative masses.

“Atomic weights” were originally referred to the atomic weight of oxygen, by

general agreement taken as 16. But whereas physicists separated isotopes in the

mass spectrometer and attributed the value 16 to one of the isotopes of oxygen,

chemists attributed that same value to the (slightly variable) mixture of isotopes

16, 17 and 18, which was for them the naturally occurring element oxygen.

Finally, an agreement between the International Union of Pure and Applied

Physics (IUPAP) and the International Union of Pure and Applied Chemistry

(IUPAC) brought this duality to an end in 1959/60. Physicists and chemists have

ever since agreed to assign the value 12, exactly, to the “atomic weight,”

correctly the relative atomic mass, of the isotope of carbon with mass number

12 (carbon 12, 12C). The unified scale thus obtained gives values of relative

atomic mass.

It remained to define the unit of amount of substance by fixing the

corresponding mass of carbon 12; by international agreement this mass was

fixed at 0.012 kg, and the unit of the quantity “amount of substance” was given

the name mole (symbol mol).

Following proposals by the IUPAP, the IUPAC and the ISO, the CIPM gave a

definition of the mole in 1967 and confirmed it in 1969: this was adopted by the

14th CGPM† (1971, Resolution 3; CR, 78 and Metrologia, 1972, 8, 36):

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; its symbol is “mol.”

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 1980 the CIPM approved the report of the CCU (1980) which specified that

In this definition, it is understood that unbound atoms of carbon 12, at rest

and in their ground state, are referred to.

2.1.1.7 Unit of luminous intensity (candela)

The units of luminous intensity based on flame or incandescent-filament

standards in use in various countries before 1948 were replaced initially by the

“new candle” based on the luminance of a Planckian radiator (a black body) at

the temperature of freezing platinum. This modification had been prepared by

the International Commission on Illumination (CIE, Commission Internationale

de l’E ́ clairage ) and by the CIPM before 1937 and the decision was promulgated

by the CIPM in 1946. It was then ratified in 1948 by the 9th CGPM which

† Editor’s note: The effect of this definition is to fix the molar mass of the carbon-12 atom, quantity symbol

M (

12C), to be exactly 1210–3 kg  mol–1, or formally M (12C) = 1210–3 kg  mol–1 exactly.

When the definition

of the mole is quoted,

it is conventional

also to include this

remark.
SI Units • 9

adopted a new international name for this unit, the candela (symbol cd); in 1967

the 13th CGPM (Resolution 5; CR, 104 and Metrologia, 1968, 4, 43-44) gave an

amended version of the 1946 definition.

In 1979, because of the experimental difficulties in realizing a Planck radiator

at high temperatures and the new possibilities offered by radiometry, i.e., the

measurement of optical radiation power, the 16th CGPM (1979, Resolution 3;

CR, 100 and Metrologia, 1980, 16, 56) adopted a new definition of the candela:

The candela is the luminous intensity, in a given direction, of a source

that emits monochromatic radiation of frequency 5401012 hertz and

that has a radiant intensity in that direction of 1/683 watt per

steradian.

2.1.2 Symbols for base units

The base units of the International System are listed in Table l which relates the

base quantity to the unit name and unit symbol [10th CGPM (1954, Resolution

6; CR, 80); 11th CGPM (1960, Resolution 12; CR, 87); 13th CGPM (1967-

1968, Resolution 3; CR, 104 and Metrologia, 1968, 4, 43); 14th CGPM (1971,

Resolution 3; CR, 78 and Metrologia, 1972, 8, 36)].

2.2 SI derived units

Derived units are units which may be expressed in terms of base units by means

of the mathematical symbols of multiplication and division. Certain derived

units have been given special names and symbols, and these special names and

symbols may themselves be used in combination with those for base and other

derived units to express the units of other quantities.

2.2.1 Units expressed in terms of base units

Table 2 lists some examples of derived units expressed directly in terms of base

units. The derived units are obtained by multiplication and division of base

units.

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
10 • SI Units

2.2.2 Units with special names and symbols; units which incorporate units

with special names and symbols

For convenience, certain derived units, which are listed in Table 3, have been

given special names and symbols. These names and symbols may themselves be

used to express other derived units: Table 4 shows some examples. The special

names and symbols are a compact form for the expression of units which are

used frequently.

Among these names and symbols, the last four entries in Table 3 are of

particular note since they were accepted by the 15th CGPM (1975, Resolutions

8 and 9; CR, 105 and Metrologia, 1975, 11, 180), the 16th CGPM (1979,

Resolution 5; CR, 100 and Metrologia, 1980, 16, 56), and the 21st CGPM

(1999, Resolution 12; CR, 444)† specifically with a view to safeguarding

human health.

In Tables 3 and 4, the final column shows how the SI units concerned may be

expressed in terms of SI base units. In this column, factors such as m0

, kg0 ...,

which are all equal to 1, are not shown explicitly.

† Editor’s note: This last phrase is given in Supplement 2000: addenda and corrigenda to the 7th edition

(1998); June 2000.

Table 2. Examples of SI derived units expressed in terms of 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 m1

density, mass 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

concentration (of amount of substance) mole per cubic meter mol/m3

luminance candela per square meter cd/m2

refractive index (the number) one 1(a)

(a) The symbol “1” is generally omitted in combination with a numerical value.
SI Units • 11

Table 3. SI derived units with special names and symbols

SI derived unit

Expressed Expressed

in terms of in terms of

Derived quantity Name Symbol other SI units SI base units

plane angle radian(a) rad m  m1 = 1(b)

solid angle steradian(a) sr(c ) m2  m2 = 1(b)

frequency hertz Hz s1

force newton N m  kg  s

2

pressure, stress pascal Pa N/m2 m1  kg  s

2

energy, work, quantity of heat joule J N  m m2  kg  s

2

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

3

electric charge, quantity of electricity coulomb C s  A

electric potential difference,†

electromotive force volt V W/A m2  kg  s

3  A1

capacitance farad F C/V m2  kg1  s

4  A2

electric resistance ohm  V/A m2  kg  s

3  A2

electric conductance siemens S A/V m2  kg1  s

3  A2

magnetic flux weber Wb V  s m2  kg  s

2  A1

magnetic flux density tesla T Wb/m2 kg  s

2  A1

inductance henry H Wb/A m2  kg  s

2  A2

Celsius temperature degree

Celsius(d) C K

luminous flux lumen lm cd  sr(c ) m2  m–2  cd = cd

illuminance lux lx lm/m2 m2  m–4  cd = m–2  cd

activity (referred to a radionuclide) becquerel Bq s1

absorbed dose, specific energy

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

2

dose equivalent,

ambient dose equivalent,

directional dose equivalent,

personal dose equivalent,

organ equivalent dose sievert Sv J/kg m2  s

2

catalytic activity‡ katal kat s–1  mol

(a) The radian and steradian may be used with advantage in expressions for derived units to distinguish

between quantities of different nature but the same dimension. Some examples of their use in forming

derived units are given in Table 4.

(b) In practice, the symbols rad and sr are used where appropriate, but the derived unit “1” is generally

omitted in combination with a numerical value.

(c) In photometry, the name steradian and the symbol sr are usually retained in expressions for units.

(d) This unit may be used in combination with SI prefixes, e.g., millidegree Celsius, mC.

† Editor’s note: electric potential difference is also called “voltage” in the United States and in many other

countries, as well as “electric tension” or simply “tension” in some countries.

‡ Editor’s note: This derived quantity and its unit are given in Supplement 2000: addenda and corrigenda

to the 7th edition (1998); June 2000.
12 • SI Units

A single SI unit may correspond to several different quantities, as noted in

paragraph 1.2 (p. 3). In the above table, which is not exhaustive, there are

several examples. Thus the joule per kelvin (J/K) is the SI unit for the quantity

heat capacity as well as for the quantity entropy; also the ampere (A) is the SI

unit for the base quantity electric current as well as for the derived quantity

magnetomotive force. It is therefore important not to use the unit alone to

specify the quantity. This rule applies not only to scientific and technical texts

but also, for example, to measuring instruments (i.e., an instrument should

indicate both the unit and the quantity measured).

† Editor’s note: This derived quantity and its unit are given in Supplement 2000: addenda and corrigenda

to the 7th edition (1998); June 2000.

Table 4. Examples of SI derived units whose names and symbols include SI derived units with special names

and symbols

SI derived unit

Expressed

in terms of

Derived quantity Name Symbol SI base units

dynamic viscosity pascal second Pa  s m1  kg  s

1

moment of force newton meter N  m m2  kg  s

2

surface tension newton per meter N/m kg  s

2

angular velocity radian per second rad/s m  m1  s1 = s1

angular acceleration radian per second squared rad/s2 m  m1  s2 = s2

heat flux density, irradiance watt per square meter W/m2 kg  s

3

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

2  K1

specific heat capacity, joule per kilogram

specific entropy kelvin J/(kg  K) m2  s

2  K1

specific energy joule per kilogram J/kg m2  s

2

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

3  K1

energy density joule per cubic meter J/m3 m1  kg  s

2

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

3  A1

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

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

permittivity farad per meter F/m m3  kg1  s

4  A2

permeability henry per meter H/m m  kg  s

2  A2

molar energy joule per mole J/mol m2  kg  s

2  mol1

molar entropy, molar

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

2  K1  mol1

exposure (x and 	 rays) coulomb per kilogram C/kg kg1  s  A

absorbed dose rate gray per second Gy/s m2  s

3

radiant intensity watt per steradian W/sr m4  m2  kg  s

3

= m2  kg  s

3

radiance watt per square W/(m2  sr) m2  m2 kg  s

3

meter steradian = kg  s

3

catalytic (activity) concentration† katal per cubic meter kat/m3 m3  s

1  mol
SI Units • 13

A derived unit can often be expressed in different ways by combining the names

of base units with special names for derived units. This, however, is an algebraic

freedom to be governed by common-sense physical considerations. Joule, for

example, may formally be written newton meter, or even kilogram meter

squared per second squared, but in a given situation some forms may be more

helpful than others.

In practice, with certain quantities preference is given to the use of certain

special unit names, or combinations of unit names, in order to facilitate

the distinction between different quantities having the same dimension. For

example, the SI unit of frequency is designated the hertz, rather than the

reciprocal second, and the SI unit of angular velocity is designated the radian

per second rather than the reciprocal second (in this case retaining the word

radian emphasizes that angular velocity is equal to 2 times the rotational

frequency). Similarly the SI unit of moment of force is designated the newton

meter rather than the joule.

In the field of ionizing radiation, the SI unit of activity is designated the

becquerel rather than the reciprocal second, and the SI units of absorbed dose

and dose equivalent the gray and sievert, respectively, rather than the joule

per kilogram. In the field of catalysis, the SI unit of catalytic activity is

designated the katal rather than the mole per second.† The special names

becquerel, gray, sievert and katal were specifically introduced because of the

dangers to human health which might arise from mistakes involving the units

reciprocal second, joule per kilogram and mole per second.

2.2.3 Units for dimensionless quantities, quantities of dimension one

Certain quantities are defined as the ratios of two quantities of the same kind,

and thus have a dimension which may be expressed by the number one. The unit

of such quantities is necessarily a derived unit coherent with the other units of

the SI and, since it is formed as the ratio of two identical SI units, the unit also

may be expressed by the number one. Thus the SI unit of all quantities having

the dimensional product one is the number one. Examples of such quantities are

refractive index, relative permeability, and friction factor. Other quantities

having the unit 1 include “characteristic numbers” like the Prandtl number


 cp/and numbers which represent a count, such as a number of molecules,

degeneracy (number of energy levels) and partition function in statistical

thermodynamics. All of these quantities are described as being dimensionless,

or of dimension one, and have the coherent SI unit 1. Their values are simply

expressed as numbers and, in general, the unit 1 is not explicitly shown. In a few

cases, however, a special name is given to this unit, mainly to avoid confusion

between some compound derived units. This is the case for the radian, steradian

and neper.

† Editor’s note: This sentence and portions of the subsequent sentence are given in Supplement

2000: addenda and corrigenda to the 7th edition (1998); June 2000.

The CIPM,

recognizing the

particular importance

of the health-related

units, approved a

detailed text on the

sievert for the 5th

edition of the BIPM

SI Brochure. That

text is given in

Recommendation 1

(CI-1984) adopted

by the CIPM

(PV, 1984, 52, 31

and Metrologia, 1985,

21, 90); see p. 38.
14

3 Decimal multiples and submultiples of SI units

3.1 SI prefixes

The 11th CGPM (1960, Resolution 12; CR, 87) adopted a series of prefixes and

prefix symbols to form the names and symbols of the decimal multiples and

submultiples of SI units ranging from 1012 to 10–12. Prefixes for 10–15 and 10–18

were added by the 12th CGPM (1964, Resolution 8; CR, 94), for 1015 and 1018

by the 15th CGPM (1975, Resolution 10; CR, 106 and Metrologia, 1975,

11, 180-181), and for 1021, 1024, 10–21 and 10–24 by the 19th CGPM (1991,

Resolution 4; CR, 185 and Metrologia, 1992, 29, 3). Table 5 lists all approved

prefixes and symbols.

3.2 The kilogram

Among the base units of the International System, the unit of mass is the

only one whose name, for historical reasons, contains a prefix. Names and

symbols for decimal multiples and submultiples of the unit of mass are formed

by attaching prefix names to the unit name “gram” and prefix symbols to the

unit symbol “g” (CIPM, 1967, Recommendation 2; PV, 35, 29 and Metrologia,

1968, 4, 45),

Example : 10–6 kg = 1 mg (1 milligram)

but not 1 kg (1 microkilogram).

These SI prefixes

refer strictly to

powers of 10.

They should not

be used to indicate

powers of 2 (for

example, one kilobit

represents 1000 bits

and not 1024 bits).

Editor’s note: The IEC

has adopted prefixes

for binary multiples in

International Standard

IEC 60027-2,

Second edition, 2000-11,

Letter symbols

to be used in electrical

technology—Part 2:

Telecommunications

and electronics. The

names and symbols

for the prefixes

corresponding to 210, 220,

230, 240, 250, and 260

are, respectively: kibi, Ki;

mebi, Mi; gibi, Gi;

tebi, Ti; pebi, Pi; and

exbi, Ei. Thus, for

example, one kibibyte

would be written

1 KiB=210 B=1024 B.

Although these prefixes

are not part of the SI,

they should be used in

the field of information

technology to avoid the

incorrect usage of the

SI prefixes.

Table 5. SI prefixes

Factor Name Symbol Factor Name Symbol

1024 yotta Y 101 deci d

1021 zetta Z 102 centi c

1018 exa E 103 milli m

1015 peta P 106 micro 

1012 tera T 109 nano n

109 giga G 1012 pico p

106 mega M 1015 femto f

103 kilo k 1018 atto a

102 hecto h 1021 zepto z

101 deka da 1024 yocto y
15

4 Units outside the SI

SI units are recommended for use throughout science, technology, and

commerce. They are adopted internationally by the CGPM, and provide the

reference in terms of which all other units are now defined. The SI base units

and SI derived units, including those with special names, have the important

advantage of forming a coherent set with the effect that unit conversions are not

required when inserting particular values for quantities in quantity equations.

Nonetheless it is recognized that some non-SI units still appear widely in the

scientific, technical and commercial literature, and some will probably continue

to be used for many years. Other non-SI units, such as the units of time, are so

widely used in everyday life, and are so deeply embedded in the history and

culture of the human race, that they will continue to be used for the foreseeable

future. For these reasons some of the more important non-SI units are listed in

the tables below.

The inclusion of tables of non-SI units in this text does not imply that the use of

non-SI units is to be encouraged. With a few exceptions discussed below, SI

units are always to be preferred to non-SI units. It is desirable to avoid

combining non-SI units with units of the SI; in particular the combination of

such units with SI units to form compound units should be restricted to special

cases so as to retain the advantage of coherence conferred by the use of SI units.

4.1 Units used with the SI

The CIPM (1969), recognizing that users would wish to employ the SI with

units which are not part of it but are important and widely used, listed three

categories of non-SI units: units to be maintained; to be tolerated temporarily;

and to be avoided. In reviewing this categorization the CIPM (1996) adopted a

new classification of non-SI units: units accepted for use with the SI, Table 6;

units accepted for use with the SI whose values are obtained experimentally,

Table 7; and other units currently accepted for use with the SI to satisfy the

needs of special interests, Table 8.

Table 6 lists non-SI units which are accepted for use with the SI. It includes

units which are in continuous everyday use, in particular the traditional units

of time and of angle, together with a few other units which have assumed

increasing technical importance.
16 • Units outside the SI

(a) The symbol of this unit is included in Resolution 7 of the 9th CGPM (1948; CR, 70).

(b) ISO 31 recommends that the degree be subdivided decimally rather than using the minute and second.

(c) This unit and the symbol l were adopted by CIPM in 1879 (PV, 1879, 41). The alternative symbol, L,

was adopted by the 16th CGPM (1979, Resolution 6; CR, 101 and Metrologia, 1980, 16, 56-57) in order

to avoid the risk of confusion between the letter l and the number 1. The present definition of the liter

is given in Resolution 6 of the 12th CGPM (1964; CR, 93).

Editor’s note: The preferred symbol for liter in the United States is L; see the Federal Register notice

of July 28, 1998, “Metric System of Measurement: Interpretation of the International System of Units

for the United States” (63 FR 40334 –40340).

(d) This unit and its symbol were adopted by the CIPM in 1879 (PV, 1879, 41).

(e) Editor’s note: This is the name to be used for this unit in the United States (see the above-mentioned

Federal Register notice). The original BIPM English text uses the CGPM adopted name “tonne” and

footnote (e) reads as follows: In some English-speaking countries this unit is called “metric ton.”

(f) The neper is used to express values of such logarithmic quantities as field level, power level, sound

pressure level, and logarithmic decrement. Natural logarithms are used to obtain the numerical values of

quantities expressed in nepers. The neper is coherent with the SI, but is not yet adopted by the CGPM

as an SI unit. For further information see International Standard ISO 31.

(g) The bel is used to express values of such logarithmic quantities as field level, power level, sound-pressure

level, and attenuation. Logarithms to base ten are used to obtain the numerical values of quantities

expressed in bels. The submultiple decibel, dB, is commonly used. For further information see

International Standard ISO 31.

(h) In using these units it is particularly important that the quantity be specified. The unit must not be used

to imply the quantity.

(i) Np is enclosed in parentheses because, although the neper is coherent with the SI, it has not yet been

adopted by the CGPM.

Table 7 lists three non-SI units which are also accepted for use with the SI,

whose values expressed in SI units must be obtained by experiment and

are therefore not known exactly. Their values are given with their combined

standard uncertainties (coverage factor k = 1), which apply to the last two digits,

shown in parentheses. These units are in common use in certain specialized

fields.

Table 6. Non-SI units accepted for use with the International System

Name Symbol Value in SI units

minute min 1 min =60 s

hour(a) h 1 h = 60 min = 3600 s

day d 1 d = 24 h = 86 400 s

degree(b)  1 = (/180) rad

minute ' 1' = (1/60)= (/10 800) rad

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

liter(c) l, L 1 L = 1 dm3 = 103 m3

metric ton(d, e) t 1 t = 103 kg

neper(f, h) Np 1 Np =1

bel(g, h) B 1 B = (1/2) ln 10 (Np)(i)
Units outside the SI • 17

Table 8 lists some other non-SI units which are currently accepted for use with

the SI to satisfy the needs of commercial, legal, and specialized scientific

interests. These units should be defined in relation to the SI in every document

in which they are used. Their use is not encouraged.

Table 7. Non-SI units accepted for use with the International System, whose values in SI units are obtained

experimentally

Name Symbol Definition Value in SI units

electronvolt(a) eV (b) 1 eV = 1.602 177 33(49)  10–19 J

unified atomic mass unit(a ) u (c ) 1 u = 1.660 540 2(10)  10–27 kg

astronomical unit(a) ua (d) 1 ua = 1.495 978 70(30)  1011 m

(a) For the electronvolt and the unified atomic mass unit, values are quoted from CODATA Bulletin, 1986,

No. 63.

Editor’s note: The most recent (1998) CODATA values are given in: P. J. Mohr and B. N. Taylor,

J. Phys. Chem. Ref. Data 28, 1713 (1999) and Rev. Mod. Phys. 72, 351 (2000). They

are: 1.602 176 462(63)  10–19 J and 1.660 538 73(13)  10–27 kg.

The value given for the astronomical unit is quoted from the IERS Conventions (1996), D. D.

McCarthy ed., IERS Technical Note 21, Observatoire de Paris, July 1996.

(b) The electronvolt is the kinetic energy acquired by an electron in passing through a potential difference

of 1 V in vacuum.

(c) The unified atomic mass unit is equal to 1/12 of the mass of an unbound atom of the nuclide 12C, at

rest, and in its ground state. In the field of biochemistry, the unified atomic mass unit is also called the

dalton, symbol Da.

Editor’s note: The dalton is not recognized by the CGPM, CIPM, IEC, or ISO.

(d) The astronomical unit is a unit of length approximately equal to the mean Earth-Sun distance. Its

value is such that, when used to describe the motion of bodies in the Solar System, the heliocentric

gravitational constant is (0.017 202 098 95)2 ua3  d–2.

Table 8. Other non-SI units currently accepted for use with the International System

Name Symbol Value in SI units

nautical mile(a) 1 nautical mile = 1852 m

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

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

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

bar(c) bar 1 bar=0.1 MPa=100 kPa=1000 hPa=105 Pa

ångstro ̈m Å 1 Å = 0.1 nm = 1010 m

barn(d) b 1 b = 100 fm2 = 1028 m2

curie Ci

roentgen R

rad rad

rem rem

(a) The nautical mile is a special unit employed for marine and aerial navigation to express distance.

The conventional value given above was adopted by the First International Extraordinary

Hydrographic Conference, Monaco, 1929, under the name “International nautical mile.” As yet there

is no internationally accepted symbol. This unit was originally chosen because one nautical mile on the

surface of the Earth subtends approximately one minute of angle at the center.

(b) The units are and hectare and their symbols were adopted by the CIPM in 1879

(PV, 1879, 41) and are used to express areas of land.

(c) The bar and its symbol are included in Resolution 7 of the 9th CGPM (1948; CR, 70).

(d) The barn is a special unit employed in nuclear physics to express effective cross-sections.

† Editor’s note: As yet there also is no internationally accepted symbol for the knot.

Editor’s note: Although these last four units do not

appear in Table 8 of the BIPM SI Brochure, they are

included in this version of Table 8 because they are still

accepted for use with the SI in the United States; see

63 FR 40334-40340. For their values in SI units, see

Table 10.
18 • Units outside the SI

4.2 Other non-SI units

Certain other non-SI units are still occasionally used. Some are important for

the interpretation of older scientific texts. These are listed in Tables 9 and 10, but

their use is not encouraged.

Table 9 deals with the relationship between CGS units and the SI, and lists those

CGS units that were assigned special names. In the field of mechanics, the CGS

system of units was built upon three quantities and the corresponding base units:

the centimeter, the gram and the second. In the field of electricity and magnetism, units were expressed in terms of these three base units. Because this can

be done in different ways, it led to the establishment of several different systems,

for example the CGS Electrostatic System, the CGS Electromagnetic System

and the CGS Gaussian System. In these three last-mentioned systems, the

system of quantities and the corresponding system of equations differ from those

used with SI units.

Table 9. Derived CGS units with special names

Name Symbol Value in SI units

erg (a) erg 1 erg = 10–7 J

dyne (a) dyn 1 dyn = 10–5 N

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

stokes St 1 St = 1 cm2/s = 10–4 m2/s

gauss (b) G 1G ∧= 10–4 T

oersted (b) Oe 1 Oe ∧= (1000/4) A/m

maxwell (b) Mx 1 Mx ∧= 10–8 Wb

stilb (a) sb 1 sb = 1 cd/cm2 = 104 cd/m2

phot ph 1 ph = 104 lx

gal (c) Gal 1 Gal = 1 cm/s2 = 10–2 m/s2

(a) This unit and its symbol were included in Resolution 7 of the 9th CGPM (1948; CR, 70).

(b) This unit is part of the so-called “electromagnetic” three-dimensional CGS system and cannot strictly be

compared with the corresponding unit of the International System, which has four dimensions when only

mechanical and electric quantities are considered. For this reason, this unit is linked to the SI unit using

the mathematical symbol for “corresponds to” (∧=).

(c) The gal is a special unit employed in geodesy and geophysics to express acceleration due to gravity.
Units outside the SI • 19

Table 10 lists units which are common in older texts. For current texts, it should

be noted that if these units are used the advantages of the SI are lost. The

relation of these units to the SI should be specified in every document in which

they are used.

Table 10. Examples of other non-SI units†

Name Symbol Value in SI units

curie(a) Ci 1 Ci = 3.7  1010 Bq

roentgen(b) R 1 R = 2.58  10–4 C/kg

rad(c,f) rad 1 rad = 1 cGy = 10–2 Gy

rem(d,f) rem 1 rem = 1 cSv = 10–2 Sv

X unit(e) 1 X unit  1.00210–4 nm

gamma(f) 1 = 1 nT = 10–9 T

jansky Jy 1 Jy = 10–26 W  m–2  Hz–1

fermi(f) 1 fermi = 1 fm = 10–15 m

metric carat(g) 1 metric carat = 200 mg = 210–4 kg

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

standard atmosphere atm(h) 1 atm = 101 325 Pa

calorie cal various(i)

micron(f) (j) 1  = 1 m = 10–6 m

(a) The curie is a special unit employed in nuclear physics to express activity of radionuclides

(12th CGPM, 1964, Resolution 7; CR, 94).

(b) The roentgen is a special unit employed to express exposure to x or radiation.

Editor’s note: Outside the United States this unit is spelled “ro ̈ntgen,” and this is the spelling used in

the original BIPM text.

(c ) The rad is a special unit employed to express absorbed dose of ionizing radiation. When there is risk of

confusion with the symbol for radian, rd may be used as the symbol for the rad.

(d) The rem is a special unit used in radioprotection to express dose equivalent.

(e ) The X unit was employed to express the wavelengths of x rays. Its relationship with the SI unit is an

approximate one.

(f) Note that this non-SI unit is exactly equivalent to an SI unit with an appropriate submultiple prefix.

(g) The metric carat was adopted by the 4th CGPM in 1907 (CR, 89-91) for commercial dealings in

diamonds, precious stones, and pearls.

(h) Resolution 4 of the 10th CGPM (1954; CR, 79). The designation “standard atmosphere” for a reference

pressure of 101 325 Pa is still acceptable.

(i) Several “calories” have been in use:

• a calorie labeled “at 15 C’’: 1 cal15 = 4.1855 J (value adopted by the CIPM in 1950; PV, 1950, 22,

79-80);

• a calorie labeled “IT” (International Table): 1 calIT = 4.1868 J (5th International Conference on the

Properties of Steam, London, 1956);

• a calorie labeled “thermochemical’’: 1 calth = 4.184 J.

Editor’s note: The calorie commonly used to express the energy content of food is the kilocalorie, but

in practice the prefix “kilo” is omitted.

(j) The micron and its symbol, adopted by the CIPM in 1879 (PV, 1879, 41) and repeated in Resolution

7 of the 9th CGPM (1948; CR, 70) were abolished by the 13th CGPM (1967-1968, Resolution 7; CR,

105 and Metrologia, 1968, 4, 44).

† Editor’s note: The curie, roentgen, rad, and rem are included only in Table 10 of the original BIPM text,

but these four units are also included in Table 8, “Other non-SI units currently accepted for use with the

International System,” of this U.S. version of the BIPM text to be in accord with the U.S. interpretation of

the SI.
20

5 The writing of SI unit names and symbols

5.1 General principles

General principles for the writing of unit symbols and numbers were first

proposed by the 9th CGPM (1948, Resolution 7). These were subsequently

adopted and elaborated by ISO/TC 12 (ISO 31, Quantities and units).

5.2 SI unit symbols

SI unit symbols (and also many non-SI unit symbols) are written as follows:

1. Roman (upright) type is used for the unit symbols. In general, unit symbols

are written in lower case but, if the name of the unit is derived from the

proper name of a person, the first letter of the symbol is a capital. When the

name of a unit is spelled out, it is always written in lower case, except when

the name is the first word of a sentence or is the name “degree Celsius.”

2. Unit symbols are unaltered in the plural.

3. Unit symbols are not followed by a full stop (period), except as normal

punctuation at the end of a sentence.

5.3 Algebra of SI unit symbols

In accord with the general principles adopted by ISO/TC 12 (ISO 31), the

CIPM recommends that algebraic expressions involving SI unit symbols be

expressed in standard forms.

1. Half-high dots or spaces are used to express a derived unit formed from two

or more other units by multiplication.

Example : N  m or N m.

2. A solidus (oblique stroke, /), a horizontal line, or a negative exponent is

used to express a derived unit formed from two other units by division.

Example: m/s or m

s

or m  s–1.

3. The solidus is not followed by a multiplication sign or by a division sign on

the same line unless ambiguity is avoided by parentheses. In complicated

cases, negative exponents or parentheses are used to avoid ambiguity.

Examples: m/s2 or ms–2 but not m/s/s

m kg/(s3 A) or m kgs–3 A–1 but neither m kg/s3

/A

nor mkg/s3 A.
The writing of SI names and symbols • 21

5.4 Rules for using SI prefixes

In accord with the general principles adopted by the ISO (ISO 31), the CIPM

recommends that the following rules be observed when using the SI prefixes:

1. Prefix symbols are printed in roman (upright) type with no space between

the prefix symbol and the unit symbol.

2. The grouping formed by the prefix symbol attached to the unit symbol

constitutes a new inseparable symbol (of a multiple or submultiple of the

unit concerned) which can be raised to a positive or negative power and

combined with other unit symbols to form compound unit symbols.

Examples:

1 cm3 = (10–2 m)3 = 10–6 m3

1 s–1 = (10–6 s)–1 = 106 s–1

1 V/cm = (1 V)/(10–2 m) = 102 V/m

1 cm–1 = (10–2 m)–1 = 102 m–1.

3. Compound prefixes, i.e., prefixes formed by the juxtaposition of two or

more SI prefixes, are not used.

Example: 1 nm but not 1 mm

4. A prefix is never used in isolation.

Example : 106

/m3 but not M/m3.
22

Appendix 1. Decisions of the CGPM and the CIPM

This appendix lists those decisions of the CGPM and the CIPM which bear

directly upon definitions of the units of the SI, prefixes defined for use as part

of the SI, and conventions for the writing of unit symbols and numbers. It is not

a complete list of CGPM and CIPM decisions. For a complete list, reference

must be made to successive volumes of the Comptes Rendus des Se ́ ances de la

Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CR) and Proce`s-Verbaux des

Se ́ances du Comite ́ International des Poids et Mesures (PV) or, for recent

decisions, to Metrologia.

Since the SI is not a static convention, but evolves following developments in the

science of measurement, some decisions have been abrogated or modified;

others have been clarified by additions. Decisions which have been subject to

such changes are identified by an asterisk (*) and are linked by a note to the

modifying decision.

The original text of each decision (or its translation) is shown in a different font

of normal weight to distinguish it from the main text. The asterisks and notes

were added by the BIPM to make the text more understandable. They do not

form part of the original text.

1 Decisions relating to the establishment of the International

System of Units, SI

1.1 Practical system of units: establishment of the SI

■ 9th CGPM, 1948, Resolution 6 (CR, 64): proposal for establishing a

practical system of units of measurement

The Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering

• that the Comite ́ International des Poids et Mesures (CIPM) has

been requested by the International Union of Physics to adopt for

international use a practical Syste`me International d’Unite ́ s; that the

International Union of Physics recommends the MKS system and one

electric unit of the absolute practical system, but does not recommend

that the CGS system be abandoned by physicists;

• that the CGPM has itself received from the French Government

a similar request, accompanied by a draft to be used as basis of

discussion for the establishment of a complete specification of units of

measurement;
Appendix 1. Decisions of the CGPM and the CIPM • 23

instructs the CIPM:

• to seek by an energetic, active, official inquiry the opinion of scientific,

technical and educational circles of all countries (offering them, in fact,

the French document as basis);

• to gather and study the answers;

• to make recommendations for a single practical system of units of

measurement, suitable for adoption by all countries adhering to the

Meter Convention.

■ 10th CGPM, 1954, Resolution 6 (CR, 80): practical system of units*

In accordance with the wish expressed by the 9th Confe ́ rence

Ge ́ ne ́ rale des Poids et Mesures (CGPM) in its Resolution 6

concerning the establishment of a practical system of units of

measurement for international use, the 10th CGPM

decides to adopt as base units of the system, the following units:

length meter

mass kilogram

time second

electric current ampere

thermodynamic temperature degree Kelvin

luminous intensity candela

1.2 The SI

■ CIPM, 1956, Resolution 3 (PV, 25, 83): Syste`me International d’Unite ́s

The Comite ́ International des Poids et Mesures,

considering

• the task entrusted to it by Resolution 6 of the 9th Confe ́ rence Ge ́ne ́ rale

des Poids et Mesures (CGPM) concerning the establishment of a

practical system of units of measurement suitable for adoption by all

countries adhering to the Meter Convention,

• the documents received from twenty-one countries in reply to the

inquiry requested by the 9th CGPM,

• Resolution 6 of the 10th CGPM, fixing the base units of the system to

be established,

recommends

1. that the name “Syste`me International d’Unite ́ s” be given to the system

founded on the base units adopted by the 10th CGPM, viz.:

[This is followed by the list of the six base units with their symbols,

reproduced in Resolution 12 of the 11th CGPM (1960).]

2. that the units listed in the table below be used, without excluding

others which might be added later:

[This is followed by the table of units reproduced in paragraph 4 of

Resolution 12 of the 11th CGPM (1960).]

* The unit name

“degree kelvin” was

changed to “kelvin”

in 1967 (13th CGPM,

Resolution 3,

see p. 34).
24 • Appendix 1. Decisions of the CGPM and the CIPM

■ 11th CGPM, 1960, Resolution 12 (CR, 87): Syste`me International

d’Unite ́s*

The 11th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering

• Resolution 6 of the 10th CGPM, by which it adopted six base units on

which to establish a practical system of measurement for international

use:

length meter m

mass kilogram kg

time second s

electric current ampere A

thermodynamic temperature degree Kelvin K

luminous intensity candela cd

• Resolution 3 adopted by the Comite ́ International des Poids et

Mesures (CIPM) in 1956,

• the recommendations adopted by the CIPM in 1958 concerning an

abbreviation for the name of the system, and prefixes to form multiples

and submultiples of the units,

decides

1. the system founded on the six base units above is called the “Syste`me

International d’Unite ́ s’’;

2. the international abbreviation of the name of the system is: SI;

3. names of multiples and submultiples of the units are formed by means

of the following prefixes:

4. the units listed below are used in the system, without excluding others

which might be added later.

Supplementary units

plane angle radian rad

solid angle steradian sr

* The CGPM later

abrogated certain of

its decisions and

extended the list of

prefixes: see notes

below.

The name and

symbol for the unit

of thermodynamic

temperature were

modified by the

13th CGPM (1967-

1968, Resolution 3,

see p. 34).

A seventh base

unit, the mole,

was adopted by the

14th CGPM (1971,

Resolution 3,

see p. 35).

Further prefixes

were adopted

by the 12th CGPM

(1964, Resolution 8,

see p. 41), the

15th CGPM (1975,

Resolution 10,

see p. 41) and

the 19th CGPM

(1991, Resolution 4,

see p. 41).

The 20th CGPM

abrogated the class of

supplementary units

in the SI (1995,

Resolution 8, see

p. 40). These are

now considered to be

derived units.

Prefix Prefix

Multiplying factor Symbol Multiplying factor Symbol

1 000 000 000 000 = 1012 tera T 0.1 = 10–1 deci d

1 000 000 000 = 109 giga G 0.01 = 10–2 centi c

1 000 000 = 106 mega M 0.001 = 10–3 milli m

1 000 = 103 kilo k 0.000 001 = 10–6 micro 

100 = 102 hecto h 0.000 000 001 = 10–9 nano n

10 = 101 deka da 0.000 000 000 001 = 10–12 pico p
Appendix 1. Decisions of the CGPM and the CIPM • 25

Derived units

area square meter m2

volume cubic meter m3

frequency hertz Hz 1/s

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

speed, velocity meter per second m/s

angular velocity radian per second rad/s

acceleration meter per second squared m/s2

angular acceleration radian per second squared rad/s2

force newton N kg  m/s2

pressure (mechanical stress) newton per square meter N/m2

kinematic viscosity square meter per second m2/s

dynamic viscosity newton-second

per square meter N  s/m2

work, energy,

quantity of heat joule J N  m

power watt W J/s

quantity of electricity coulomb C A  s

tension (voltage),

potential difference,

electromotive force volt V W/A

electric field strength volt per meter V/m

electric resistance ohm  V/A

capacitance farad F A  s/V

magnetic flux weber Wb V  s

inductance henry H V  s/A

magnetic flux density tesla T Wb/m2

magnetic field strength ampere per meter A/m

magnetomotive force ampere A

luminous flux lumen lm cd  sr

luminance candela per square meter cd/m2

illuminance lux lx lm/m2

■ CIPM, 1969, Recommendation 1 (PV, 37, 30 and Metrologia, 1970, 6, 66):

Syste`me International d’Unite ́s, Rules for application of Resolution 12 of the 11th

CGPM (1960)*

The Comite ́ International des Poids et Mesures,

considering that Resolution 12 of the 11th Confe ́ rence Ge ́ ne ́ rale des Poids et

Mesures (CGPM) (1960), concerning the Syste`me International d’Unite ́ s, has

provoked discussions on certain of its aspects,

declares

1. the base units, the supplementary units and the derived units of the

Syste`me International d’Unite ́ s, which form a coherent set, are denoted by

the name “SI units”;

2. the prefixes adopted by the CGPM for the formation of decimal multiples

and submultiples of SI units are called “SI prefixes”;

The 13th CGPM

(1967-1968,

Resolution 6, see

p. 37) specified

other units which

should be added to

this list. In principle,

this list of derived

units is without limit.

* The 20th CGPM

decided to abrogate

the class of

supplementary

units in the SI

(1995, Resolution 8,

see p. 40).
26 • Appendix 1. Decisions of the CGPM and the CIPM

and recommends

3. the use of SI units and of their decimal multiples and submultiples

whose names are formed by means of SI prefixes.

Note: The name “supplementary units,’’ appearing in Resolution 12 of the 11th CGPM (and

in the present Recommendation), is given to SI units for which the General Conference

declines to state whether they are base units or derived units.

2 Decisions relating to base units of the International System

2.1 Length

■ 1st CGPM, 1889 (CR, 34-38): sanction of the international prototypes of

the meter and the kilogram*

The Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures,

considering

• the “Compte rendu of the President of the Comite ́ International des

Poids et Mesures (CIPM)” and the “Report of the CIPM,” which show

that, by the collaboration of the French section of the International

Meter Commission and of the CIPM, the fundamental measurements

of the international and national prototypes of the meter and of the

kilogram have been made with all the accuracy and reliability which

the present state of science permits;

• that the international and national prototypes of the meter and the

kilogram are made of an alloy of platinum with 10 per cent iridium, to

within 0.0001;

• the equality in length of the international Meter and the equality in

mass of the international Kilogram with the length of the Meter and the

mass of the Kilogram kept in the Archives of France;

• that the differences between the national Meters and the international

Meter lie within 0.01 millimeter and that these differences are based

on a hydrogen-thermometer scale which can always be reproduced

thanks to the stability of hydrogen, provided identical conditions are

secured;

• that the differences between the national Kilograms and the

international Kilogram lie within 1 milligram;

• that the international Meter and Kilogram and the national Meters and

Kilograms fulfill the requirements of the Meter Convention,

sanctions

A. As regards international prototypes:

1. The Prototype of the meter chosen by the CIPM. This prototype, at the

temperature of melting ice, shall henceforth represent the metric unit

of length.

2. The Prototype of the kilogram adopted by the CIPM. This prototype

shall henceforth be considered as the unit of mass.

3. The hydrogen-thermometer centigrade scale in terms of which the

equations of the prototype Meters have been established.

B. As regards national prototypes:

...

* The definition of

the meter was

abrogated in 1960

(11th CGPM,

Resolution 6, given

below).
Appendix 1. Decisions of the CGPM and the CIPM • 27

■ 7th CGPM, 1927 (CR, 49): definition of the meter by the international

Prototype*

The unit of length is the meter, defined by the distance, at 0, between the

axes of the two central lines marked on the bar of platinum-iridium kept at

the Bureau International des Poids et Mesures and declared Prototype of

the meter by the 1st Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures, this bar

being subject to standard atmospheric pressure and supported on two

cylinders of at least one centimeter diameter, symmetrically placed in the

same horizontal plane at a distance of 571 mm from each other.

■ 11th CGPM, 1960, Resolution 6 (CR, 85): definition of the meter*

The 11th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering

• that the international Prototype does not define the meter with an

accuracy adequate for the present needs of metrology,

• that it is moreover desirable to adopt a natural and indestructible

standard,

decides

1. The meter is the length equal to 1 650 763.73 wavelengths in vacuum

of the radiation corresponding to the transition between the levels 2p10

and 5d5 of the krypton 86 atom.

2. The definition of the meter in force since 1889, based on the

international Prototype of platinum-iridium, is abrogated.

3. The international Prototype of the meter sanctioned by the 1st CGPM

in 1889 shall be kept at the BIPM under the conditions specified in

1889.

■ 15th CGPM, 1975, Resolution 2 (CR, 103 and Metrologia, 1975, 11,

179-180): recommended value for the speed of light

The 15th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures,

considering the excellent agreement among the results of wavelength

measurements on the radiations of lasers locked on a molecular

absorption line in the visible or infrared region, with an uncertainty

estimated at  4  10–9 which corresponds to the uncertainty of the

realization of the meter,

considering also the concordant measurements of the frequencies of

several of these radiations,

recommends the use of the resulting value for the speed of propagation of

electromagnetic waves in vacuum c = 299 792 458 meters per second.

■ 17th CGPM, 1983, Resolution 1 (CR, 97 and Metrologia, 1984, 20, 25):

definition of the meter

The 17th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering

• that the present definition does not allow a sufficiently precise

realization of the meter for all requirements,

* This definition

was abrogated

in 1960 (11th CGPM,

Resolution 6, given

below).

* This definition

was abrogated

in 1983 (17th CGPM,

Resolution 1, given

below).

The relative

uncertainty quoted

here is believed to

correspond to three

standard deviations in

the data considered.
28 • Appendix 1. Decisions of the CGPM and the CIPM

• that progress made in the stabilization of lasers allows radiations to be

obtained that are more reproducible and easier to use than the

standard radiation emitted by a krypton 86 lamp,

• that progress made in the measurement of the frequency and

wavelength of these radiations has resulted in concordant

determinations of the speed of light whose accuracy is limited

principally by the realization of the present definition of the meter,

• that wavelengths determined from frequency measurements and a

given value for the speed of light have a reproducibility superior to

that which can be obtained by comparison with the wavelength of the

standard radiation of krypton 86,

• that there is an advantage, notably for astronomy and geodesy, in

maintaining unchanged the value of the speed of light recommended

in 1975 by the 15th CGPM in its Resolution 2 (c = 299 792 458 m/s),

• that a new definition of the meter has been envisaged in various

forms all of which have the effect of giving the speed of light an exact

value, equal to the recommended value, and that this introduces no

appreciable discontinuity into the unit of length, taking into account the

relative uncertainty of 4  10–9 of the best realizations of the present

definition of the meter,

• that these various forms, making reference either to the path traveled

by light in a specified time interval or to the wavelength of a radiation

of measured or specified frequency, have been the object of

consultations and deep discussions, have been recognized as being

equivalent and that a consensus has emerged in favour of the first

form,

• that the Consultative Committee pour la De ́ finition du Me`tre (CCDM)

is now in a position to give instructions for the practical realization

of such a definition, instructions which could include the use of the

orange radiation of krypton 86 used as standard up to now, and which

may in due course be extended or revised,

decides

1. 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.

2. The definition of the meter in force since 1960, based upon the

transition between the levels 2p10 and 5d5 of the atom of krypton 86, is

abrogated.

■ 17th CGPM, 1983, Resolution 2 (CR, 98 and Metrologia, 1984, 20, 25-26):

on the realization of the definition of the meter

The 17th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures

invites the Comite ́ International des Poids et Mesures

• to draw up instructions for the practical realization of the new definition

of the meter,

• to choose radiations which can be recommended as standards of

wavelength for the interferometric measurement of length and to draw

up instructions for their use,

• to pursue studies undertaken to improve these standards.

The relative

uncertainty given

here corresponds to

three standard

deviations in the data

considered.

See

Recommendation 1

(CI-1997) of the

CIPM on the revision

of the practical

realization of the

definition of the

meter (Appendix 2,

p. 45).
Appendix 1. Decisions of the CGPM and the CIPM • 29

2.2 Mass

■ 1st CGPM, 1889 (CR, 34-38): sanction of the international prototypes of

the meter and the kilogram

(see p. 26)

■ 3rd CGPM, 1901 (CR, 70): declaration on the unit of mass and on the

definition of weight; conventional value of gn

†

Taking into account the decision of the Comite ́ International des Poids et

Mesures of 15 October 1887, according to which the kilogram has been

defined as unit of mass;

Taking into account the decision contained in the sanction of the

prototypes of the Metric System, unanimously accepted by the Confe ́ rence

Ge ́ ne ́ rale des Poids et Mesures on 26 September 1889;

Considering the necessity to put an end to the ambiguity which in current

practice still exists on the meaning of the word weight, used sometimes for

mass, sometimes for mechanical force;

The Conference declares

1. The kilogram is the unit of mass; it is equal to the mass of the

international prototype of the kilogram;

2. The word “weight” denotes a quantity of the same nature as a “force”:

the weight of a body is the product of its mass and the acceleration

due to gravity; in particular, the standard weight of a body is the

product of its mass and the standard acceleration due to gravity;‡

3. The value adopted in the International Service of Weights and

Measures for the standard acceleration due to gravity is

980.665 cm/s2

, value already stated in the laws of some countries.

■ CIPM, 1967, Recommendation 2 (PV, 35, 29 and Metrologia, 1968, 4, 45):

decimal multiples and submultiples of the unit of mass

The Comite ́ International des Poids et Mesures,

considering that the rule for forming names of decimal multiples and

submultiples of the units of paragraph 3 of Resolution 12 of the 11th

Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM) (1960) might be

interpreted in different ways when applied to the unit of mass,

declares that the rules of Resolution 12 of the 11th CGPM apply to the

kilogram in the following manner: the names of decimal multiples and

submultiples of the unit of mass are formed by attaching prefixes to the

word “gram.”

2.3 Time

■ CIPM, 1956, Resolution 1 (PV, 25, 77): definition of the unit of time

(second)*

In virtue of the powers invested in it by Resolution 5 of the 10th Confe ́ rence

Ge ́ ne ́ rale des Poids et Mesures, the Comite ́ International des Poids et

Mesures,

considering

1. that the 9th General Assembly of the International Astronomical Union

(Dublin, 1955) declared itself in favor of linking the second to the

tropical year,

† Editor’s note: gn is the quantity symbol for the standard acceleration due to gravity.

‡ Editor’s note: In the United States the term “weight” is used to mean both force and mass. In science and

technology this declaration of the 1st CGPM is usually followed, with the newton (N) the SI unit of force and

thus weight. In commercial and everyday use, and especially in common parlance, weight is usually used as

a synonym for mass, the SI unit of which is the kilogram (kg).

This value of gn

was the conventional

reference for

calculating the now

obsolete unit

kilogram force.

* This definition

was abrogated in

1967 (13th CGPM,

Resolution 1, given

below).
30 • Appendix 1. Decisions of the CGPM and the CIPM

2. that, according to the decisions of the 8th General Assembly of

the International Astronomical Union (Rome, 1952), the second of

ephemeris time (ET) is the fraction

12 960 276 813

408 986 496 10–9 of the tropical year for 1900 January 0 at 12 h ET,

decides “The second is the fraction 1/31 556 925.9747 of the tropical year

for 1900 January 0 at 12 hours ephemeris time.’’

■ 11th CGPM, 1960, Resolution 9 (CR, 86): definition of the unit of time

(second)*

The 11th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering

• the powers given to the Comite ́ International des Poids et Mesures

(CIPM) by the 10th CGPM to define the fundamental unit of time,

• the decision taken by the CIPM in 1956,

ratifies the following definition:

“The second is the fraction 1/31 556 925.9747 of the tropical year for 1900

January 0 at 12 hours ephemeris time.”

■ 12th CGPM, 1964, Resolution 5 (CR, 93): atomic standard of frequency

The 12th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering

• that the 11th CGPM noted in its Resolution 10 the urgency, in the

interests of accurate metrology, of adopting an atomic or molecular

standard of time interval,

• that, in spite of the results already obtained with cesium atomic

frequency standards, the time has not yet come for the CGPM to adopt

a new definition of the second, base unit of the Syste`me International

d’Unite ́ s, because of the new and considerable improvements likely to

be obtained from work now in progress,

considering also that it is not desirable to wait any longer before time

measurements in physics are based on atomic or molecular frequency

standards,

empowers the Comite ́ International des Poids et Mesures to name the

atomic or molecular frequency standards to be employed for the time

being,

requests the organizations and laboratories knowledgeable in this

field to pursue work connected with a new definition of the second.

■ Declaration of the CIPM, 1964 (PV, 32, 26 and CR, 93)

The Comite ́ International des Poids et Mesures,

empowered by Resolution 5 of the 12th Confe ́ rence Ge ́ ne ́ rale des

Poids et Mesures to name atomic or molecular frequency standards for

temporary use for time measurements in physics,

declares that the standard to be employed is the transition between the

hyperfine levels F = 4, M = 0 and F = 3, M = 0 of the ground state 2

S1/2 of

the cesium 133 atom, unperturbed by external fields, and that the

frequency of this transition is assigned the value 9 192 631 770 hertz.

* This definition

was abrogated in

1967 (13th CGPM,

Resolution 1, given

below).
Appendix 1. Decisions of the CGPM and the CIPM • 31

■ 13th CGPM, 1967-1968, Resolution 1 (CR, 103 and Metrologia, 1968,

4, 43): SI unit of time (second)

The 13th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering

• that the definition of the second adopted by the Comite ́ International

des Poids et Mesures (CIPM) in 1956 (Resolution 1) and ratified by

Resolution 9 of the 11th CGPM (1960), later upheld by Resolution 5

of the 12th CGPM (1964), is inadequate for the present needs of

metrology,

• that at its meeting of 1964 the Comite ́ International des Poids et

Mesures (CIPM), empowered by Resolution 5 of the 12th CGPM

(1964), recommended, in order to fulfill these requirements, a cesium

atomic frequency standard for temporary use,

• that this frequency standard has now been sufficiently tested and

found sufficiently accurate to provide a definition of the second

fulfilling present requirements,

• that the time has now come to replace the definition now in force of

the unit of time of the Syste`me International d’Unite ́ s by an atomic

definition based on that standard,

decides

1. The SI unit of time is the second defined as follows:

“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”;

2. Resolution 1 adopted by the CIPM at its meeting of 1956 and

Resolution 9 of the 11th CGPM are now abrogated.

■ 14th CGPM, 1971, Resolution 1 (CR, 77 and Metrologia, 1972, 8, 35):

International Atomic Time, function of CIPM

The 14th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering

• that the second, unit of time of the Syste`me International d’Unite ́ s, has

since 1967 been defined in terms of a natural atomic frequency, and

no longer in terms of the time scales provided by astronomical

motions,

• that the need for an International Atomic Time (TAI) scale is a

consequence of the atomic definition of the second,

• that several international organizations have ensured and are still

successfully ensuring the establishment of the time scales based on

astronomical motions, particularly thanks to the permanent services of

the Bureau International de l’Heure (BIH),

• that the BIH has started to establish an atomic time scale of

recognized quality and proven usefulness,

• that the atomic frequency standards for realizing the second have

been considered and must continue to be considered by the Comite ́

International des Poids et Mesures (CIPM) helped by a Consultative

Committee, and that the unit interval of the International Atomic Time

scale must be the second realized according to its atomic definition,

At its 1997 meeting,

the CIPM affirmed

that this definition

refers to a

cesium atom in

its ground state at a

thermodynamic

temperature of 0 K.

Editor’s note: See

Section 2.1.1.3, p. 6,

for the current wording

of the CIPM

affirmation.
32 • Appendix 1. Decisions of the CGPM and the CIPM

• that all the competent international scientific organizations and the

national laboratories active in this field have expressed the wish that

the CIPM and the CGPM should give a definition of International

Atomic Time, and should contribute to the establishment of the

International Atomic Time scale,

• that the usefulness of International Atomic Time entails close

coordination with the time scales based on astronomical motions,

requests the CIPM

1. to give a definition of International Atomic Time,

2. to take the necessary steps, in agreement with the international organizations concerned, to ensure that available scientific competence

and existing facilities are used in the best possible way to realize the

International Atomic Time scale and to satisfy the requirements of

users of International Atomic Time.

■ 15th CGPM, 1975, Resolution 5 (CR, 104 and Metrologia, 1975, 11, 180):

Coordinated Universal Time (UTC)

The 15th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures,

considering that the system called “Coordinated Universal Time” (UTC) is

widely used, that it is broadcast in most radio transmissions of time signals,

that this wide diffusion makes available to the users not only frequency

standards but also International Atomic Time and an approximation to

Universal Time (or, if one prefers, mean solar time),

notes that this Coordinated Universal Time provides the basis of civil time,

the use of which is legal in most countries,

judges that this usage can be strongly endorsed.

2.4 Electric current

■ CIPM, 1946, Resolution 2 (PV, 20, 129-137): definitions of electric units

...

4. (A) Definitions of the mechanical units which enter the definitions of

electric units:

Unit of force—The unit of force [in the MKS (meter, kilogram, second)

system] is the force which gives to a mass of 1 kilogram an

acceleration of 1 meter per second, per second.

Joule (unit of energy or work)—The joule is the work done when the point

of application of 1 MKS unit of force [newton] moves a distance of

1 meter in the direction of the force.

Watt (unit of power)—The watt is the power which in one second gives rise

to energy of 1 joule.

(B) Definitions of electric units. The Comite ́ International des Poids et

Mesures (CIPM) accepts the following propositions which define the

theoretical value of the electric units:

Ampere (unit of electric current)—The ampere is that constant current

which, if maintained in two straight parallel conductors of infinite

For the CIPM

and CCDS

(now the CCTF)

recommendations

concerning the

definition of

International Atomic

Time, see

Appendix 2, p. 53.

The definitions

contained in this

Resolution were

ratified by the

9th CGPM, 1948

(CR, 49), which

also adopted the

name newton

(Resolution 7) for

the MKS unit of

force.
Appendix 1. Decisions of the CGPM and the CIPM • 33

length, of negligible circular cross-section, and placed 1 meter apart in

vacuum, would produce between these conductors a force equal to

210–7 MKS unit of force [newton] per meter of length.

Volt (unit of potential difference and of electromotive force)—The volt is the

potential difference between two points of a conducting wire carrying a

constant current of 1 ampere, when the power dissipated between

these points is equal to 1 watt.

Ohm (unit of electric resistance)—The ohm is the electric resistance

between two points of a conductor when a constant potential

difference of 1 volt, applied to these points, produces in the conductor

a current of 1 ampere, the conductor not being the seat of any

electromotive force.

Coulomb (unit of quantity of electricity)—The coulomb is the quantity of

electricity carried in 1 second by a current of 1 ampere.

Farad (unit of capacitance)—The farad is the capacitance of a capacitor

between the plates of which there appears a potential difference of

1 volt when it is charged by a quantity of electricity of 1 coulomb.

Henry (unit of electric inductance)—The henry is the inductance of a

closed circuit in which an electromotive force of 1 volt is produced

when the electric current in the circuit varies uniformly at the rate of

1 ampere per second.

Weber (unit of magnetic flux)—The weber is the magnetic flux which,

linking a circuit of one turn, would produce in it an electromotive force

of 1 volt if it were reduced to zero at a uniform rate in 1 second.

■ 14th CGPM, 1971 (CR, 78): pascal, siemens

The 14th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures adopted the special

names “pascal” (symbol Pa), for the SI unit newton per square meter, and

“siemens” (symbol S), for the SI unit of electric conductance [reciprocal

ohm].

2.5 Thermodynamic temperature

■ 9th CGPM, 1948, Resolution 3 (CR, 55 and 63): triple point of water;

thermodynamic scale with a single fixed point; unit of quantity of heat

(joule)

1. With present-day techniques, the triple point of water is capable of

providing a thermometric reference point with an accuracy higher than

can be obtained from the melting point of ice.

In consequence the Committe ́ Consultatif de Thermome ́ trie et

Calorime ́ trie (CCTC) considers that the zero of the centesimal

thermodynamic scale must be defined as the temperature 0.0100

degree below that of the triple point of water.

2. The CCTC accepts the principle of an absolute thermodynamic scale

with a single fundamental fixed point, at present provided by the triple

point of pure water, the absolute temperature of which will be fixed at a

later date. The introduction of this new scale does not affect in

any way the use of the International Scale, which remains the

recommended practical scale.
34 • Appendix 1. Decisions of the CGPM and the CIPM

3. The unit of quantity of heat is the joule.

Note: It is requested that the results of calorimetric experiments be as far as possible

expressed in joules. If the experiments are made by comparison with the rise of temperature

of water (and that, for some reason, it is not possible to avoid using the calorie), the

information necessary for conversion to joules must be provided. The CIPM, advised by the

CCTC, should prepare a table giving, in joules per degree, the most accurate values that can

be obtained from experiments on the specific heat of water.

A table, prepared in response to this request, was approved and published

by the CIPM in 1950 (PV, 22, 92).

■ CIPM, 1948 (PV, 21, 88) and 9th CGPM, 1948 (CR, 64): adoption of

“degree Celsius”

From three names (“degree centigrade,” “centesimal degree,” “degree

Celsius”) proposed to denote the degree of temperature, the CIPM has

chosen “degree Celsius” (PV, 21, 88).

This name is also adopted by the 9th CGPM (CR, 64).

■ 10th CGPM, 1954, Resolution 3 (CR, 79): definition of the

thermodynamic temperature scale*

The 10th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures decides to define the

thermodynamic temperature scale by choosing the triple point of water as

the fundamental fixed point, and assigning to it the temperature 273.16

degrees Kelvin, exactly.

■ 10th CGPM, 1954, Resolution 4 (CR, 79): definition of the standard

atmosphere

The 10th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM), having

noted that the definition of the standard atmosphere given by the

9th CGPM when defining the International Temperature Scale led some

physicists to believe that this definition of the standard atmosphere was

valid only for accurate work in thermometry,

declares that it adopts, for general use, the definition:

1 standard atmosphere = 1 013 250 dynes per square centimeter,

i.e., 101 325 newtons per square meter.

■ 13th CGPM, 1967-1968, Resolution 3 (CR, 104 and Metrologia, 1968, 4,

43): SI unit of thermodynamic temperature (kelvin)*

The 13th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering

• the names “degree Kelvin” and “degree,” the symbols “K” and “deg,”

and the rules for their use given in Resolution 7 of the 9th CGPM

(1948), in Resolution 12 of the 11th CGPM (1960), and the decision

taken by the Comite ́ International des Poids et Mesures in 1962 (PV,

30, 27),

• that the unit of thermodynamic temperature and the unit of

temperature interval are one and the same unit, which ought to be

denoted by a single name and a single symbol,

* The 13th CGPM

(1967-1968,

Resolution 4, given

below) explicitly

defined the kelvin.

* At its 1980 meeting

the CIPM approved

the report of the

7th meeting of the

CCU which requested

that the use of

the symbols “K” and

“deg” no longer be

permitted.
Appendix 1. Decisions of the CGPM and the CIPM • 35

decides

1. the unit of thermodynamic temperature is denoted by the name

“kelvin” and its symbol is “K”;

2. the same name and the same symbol are used to express a

temperature interval;

3. a temperature interval may also be expressed in degrees Celsius;

4. the decisions mentioned in the opening paragraph concerning the

name of the unit of thermodynamic temperature, its symbol and

the designation of the unit to express an interval or a difference of

temperatures are abrogated, but the usages which derive from these

decisions remain permissible for the time being.

■ 13th CGPM, 1967-1968, Resolution 4 (CR, 104 and Metrologia, 1968,

4, 43): definition of the SI unit of thermodynamic temperature (kelvin)*

The 13th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering that it is useful to formulate more explicitly the definition of the

unit of thermodynamic temperature contained in Resolution 3 of the 10th

CGPM (1954),

decides to express this definition as follows:

“The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of

the thermodynamic temperature of the triple point of water.”

2.6 Amount of substance

■ 14th CGPM, 1971, Resolution 3 (CR, 78 and Metrologia, 1972, 8, 36):

SI unit of amount of substance (mole)*

The 14th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering the advice of the International Union of Pure and Applied

Physics, of the International Union of Pure and Applied Chemistry, and of

the International Organization for Standardization, concerning the need to

define a unit of amount of substance,

decides

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; its symbol is “mol.”

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.

3. The mole is a base unit of the Syste`me International d’Unite ́ s.

2.7 Luminous intensity

■ CIPM, 1946, Resolution (PV, 20, 119-122): definitions of photometric

units*

...

4. The photometric units may be defined as follows:

New candle (unit of luminous intensity)—The value of the new candle

is such that the brightness of the full radiator at the temperature of

solidification of platinum is 60 new candles per square centimeter.

* See

Recommendation 5

(CI-1989) of

the CIPM on the

International

Temperature Scale of

1990 (Appendix 2,

p. 59).

* At its 1980

meeting, the CIPM

approved the report

of the 7th meeting

of the CCU (1980)

specifying that,

in this definition,

it is understood that

unbound atoms

of carbon 12, at rest

and in their ground

state, are referred to.

* The two definitions

contained in this

Resolution were ratified

by the 9th CGPM (1948),

which also approved the

name candela given to the

“new candle” (CR, 54).

For the lumen the qualifier
36 • Appendix 1. Decisions of the CGPM and the CIPM

New lumen (unit of luminous flux)—The new lumen is the luminous flux

emitted in unit solid angle (steradian) by a uniform point source having

a luminous intensity of 1 new candle.

5 ...

■ 13th CGPM, 1967-1968, Resolution 5 (CR, 104 and Metrologia, 1968, 4,

43-44): SI unit of luminous intensity (candela)*

The 13th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering

• the definition of the unit of luminous intensity ratified by the 9th CGPM

(1948) and contained in the “Resolution concerning the change of

photometric units” adopted by the Comite ́ International des Poids et

Mesures in 1946 (PV, 20, 119) in virtue of the powers conferred by the

8th CGPM (1933),

• that this definition fixes satisfactorily the unit of luminous intensity, but

that its wording may be open to criticism,

decides to express the definition of the candela as follows:

“The candela is the luminous intensity, in the perpendicular direction, of a

surface of 1/600 000 square metre of a black-body at the temperature of

freezing platinum under a pressure of 101 325 newtons per square meter.”

■ 16th CGPM, 1979, Resolution 3 (CR, 100 and Metrologia, 1980, 16, 56):

SI unit of luminous intensity (candela)

The 16th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering

• that despite the notable efforts of some laboratories there remain

excessive divergences between the results of realizations of the

candela based upon the present black body primary standard,

• that radiometric techniques are developing rapidly, allowing precisions

that are already equivalent to those of photometry and that these

techniques are already in use in national laboratories to realize the

candela without having to construct a black body,

• that the relation between luminous quantities of photometry and

radiometric quantities, namely the value of 683 lumens per watt for the

spectral luminous efficacy of monochromatic radiation of frequency

5401012 hertz, has been adopted by the Comite ́ International des

Poids et Mesures (CIPM) in 1977,

• that this value has been accepted as being sufficiently accurate for the

system of luminous photopic quantities, that it implies a change of only

about 3 % for the system of luminous scotopic quantities, and that it

therefore ensures satisfactory continuity,

• that the time has come to give the candela a definition that will allow

an improvement in both the ease of realization and the precision of

photometric standards, and that applies to both photopic and scotopic

photometric quantities and to quantities yet to be defined in the

mesopic field,

“new” was later

abandoned. This

definition was modified

by the 13th CGPM

(1967-1968, Resolution 5,

given below).

* This definition

was abrogated by the

16th CGPM (1979,

Resolution 3, given

below).
Appendix 1. Decisions of the CGPM and the CIPM • 37

decides

1. The candela is the luminous intensity, in a given direction, of a source

that emits monochromatic radiation of frequency 5401012 hertz and

that has a radiant intensity in that direction of 1/683 watt per steradian.

2. The definition of the candela (at the time called new candle) adopted

by the CIPM in 1946 by reason of the powers conferred by the 8th

CGPM in 1933, ratified by the 9th CGPM in 1948, then amended by

the 13th CGPM in 1967, is abrogated.

3 Decisions relating to SI derived and supplementary units

3.1 SI derived units

■ 12th CGPM, 1964, Resolution 7 (CR, 94): curie*

The 12th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures,

considering that the curie has been used for a long time in many countries

as unit of activity for radionuclides,

recognizing that in the Syste`me International d’Unite ́ s (SI), the unit of this

activity is the second to the power of minus one (s–1),

accepts that the curie be still retained, outside SI, as unit of activity, with

the value 3.71010 s–1. The symbol for this unit is Ci.

■ 13th CGPM, 1967-1968, Resolution 6 (CR, 105 and Metrologia, 1968,

4, 44): SI derived units*

The 13th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering that it is useful to add some derived units to the list of

paragraph 4 of Resolution 12 of the 11th CGPM (1960),

decides to add:

■ 15th CGPM, 1975, Resolutions 8 and 9 (CR, 105 and Metrologia, 1975, 11,

180): SI units for ionizing radiation (becquerel, gray)*

The 15th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures,

by reason of the pressing requirement, expressed by the International

Commission on Radiation Units and Measurements (ICRU), to extend the

use of the Syste`me International d’Unite ́ s to radiological research and

applications, by reason of the need to make as easy as possible the use of

the units for nonspecialists,

taking into consideration also the grave risks of errors in therapeutic work,

adopts the following special name for the SI unit of activity:

becquerel, symbol Bq, equal to one reciprocal second (Resolution 8),

* The name

“becquerel” (Bq)

was adopted by the

15th CGPM (1975,

Resolution 8, given

below) for the SI unit

of activity:

1 Ci = 3.71010 Bq.

* The unit of activity

was given a special

name and symbol by

the 15th CGPM

(1975, Resolution 8,

given below).

* At its 1976

meeting, the CIPM

approved the report

of the 5th meeting

of the CCU (1976),

specifying that,

following the advice

of the ICRU, the

gray may also

be used to express

specific energy

imparted, kerma and

absorbed dose index.

wave number 1 per meter m–1

entropy joule per kelvin J/K

specific heat capacity joule per kilogram kelvin J/(kg  K)

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

radiant intensity watt per steradian W/sr

activity (of a radioactive source) 1 per second s–1
38 • Appendix 1. Decisions of the CGPM and the CIPM

adopts the following special name for the SI unit of ionizing radiation:

gray, symbol Gy, equal to one joule per kilogram (Resolution 9).

Note: The gray is the SI unit of absorbed dose. In the field of ionizing radiation the gray may

also be used with other physical quantities that are also expressed in joules per kilogram; the

Comite ́ Consultatif des Unite ́ s is made responsible for studying this matter in collaboration

with the competent international organizations.

■ 16th CGPM, 1979, Resolution 5 (CR, 100 and Metrologia, 1980, 16, 56):

special name for the SI unit of dose equivalent (sievert)*

The 16th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures,

considering

• the effort made to introduce SI units into the field of ionizing radiations,

• the risk to human beings of an underestimated radiation dose, a risk

that could result from a confusion between absorbed dose and dose

equivalent,

• that the proliferation of special names represents a danger for

the Syste`me International d’Unite ́ s and must be avoided in every

possible way, but that this rule can be broken when it is a matter of

safeguarding human health,

adopts the special name sievert, symbol Sv, for the SI unit of dose

equivalent in the field of radioprotection. The sievert is equal to the joule

per kilogram.

■ CIPM, 1984, Recommendation 1 (PV, 52, 31 and Metrologia, 1985, 21, 90):

concerning the sievert

The Comite ́ International des Poids et Mesures,

considering the confusion which continues to exist on the subject of

Resolution 5, approved by the 16th Confe ́ rence Ge ́ ne ́ rale des Poids et

Mesures (1979),

decides to introduce the following explanation in the brochure “Le

Syste`me International d’Unite ́ s (SI)’’:

The quantity dose equivalent H is the product of the absorbed dose D of

ionizing radiation and the dimensionless factors Q (quality factor) and N

(product of any other multiplying factors) stipulated by the International

Commission on Radiological Protection:

H=Q  N  D.

Thus, for a given radiation, the numerical value of H in joules per kilogram

may differ from that of D in joules per kilogram depending upon the values

of Q and N. In order to avoid any risk of confusion between the absorbed

dose D and the dose equivalent H, the special names for the respective

units should be used, that is, the name gray should be used instead of

joules per kilogram for the unit of absorbed dose D and the name sievert

instead of joules per kilogram for the unit of dose equivalent H.

* The CIPM (1984,

Recommendation 1)

decided to

accompany this

Resolution with an

explanation, given

below.
Appendix 1. Decisions of the CGPM and the CIPM • 39

■ 21st CGPM, 1999, Resolution 12: Special name for the SI derived unit

mole per second, the katal, for the expression of catalytic activity†

The 21st Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures,

considering

• the importance for human health and safety of facilitating the use of SI

units in the fields of medicine and biochemistry,

• that a non-SI unit called “unit,” symbol U, equal to 1 mol  min–1,

which is not coherent with the SI, has been in widespread use in

medicine and biochemistry since 1964 for expressing catalytic activity,

• that the absence of a special name for the SI coherent derived unit

mole per second has led to results of clinical measurements being

given in various local units,

• that the use of SI units in medicine and clinical chemistry is strongly

recommended by the international unions in these fields,

• that the International Federation of Clinical Chemistry and Laboratory

Medicine has asked the Consultative Committee for Units to

recommend the special name katal, symbol kat, for the SI unit mole

per second,

• that while the proliferation of special names respresents a danger for

the SI, exceptions are made in matters related to human health and

safety (15th General Conference, 1975, Resolutions 8 and 9, 16th

General Conference, 1979, Resolution 5),

noting that the name katal, symbol kat, has been used for the SI unit mole

per second for over thirty years to express catalytic activity,

decides to adopt the special name, katal, symbol kat, for the SI unit mole

per second to express catalytic activity, especially in the fields of medicine

and biochemistry, and

recommends that when the katal is used, the measurand be specified by

reference to the measurement procedure; the measurement procedure

must identify the indicator reaction.

3.2 SI supplementary units

■ CIPM, 1980, Recommendation 1 (PV, 48, 24 and Metrologia, 1981, 17, 72):

SI supplementary units (radian and steradian)*

The Comite ́ International des Poids et Mesures (CIPM),

taking into consideration Resolution 3 adopted by ISO/TC 12 in 1978 and

Recommendation U 1 (1980) adopted by the Comite ́ Consultatif des

Unite ́ s at its 7th meeting,

considering

• that the units radian and steradian are usually introduced into

expressions for units when there is need for clarification, especially

in photometry where the steradian plays an important role in

distinguishing between units corresponding to different quantities,

† Editor’s note: This resolution is given in Supplement 2000: addenda and corrigenda to the 7th edition

(1998); June 2000.

* The class of SI

supplementary units

was abrogated

by decision of the

20th CGPM (1995,

resolution 8 given

below).
40 • Appendix 1. Decisions of the CGPM and the CIPM

• that in the equations used one generally expresses plane angle as the

ratio of two lengths and solid angle as the ratio between an area and

the square of a length, and consequently that these quantities are

treated as dimensionless quantities,

• that the study of the formalisms in use in the scientific field shows that

none exists which is at the same time coherent and convenient and in

which the quantities plane angle and solid angle might be considered

as base quantities,

considering also

• that the interpretation given by the CIPM in 1969 for the class of

supplementary units introduced in Resolution 12 of the 11th

Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM) in 1960 allows

the freedom of treating the radian and the steradian as SI base units,

• that such a possibility compromises the internal coherence of the SI

based on only seven base units,

decides

• to interpret the class of supplementary units in the International

System as a class of dimensionless derived units for which the

CGPM allows the freedom of using or not using them in expressions

for SI derived units.

■ 20th CGPM, 1995, Resolution 8 (CR, 223 and Metrologia, 1996, 33, 83):

elimination of the class of supplementary units in the SI

The 20th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering

• that the 11th Confe ́ rence Ge ́ ne ́ rale in 1960 in its Resolution 12,

establishing the Syste`me International d’Unite ́ s, SI, distinguished

between three classes of SI units: the base units, the derived units,

and the supplementary units, the last of these comprising the radian

and the steradian,

• that the status of the supplementary units in relation to the base units

and the derived units gave rise to debate,

• that the Comite ́ International des Poids et Mesures, in 1980,

having observed that the ambiguous status of the supplementary

units compromises the internal coherence of the SI, has in its

Recommendation 1 (CI-1980) interpreted the supplementary units, in

the SI, as dimensionless derived units,

approving the interpretation given by the Comite ́ International in 1980,

decides

• to interpret the supplementary units in the SI, namely the radian and

the steradian, as dimensionless derived units, the names and symbols

of which may, but need not, be used in expressions for other SI derived

units, as is convenient,

• and, consequently, to eliminate the class of supplementary units as a

separate class in the SI.
Appendix 1. Decisions of the CGPM and the CIPM • 41

4 Decisions concerning terminology and the acceptance

of units for use with the SI

4.1 SI prefixes

■ 12th CGPM, 1964, Resolution 8 (CR, 94): SI prefixes femto and atto*

The 12th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM)

decides to add to the list of prefixes for the formation of names of multiples

and submultiples of units, adopted by the 11th CGPM, Resolution 12,

paragraph 3, the following two new prefixes:

■ 15th CGPM, 1975, Resolution 10 (CR, 106 and Metrologia, 1975, 11,

180-181): SI prefixes peta and exa*

The 15th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM)

decides to add to the list of SI prefixes to be used for multiples, which

was adopted by the 11th CGPM, Resolution 12, paragraph 3, the two

following prefixes:

■ 19th CGPM, 1991, Resolution 4 (CR, 185 and Metrologia, 1992, 29, 3):

SI prefixes zetta, zepto, yotta and yocto

The 19th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM)

decides to add to the list of SI prefixes to be used for multiples and

submultiples of units, adopted by the 11th CGPM, Resolution 12,

paragraph 3, the 12th CGPM, Resolution 8 and the 15th CGPM,

Resolution 10, the following prefixes:

4.2 Unit symbols and numbers

■ 9th CGPM, 1948, Resolution 7 (CR, 70): writing and printing of unit

symbols and of numbers*

Principles

Roman (upright) type, in general lower case, is used for symbols of units;

if, however, the symbols are derived from proper names, capital roman

type is used. These symbols are not followed by a period.

* New prefixes

were added by the

15th CGPM

(1975, Resolution 10,

given below).

* New prefixes

were added by the

19th CGPM

(1991, Resolution 4,

given below).

The name zepto and zetta

are derived from septo

suggesting the number

seven (the seventh power

of 103

) and the letter “z”

is substituted for the

letter “s” to avoid the

duplicate use of the letter

“s” as a symbol. The

names yocto and yotta are

derived from octo,

suggesting the number

eight (the eighth power

of 103

); the letter “y” is

added to avoid the use

of the letter “o” as a

symbol because it may

be confused with the

number zero.

* The CGPM abrogated

certain decisions on

units and terminology,

Multiplying factor Prefix Symbol

10–15 femto f

10–18 atto a

Multiplying factor Prefix Symbol

1015 peta P

1018 exa E

Multiplying factor Prefix Symbol

1021 zetta Z

10–21 zepto z

1024 yotta Y

10–24 yocto y
42 • Appendix 1. Decisions of the CGPM and the CIPM

In numbers, the comma (French practice) or the dot (British practice) is

used only to separate the integral part of numbers from the decimal part.

Numbers may be divided in groups of three in order to facilitate reading;

neither dots nor commas are ever inserted in the spaces between groups.

4.3 Unit names

■ 13th CGPM, 1967-1968, Resolution 7 (CR, 105 and Metrologia, 1968,

4, 44): abrogation of earlier decisions (micron, new candle)

The 13th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering that subsequent decisions of the General Conference

concerning the Syste`me International d’Unite ́ s are incompatible with parts

of Resolution 7 of the 9th CGPM (1948),

decides accordingly to remove from Resolution 7 of the 9th Conference:

1. the unit name “micron,” and the symbol “” which had been given to

that unit but which has now become a prefix;

2. the unit name “new candle.”

† Editor’s note: See footnote (e) of Table 6, p. 16. The name “tonne” appears in the original BIPM text.

in particular, micron,

degree absolute

and the terms

“degree” and “deg,”

13th CGPM (1967-

1968, Resolutions 7

and 3, see below

and p. 34), and the

liter, 16th CGPM

(1979, Resolution 6,

see p. 43).

Unit Symbol Unit Symbol

• meter m ampere A

• square meter m2 volt V

• cubic meter m3 watt W

• micron  ohm 

• liter l coulomb C

• gram g farad F

• metric ton† t henry H

second s hertz Hz

erg erg poise P

dyne dyn newton N

degree Celsius C • candela

(new candle) cd

• degree absolute K lux lx

calorie cal lumen lm

bar bar stilb sb

hour h

Notes

1. The symbols whose unit names are preceded by dots are those which had already been

adopted by a decision of the CIPM.

2. The symbol for the stere, the unit of volume for firewood, shall be “st” and not “s,” which

had been previously assigned to it by the CIPM.

3. To indicate a temperature interval or difference, rather than a temperature, the word

“degree” in full, or the abbreviation “deg,” must be used.
Appendix 1. Decisions of the CGPM and the CIPM • 43

4.4 Units accepted for use with the SI; an example: the liter

■ 3rd CGPM, 1901 (CR, 38-39): declaration concerning the definition of

the liter*

...

The Conference declares

1. The unit of volume, for high-accuracy determinations, is the volume

occupied by a mass of 1 kilogram of pure water, at its maximum

density and at standard atmospheric pressure: this volume is called

“liter.”

2. . . .

■ 11th CGPM, 1960, Resolution 13 (CR, 88): cubic decimeter and liter

The 11th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering

• that the cubic decimeter and the liter are unequal and differ by about

28 parts in 106

,

• that determinations of physical quantities which involve

measurements of volume are being made more and more accurately,

thus increasing the risk of confusion between the cubic decimeter and

the liter,

requests the Comite ́ International des Poids et Mesures to study the

problem and submit its conclusions to the 12th CGPM.

■ CIPM, 1961, Recommendation (PV, 29, 34): cubic decimeter and liter

The Comite ́ International des Poids et Mesures recommends that the

results of accurate measurements of volume be expressed in units of the

International System and not in liters.

■ 12th CGPM, 1964, Resolution 6 (CR, 93): liter

The 12th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

considering Resolution 13 adopted by the 11th CGPM in 1960 and the

Recommendation adopted by the Comite ́ International des Poids et

Mesures in 1961,

1. abrogates the definition of the liter given in 1901 by the 3rd CGPM,

2. declares that the word “liter” may be employed as a special name for

the cubic decimeter,

3. recommends that the name liter should not be employed to give the

results of high-accuracy volume measurements.

■ 16th CGPM, 1979, Resolution 6 (CR, 101 and Metrologia, 1980, 16, 56-57):

symbols for the liter

The 16th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures (CGPM),

recognizing the general principles adopted for writing the unit symbols in

Resolution 7 of the 9th CGPM (1948),

* This definition

was abrogated by

the 12th CGPM

(1964, Resolution 6,

given below).
44 • Appendix 1. Decisions of the CGPM and the CIPM

considering that the symbol l for the unit liter was adopted by the Comite ́

International des Poids et Mesures (CIPM) in 1879 and confirmed in the

same Resolution of 1948,

considering also that, in order to avoid the risk of confusion between the

letter l and the number 1, several countries have adopted the symbol L

instead of l for the unit liter,

considering that the name liter, although not included in the Syste`me

International d’Unite ́ s, must be admitted for general use with the System,

decides, as an exception, to adopt the two symbols l and L as symbols to

be used for the unit liter,

considering further that in the future only one of these two symbols should

be retained,

invites the CIPM to follow the development of the use of these two

symbols and to give the 18th CGPM its opinion as to the possibility of

suppressing one of them.

The CIPM,

in 1990, considered

that it was still

too early to choose

a single symbol

for the liter.
45

Appendix 2. Practical realization of the definitions

of some important units

This appendix concerns the practical realization of the definitions of some key units of

the SI. It lists CGPM and CIPM decisions relevant to current realizations and presents

the framework within which standards laboratories must work if units they realize are to

be in conformity with those defined by the SI.

1 Length

Recommendation 1 (CI-1997) was adopted by the Comite ́ International des Poids et

Mesures (CIPM) in 1997 to specify and update the rules for the practical realization of

the definition of the meter:

The Comite ́ International des Poids et Mesures,

recalling

• that in 1983 the 17th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures

(CGPM) adopted a new definition of the meter;

• that in the same year the CGPM invited the Comite ́ International des

Poids et Mesures (CIPM)

• to draw up instructions for the practical realization of the meter,

• to choose radiations which can be recommended as standards of

wavelength for the interferometric measurement of length and draw

up instructions for their use,

• to pursue studies undertaken to improve these standards and in

due course to extend or revise these instructions;

• that in response to this invitation the CIPM adopted Recommendation 1

(CI-1983) (mise en pratique of the definition of the meter) to the effect:

• that the meter should be realized by one of the following methods:

a) by means of the length l of the path travelled in vacuum by a plane

electromagnetic wave in a time t; this length is obtained from the

measured time t, using the relation l=c0  t and the value of the

speed of light in vacuum c0 = 299 792 458 m/s,

b) by means of the wavelength in vacuum of a plane

electromagnetic wave of frequency f; this wavelength is obtained

from the measured frequency f using the relation = c0/f and the

value of the speed of light in vacuum c0 = 299 792 458 m/s,

c) by means of one of the radiations from the list below, whose stated

wavelength in vacuum or whose stated frequency can be used with

Current practice is to

use c0 to denote the

speed of light in

vacuum (ISO 31).

In the original

Recommendation

of 1983, the symbol c

was used for this

purpose.
46 • Appendix 2. Practical realization of the definitions of some important units

the uncertainty shown, provided that the given specifications and accepted

good practice are followed;

• that in all cases any necessary corrections be applied to take

account of actual conditions such as diffraction, gravitation or

imperfection in the vacuum;

• that the CIPM had recommended a list of radiations for this purpose;

recalling also that in 1992 the CIPM revised the practical realization of the

definition of the meter;

considering

• that science and technology continue to demand improved accuracy in

the realization of the meter;

• that since 1992 work in national laboratories, in the BIPM and

elsewhere has identified new radiations and methods for their

realization which lead to lower uncertainties;

• that such work has also substantially reduced the uncertainty in the

determined value of the frequency and wavelength in vacuum of one

of the previously recommended radiations;

• that a revision of the list of recommended radiations is desirable

for many applications, which include not only the direct realization

of the meter by means of optical interferometry for practical length

measurement, but also spectroscopy, atomic and molecular physics

and the determination of fundamental physical constants;

recommends

• that the list of recommended radiations given by the CIPM in 1992

[Recommendation 3 (CI-1992)] be replaced by the list of radiations

given below;

• that to the rules for the realization of the meter the following note be

added concerning general relativity:

In the context of general relativity, the meter is considered a unit of

proper length. Its definition, therefore, applies only within a spatial

extent sufficiently small that the effects of the non-uniformity of the

gravitational field can be ignored. In this case, the effects to be taken

into account are those of special relativity only. The local methods for

the realization of the meter recommended in b) and c) provide the

proper meter but not necessarily that given in a). Method a) should,

therefore, be restricted to lengths l which are sufficiently short for the

effects predicted by general relativity to be negligible with respect to

the uncertainties of realization. For advice on the interpretation of

measurements in which this is not the case, see the report of

the CCDS working group on the application of general relativity to

metrology (Application of general relativity to metrology, Metrologia,

1997, 34, 261-290).
Appendix 2. Practical realization of the definitions of some important units • 47

CIPM list of approved radiations for the practical

realization of the meter, 1997:

frequencies and vacuum wavelengths

This list replaces those published in PV, 1983, 51, 25-28, 1992, 60, 141-144 and

Metrologia, 1984, 19, 165-166, 1993/94, 30, 523-541.

In this list, the values of the frequency f and of the vacuum wavelength  should

be related exactly by the relation f = c0, with c0 = 299 792 458 m/s, but the

values of  are rounded.

The data and analysis used for the compilation of this list are set out in the

associated Appendix: Source Data for the List of Recommended Radiations,

1997 and its Annotated Bibliography.

It should be noted that for several of the listed radiations, few independent

values are available, so the estimated uncertainties may not reflect all sources

of variability.

Each of the listed radiations can be replaced, without degrading the accuracy,

by a radiation corresponding to another component of the same transition or by

another radiation, when the frequency difference is known with sufficient

accuracy. It should be also noted that to achieve the uncertainties given here it

is not sufficient just to meet the specifications for the listed parameters. In

addition, it is necessary to follow the best practice concerning methods of

stabilization as described in numerous scientific and technical publications.

References to appropriate articles, illustrating accepted good practice for a

particular radiation, may be obtained by application to a member laboratory of

the CCDM or to the BIPM.

1. Recommended radiations of stabilized lasers

1.1 Absorbing atom 1

H, 1S – 2S, two-photon transition

The values f = 1 233 030 706 593.7 kHz

 = 243 134 624.6260 fm

with a relative standard uncertainty of 8.5 10–13 apply to radiation stabilized to

the two-photon transition in a cold hydrogen beam, corrected to zero laser

power, and for atoms which are effectively stationary, i.e., the values are

corrected for second-order Doppler shift.

Other hydrogen-absorbing transitions may be similarly used and are given in

Appendix M 3 to the CCDM Report.

1.2 Absorbing molecule 127I2, transition 43-0, P(13), component a3 (or s)

The values f = 582 490 603.37 MHz

= 514 673 466.4 fm

with a relative standard uncertainty of 2.5 10–10 apply to the radiation of an Ar+

laser stabilized with an iodine cell external to the laser, having a cold-finger

temperature of (–5  2) C.

For this Appendix,

see the CCDM

Report (1997).

Editor’s note:

See also

Metrologia, 1999,

36, 211-244.

At its 1997 meeting,

the CIPM changed

the name of the

Comite ́ Consultatif

pour la De ́finition

du Me`tre (CCDM) to

Comite ́ Consultatif

des Longueurs,

Consultative

Committee for

Length (CCL).

For the specification

of operating

conditions, such as

temperature,

modulation width and

laser power, the

symbols  refer

to a tolerance, not

an uncertainty.
48 • Appendix 2. Practical realization of the definitions of some important units

1.3 Absorbing molecule 127I2, transition 32-0, R(56), component a10

The values f = 563 260 223.48 MHz

 = 532 245 036.14 fm

with a relative standard uncertainty of 7 10–11 apply to the radiation of a

frequency-doubled Nd:YAG laser, stabilized with an iodine cell external to

the laser, having a cold-finger temperature between –10 C and –20 C.

Other 127I2 absorbing transitions close to this transition may also be used by

making reference to the following frequency differences, for which the standard

uncertainty is uc = 2 kHz.

1.4 Absorbing molecule 127I2, transition 26-0, R(12), component a9

The values f = 551 579 482.96 MHz

 = 543 516 333.1 fm

with a relative standard uncertainty of 2.5 10–10 apply to the radiation

of a frequency-stabilized He-Ne laser with an external iodine cell having a

cold-finger temperature of (0  2) C.

1.5 Absorbing molecule 127I2, transition 9-2, R(47), component a7 (or o)

The values f = 489 880 354.9 MHz

 = 611 970 770.0 fm

with a relative standard uncertainty of 3 10–10 apply to the radiation of a

He-Ne laser stabilized with an iodine cell, within or external to the laser, having

a cold-finger temperature of (–5  2) C.

1.6 Absorbing molecule 127I2, transition 11-5, R(127), component a13 (or i)

The values f = 473 612 214 705 kHz

 = 632 991 398.22 fm

with a relative standard uncertainty of 2.5 10–11 apply to the radiation of a

He-Ne laser with an internal iodine cell, stabilized using the third-harmonic

detection technique, subject to the conditions:

Wavelengths for 127I2 transitions

Transition Frequency difference

x [f(x) – f(32-0, R(56), a10)]/kHz

32-0, R(57), a1 –50 946 880.4

32-0, P(54), a1 –47 588 892.5

35-0, P(119), a1 –36 840 161.5

33-0, R(86), a1 –32 190 404.0

34-0, R(106), a1 –30 434 761.5

36-0, R(134), a1 –17 173 680.4

33-0, P(83), a21 –15 682 074.1

32-0, R(56), a10 0

32-0, P(53), a1 +2 599 708.0

Here, f(x) represents the frequency of the transition denoted x and f(32-0, R(56), a10) the

frequency of the reference transition.
Appendix 2. Practical realization of the definitions of some important units • 49

• cell-wall temperature (25  5) C;

• cold-finger temperature (15  0.2) C;

• frequency modulation width, peak to peak (6  0.3) MHz;

one-way intracavity beam power (i.e., the output power divided by the

transmittance of the output mirror) (10  5) mW for an absolute value

of the power shift coefficient 1.4 kHz/mW.

These conditions are by themselves insufficient to ensure that the stated

standard uncertainty will be achieved. It is also necessary for the optical

and electronic control systems to be operating with the appropriate technical

performance. The iodine cell may also be operated under relaxed conditions,

leading to the larger uncertainty specified in Appendix M 2 of the CCDM Report

(1997).

1.7 Absorbing molecule 127I2, transition 8-5, P(10), component a9 (or g)

The values f = 468 218 332.4 MHz

 = 640 283 468.7 fm

with a relative standard uncertainty of 4.5 10–10 apply to the radiation

of a He-Ne laser stabilized with an internal iodine cell having a cold-finger

temperature of (16  1) C and a frequency modulation width, peak to peak, of

(6  1) MHz.

1.8 Absorbing atom 40Ca, transition 1

S0 – 3P1; mJ = 0

The values f = 455 986 240 494.15 kHz

 = 657 459 439.2917 fm

with a relative standard uncertainty of 6 10–13 apply to the radiation of a laser

stabilized to Ca atoms. The values correspond to the mean frequency of the two

recoil-split components for atoms which are effectively stationary, i.e., the

values are corrected for second-order Doppler shift.

1.9 Absorbing ion 88Sr+

, transition 5 2S1/2 – 4 2D5/2

The values f = 444 779 044.04 MHz

 = 674 025 590.95 fm

with a relative standard uncertainty of 1.3 10–10 apply to the radiation of a

laser stabilized to the transition observed with a trapped and cooled strontium

ion. The values correspond to the centre of the Zeeman multiplet.

1.10 Absorbing atom 85Rb, 5S1/2 (F = 3) – 5D5/2 (F = 5), two-photon transition

The values f = 385 285 142 378 kHz

 = 778 105 421.22 fm

with a relative standard uncertainty of 1.3 10–11 apply to the radiation of a

laser stabilized to the center of the two-photon transition. The values apply to a

rubidium cell at a temperature below 100 C, are corrected to zero laser power,

and for second-order Doppler shift.

Other rubidium absorbing transitions may also be used, and are given in

Appendix M 3 to the CCDM Report.

1.11 Absorbing molecule CH4, transition 3, P(7), component F(2)

2

1.11.1 The values f = 88 376 181 600.18 kHz

 = 3 392 231 397.327 fm
50 • Appendix 2. Practical realization of the definitions of some important units

with a relative standard uncertainty of 3 10–12 apply to the radiation of a

He-Ne laser stabilized to the central component [(7-6) transition] of the resolved

hyperfine-structure triplet. The values correspond to the mean frequency of the

two recoil-split components for molecules which are effectively stationary, i.e.,

the values are corrected for second-order Doppler shift.

1.11.2 The values f = 88 376 181 600.5 kHz

 = 3 392 231 397.31 fm

with a relative standard uncertainty of 2.3 10–11 apply to the radiation of a

He-Ne laser stabilized to the center of the unresolved hyperfine structure of a

methane cell, within or external to the laser, held at room temperature and

subject to the following conditions:

• methane pressure 3 Pa;

• mean one-way intracavity surface power density (i.e., the output

power density divided by the transmittance of the output mirror)

104 W  m–2;

• radius of wavefront curvature 	1 m;

• inequality of power between counter-propagating waves 5 %;

• servo referenced to a detector placed at the output facing the laser

tube.

1.12 Absorbing molecule OsO4, transition in coincidence with the 12C16O2, R(12)

laser line

The values f = 29 096 274 952.34 kHz

 = 10 303 465 254.27 fm

with a relative standard uncertainty of 6 10–12 apply to the radiation of a CO2

laser stabilized with an external OsO4 cell at a pressure below 0.2 Pa.

Other transitions may also be used, and are given in Appendix M 3 of the CCDM

Report (1997).

2. Recommended values for radiations of spectral lamps and other sources

2.1 Radiation corresponding to the transition between the levels 2p10 and 5d5

of the atom of 86Kr

The value  = 605 780 210.3 fm

with a relative expanded uncertainty, U = kuc (k = 3), of 4 10–9 [equal to three

times the relative standard uncertainty of 1.3 10–9] , applies to the radiation

emitted by a discharge lamp operated under the conditions recommended by

the CIPM in 1960 (PV, 28, 71-72 and CR, 1960, 85). These are as follows:

The radiation of 86Kr is obtained by means of a hot cathode discharge lamp

containing 86Kr, of a purity not less than 99 %, in sufficient quantity to assure

the presence of solid krypton at a temperature of 64 K, this lamp having a

capillary with the following characteristics: inner diameter from 2 mm to 4 mm,

wall thickness about 1 mm.

It is estimated that the wavelength of the radiation emitted by the positive

column is equal, to within 1 part in 108

, to the wavelength corresponding to the

transition between the unperturbed levels, when the following conditions are

satisfied:

The uncertainty

quoted in the 1960

document was 1 10–8

and was subsequently

improved to 4 10–9

(BIPM Com. Cons.

De ́f. du Me`tre, 1973,

5, M 12).
Appendix 2. Practical realization of the definitions of some important units • 51

1. the capillary is observed end-on from the side closest to the anode;

2. the lower part of the lamp, including the capillary, is immersed in a cold

bath maintained at a temperature within one degree of the triple point of

nitrogen;

3. the current density in the capillary is (0.3  0.1) A/cm2

.

2.2 Radiations for atoms of 86Kr, 198Hg and 114Cd

In 1963 the CIPM (BIPM Com. Cons. De ́f. Me`tre, 1962, 3, 18-19 and PV, 52,

26-27) specified values for the vacuum wavelengths, , operating conditions,

and corresponding uncertainties, for certain transitions in 86Kr, 198Hg and 114Cd.

For 86Kr, the above values apply, with a relative uncertainty of 2 10–8, to

radiations emitted by a lamp operated under conditions similar to those

specified in Section 2.1.

For 198Hg, the above values apply, with a relative uncertainty of 5 10–8, to

radiations emitted by a discharge lamp when the following conditions are met:

a) the radiations are produced using a discharge lamp without electrodes

containing 198Hg, of a purity not less than 98 %, and argon at a pressure

from 0.5 mm Hg to 1.0 mm Hg (66 Pa to 133 Pa);

b) the internal diameter of the capillary of the lamp is about 5 mm, and the

radiation is observed transversely;

c) the lamp is excited by a high-frequency field at a moderate power and is

maintained at a temperature less than 10 C;

d) it is preferred that the volume of the lamp be greater than 20 cm3

.

The uncertainties

quoted throughout

Section 2.2 are

judged to correspond

to relative expanded

uncertainties U = kuc

(k = 3), equal

to three times the

relative combined

standard

uncertainties.

Vacuum wavelengths, , for 86Kr transitions

Transition  /pm

2p9 – 5d'4 645 807.20

2p8 – 5d4 642 280.06

1s3 – 3p10 565 112.86

1s4 – 3p8 450 361.62

Vacuum wavelengths, , for 198Hg transitions

Transition  /pm

61

P1 – 61D2 579 226.83

61P1 – 63D2 577 119.83

63

P2 – 73S1 546 227.05

63

P1 – 73S1 435 956.24

Vacuum wavelengths, , for 114Cd transitions

Transition  /pm

51

P1 – 51D2 644 024.80

53

P2 – 63S1 508 723.79

53

P1 – 63S1 480 125.21

53

P0 – 63S1 467 945.81
52 • Appendix 2. Practical realization of the definitions of some important units

For 114Cd, the above values apply, with a relative uncertainty of 7 10–8, to

radiations emitted by a discharge lamp under the following conditions:

a) the radiations are generated using a discharge lamp without electrodes,

containing 114Cd of a purity not less than 95 %, and argon at a pressure of

about 1 mm Hg (133 Pa) at ambient temperature;

b) the internal diameter of the capillary of the lamp is about 5 mm, and the

radiation is observed transversely;

c) the lamp is excited by a high-frequency field of moderate power and is

maintained at a temperature such that the green line is not reversed.

2.3 Absorbing molecule 127I2, transition 17-1, P(62) component a1, as

recommended by the CIPM in 1992 (BIPM Com. Cons. De ́f. Me`tre,

1992, 8, M18 and M137, and Mise en Pratique of the Definition of the

Meter (1992), Metrologia, 1993/94, 30, 523-541).

The values f = 520 206 808.4 MHz

 = 576 294 760.4 fm

with a relative standard uncertainty of 4 10–10, apply to the radiation of a dye

laser (or frequency-doubled He-Ne laser) stabilized with an iodine cell, within or

external to the laser, having a cold-finger temperature of (6  2) C.

2 Mass

The unit of mass, the kilogram, is the mass of the international prototype of the

kilogram kept at the BIPM. It is a cylinder made of an alloy for which the mass

fraction of platinum is 90 % and the mass fraction of iridium is 10 %. The

masses of 1 kg secondary standards of the same alloy or of stainless steel are

compared with the mass of the international prototype by means of balances

with a relative uncertainty approaching 1 part in 109

.

The mass of the international prototype increases by approximately 1 part in 109

per year due to the inevitable accumulation of contaminants on its surface. For

this reason, the CIPM declared that, pending further research, the reference

mass of the international prototype is that immediately after cleaning and

washing by a specified method (PV, 1989, 57, 104-105 and PV, 1990, 58,

95-97). The reference mass thus defined is used to calibrate national standards

of platinum-iridium alloy (Metrologia, 1994, 31, 317-336).

In the case of stainless-steel 1 kg standards, the relative uncertainty of

comparisons is limited to about 1 part in 108 by the uncertainty in the correction

for air buoyancy. The results of comparisons made in vacuum, though

unaffected by air buoyancy, are subject to additional corrections to account

for changes in mass of the standards when cycled between vacuum and

atmospheric pressure.

Mass standards representing multiples and submultiples of the kilogram can be

calibrated by a conceptually simple procedure.
Appendix 2. Practical realization of the definitions of some important units • 53

3 Time

3.1 Unit of time

A small number of national metrology laboratories realize the unit of time with

the highest accuracy. To do so, they design and build primary frequency

standards that produce electric oscillations at a frequency whose relationship to

the transition frequency of the atom of cesium 133, which defines the second, is

known. In 1997, the best of these primary standards produces the SI second

with a relative combined standard uncertainty of 2 parts in 1015. It is important

to note that the definition of the second should be understood as the definition

of the unit of proper time: it applies in a small spatial domain which shares the

motion of the cesium atom. In a laboratory sufficiently small to allow the

effects of the non-uniformity of the gravitational field to be neglected when

compared to the uncertainties of the realization of the second, the proper second

is obtained after application of the special relativistic correction for the velocity

of the atom in the laboratory. It is wrong to correct for the local gravitational

field.

Primary frequency standards can also be used for calibration of the frequency of

secondary time standards used in national time-service laboratories. These are

generally commercial cesium clocks characterized by extreme long-term

stability: able to maintain a frequency with a stability better than 1 part in 1014

over a few months, they constitute very good “time-keepers.” The relative

uncertainty of their frequencies is on the order of 10–12. Time metrology

laboratories also use hydrogen masers with good short-term stability. These

instruments are used in all applications which require a stable reference over

intervals of less than one day (stability of 1 part in 1015 at 10 000 s). In

their basic form, hydrogen masers are subject to frequency drifts that become

apparent when their mean frequencies are compared with that of a cesium clock

over a few days. This drift is greatly reduced when the masers are operated in an

active mode with a self-servo-controlled cavity. Cesium clocks and hydrogen

masers must be operated under carefully controlled environmental conditions.

3.2 Clock comparisons, time scales

National laboratories usually operate a number of clocks. These are run

independently of one another and their data are combined to generate a

perennial time scale. This scale is more stable and more accurate than that of

any individual contributing clock. The scale is based on the results of local

clock comparisons in the laboratory, and often has an uncertainty of less than

100 ps. These time scales are generally designated TA(k) for laboratory k.

The synchronization of clocks operating in widely separated laboratories is an

important concern for time metrology. It calls for accurate methods of clock

comparison that can be operated everywhere on Earth, at any time. The satellite

system of the Global Positioning System (GPS) provides a satisfactory solution

to this problem: made up of twenty-four non-geostationary satellites, this system

is designed for positioning, but has the particular feature that the satellites are
54 • Appendix 2. Practical realization of the definitions of some important units

equipped with cesium clocks which broadcast time signals. These signals are

used in the following way: clocks in two distant laboratories are compared

individually with a clock on board a satellite which is visible simultaneously

from both laboratories and the difference is calculated. For a comparison

extending over ten minutes, the uncertainty thus obtained may be a few

nanoseconds, even for clocks which are separated by several thousand

kilometers. To reduce these uncertainties to this limit the data must be

considered very carefully: results obtained from views that are not strictly

simultaneous must be systematically rejected and a correction must be applied

to take account of the exact position of the satellite, data known only a few days

later.

The GPS is used on a regular basis to link national laboratories in many

countries and it will shortly be complemented by a similar Russian system: the

Global Navigation Satellite System (GLONASS). Among other methods under

study are bidirectional techniques based on the transmission of an optical or

radiofrequency signal from one laboratory to another and back, via a satellite.

Such methods should lead to subnanosecond accuracy before the end of the

century. All these methods of time comparison are subject to relativistic effects

which may exceed 100 ns, so corrections must be applied to take them into

account.

Optimal combination of all the results of comparisons between the clocks

maintained in the national time-service laboratories results in a world reference

time scale, International Atomic Time (TAI), approved by the 14th CGPM in

1971 (Resolution 1; CR, 77 and Metrologia, 1972, 8, 35). The first definition

of TAI was that submitted by the then CCDS in 1970 to the CIPM

(Recommendation S2; PV, 38, 110 and Metrologia, 1971, 7, 43):

International Atomic Time (TAI) is the time reference coordinate established

by the Bureau International de l’Heure on the basis of the readings of atomic

clocks operating in various establishments in accordance with the definition

of the second, the unit of time of the International System of Units.

In the framework of general relativity, TAI must be regarded as a time

coordinate (or coordinate time ): its definition was therefore completed as

follows (declaration of the CCDS, BIPM Com. Cons. De ́f. Seconde , 1980, 9, S15

and Metrologia, 1981, 17, 70):

TAI is a coordinate time scale defined in a geocentric reference frame with

the SI second as realized on the rotating geoid as the scale unit.

This definition was amplified by the International Astronomical Union in 1991,

Resolution A4:

TAI is a realized time scale whose ideal form, neglecting a constant offset of

32.184 s, is Terrestrial Time (TT), itself related to the time coordinate of the

geocentric reference frame, Geocentric Coordinate Time (TCG), by a

constant rate.

For details see the

proceedings

of the 21st General

Assembly of the IAU,

Buenos Aires,

IAU Trans. 1991,

vol. XXIB (Kluwer).
Appendix 2. Practical realization of the definitions of some important units • 55

Responsibility for TAI was accepted by the CIPM from the Bureau

International de l’Heure on 1 January 1988. TAI is processed in two steps. A

weighted average based on some 200 clocks maintained under metrological

conditions in about fifty laboratories is first calculated. The algorithm used is

optimized for long-term stability, which requires observation of the behavior of

clocks over a long duration. In consequence, TAI is a deferred-time time scale,

available with a delay of a few weeks. In 1997, the relative frequency stability of

TAI was estimated to be 2 parts in 1015 for mean durations of two months. The

frequency accuracy of TAI is evaluated by comparing the TAI scale unit with

various realizations of the SI second of primary frequency standards. This

requires the application of a correction to compensate for the relativistic

frequency shift between the location of the primary standard and a point fixed

on the rotating geoid. The magnitude of this correction is, between points fixed

on the surface of the Earth, of the order of 1 part in 1016 per meter of altitude.

In 1997, the difference between the TAI scale unit and the SI second on

the rotating geoid was +2 10–14 s, and was known with an uncertainty of

5 10–15 s. This difference is reduced by steering the frequency of TAI by the

application of corrections, of magnitude 1 part in 1015, every two months. This

method improves the accuracy of TAI while not degrading its middle-term

stability.

3.3 Legal time

TAI is not distributed directly in everyday life. The time in common use (broadcast by radio, television, the telephone . . .) is referred to a time scale called

Coordinated Universal Time (UTC) as recommended by the 15th CGPM in its

Resolution 5 in 1975 (CR, 104 and Metrologia, 1975, 11, 180). UTC differs

from TAI by a whole number of seconds, equal to –31 s on 1 July 1997. This

difference can be modified in steps of 1 s, using a positive or negative

leap second, in order to keep UTC in agreement with the time defined by

the rotation of the Earth such that, when averaged over a year, the Sun crosses

the Greenwich meridian at noon UTC to within 0.9 s. In addition, the legal time

of most countries is offset from UTC by a whole number of hours (time

zones and “summer time”). National time-service laboratories maintain an

approximation of UTC known as UTC(k ) for laboratory k. The differences

between UTC(k ) and UTC are in general no more than a few hundreds of

nanoseconds.

4 Electrical quantities

The realization to high accuracy of the ampere (a base unit of the SI), the ohm

and the volt (derived units of the SI) directly in terms of their definitions is

difficult and time-consuming. The best such realizations of the ampere are now

obtained through combinations of realizations of the watt, the ohm and the volt.

The watt realized electrically is compared by beam-balance experiments with

the watt realized mechanically. These experiments employ a coil in a magnetic

flux and are devised in such a way that it is not necessary to know either the

dimensions of the coil or the magnitude of the flux density. The ohm is realized

using a Thompson-Lampard capacitor whose value can be changed by an amount
56 • Appendix 2. Practical realization of the definitions of some important units

that depends only on the magnitude of a linear displacement of a guard

electrode. The volt is realized by means of a balance in which an electro-static

force is measured in terms of a mechanical force. The ampere may thus be

deduced from combinations of any two of these units. The relative uncertainty

in the value of the ampere obtained in this way is estimated to be a few parts in

107

. The ampere, ohm and volt may also be determined from measurements of

various combinations of physical constants. Laboratory reference standards for

the volt and the ohm based upon the Josephson and quantum-Hall effects are,

however, significantly more reproducible and stable than a few parts in 107

. In

order to take advantage of these highly stable methods of maintaining laboratory

reference standards of the electrical units while at the same time taking care not

to change their SI definitions, the 18th CGPM in 1987 adopted Resolution 6

which calls for representations of the volt and the ohm to be based on

conventional values for the Josephson constant KJ and the von Klitzing constant

RK.

■ 18th CGPM, 1987, Resolution 6 (CR, 100 and Metrologia, 1988, 25, 115):

forthcoming adjustment to the representations of the volt and of the ohm

The 18th Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures,

considering

• that world-wide uniformity and long-term stability of national

representations of the electrical units are of major importance for

science, commerce and industry from both the technical and

economic points of view,

• that many national laboratories use the Josephson effect and are

beginning to use the quantum Hall effect to maintain, respectively,

representations of the volt and of the ohm, as these offer the best

guarantees of long-term stability,

• that because of the importance of coherence among the units of

measurement of the various physical quantities the values adopted for

these representations must be as closely as possible in agreement

with the SI,

• that the results of recent and current experiment will permit the

establishment of an acceptable value, sufficiently compatible with

the SI, for the coefficient which relates each of these effects to the

corresponding electrical unit,

invites the laboratories whose work can contribute to the establishment of

the quotient voltage/frequency in the case of the Josephson effect and of

the quotient voltage/current for the quantum Hall effect to vigorously

pursue these efforts and to communicate their results without delay to the

Comite ́ International des Poids et Mesures, and

instructs the Comite ́ International des Poids et Mesures to recommend,

as soon as it considers it possible, a value for each of these quotients

together with a date for them to be put into practice simultaneously in all

countries; these values should be announced at least one year in advance

and would be adopted on 1 January 1990.

In 1988 the CIPM adopted Recommendations 1 (CI-1988) and 2 (CI-1988)

which set exact values for the Josephson and von Klitzing constants, and called

for laboratories to base their standards on these values from 1 January 1990.
Appendix 2. Practical realization of the definitions of some important units • 57

■ CIPM, 1988, Recommendation 1 (PV, 56, 44 and Metrologia, 1989,

26, 69): representation of the volt by means of the Josephson effect

The Comite ́ International des Poids et Mesures

acting in accordance with instructions given in Resolution 6 of the 18th

Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures concerning the forthcoming

adjustment of the representations of the volt and the ohm,

considering

• that a detailed study of the results of the most recent determinations

leads to a value of 483 597.9 GHz/V for the Josephson constant, KJ,

that is to say, for the quotient of frequency divided by the potential

difference corresponding to the n = 1 step in the Josephson effect,

• that the Josephson effect, together with this value of KJ, can be used

to establish a reference standard of electromotive force having a

one-standard-deviation uncertainty with respect to the volt estimated

to be 4 parts in 107

, and a reproducibility which is significantly better,

recommends

• that 483 597.9 GHz/V exactly be adopted as a conventional value,

denoted by KJ-90 for the Josephson constant, KJ,

• that this new value be used from 1 January 1990, and not before, to

replace the values currently in use,

• that this new value be used from this same date by all laboratories

which base their measurements of electromotive force on the

Josephson effect, and

• that from this same date all other laboratories adjust the value of their

laboratory reference standards to agree with the new adopted value,

is of the opinion that no change in this recommended value of the

Josephson constant will be necessary in the foreseeable future, and

draws the attention of laboratories to the fact that the new value is greater

by 3.9 GHz/V, or about 8 parts in 106

, than the value given in 1972 by the

Comite ́ Consultatif d’E ́ lectricite ́ in its Declaration E-72.

■ CIPM, 1988, Recommendation 2 (PV, 56, 45 and Metrologia, 1989, 26, 70):

representation of the ohm by means of the quantum Hall effect

The Comite ́ International des Poids et Mesures,

acting in accordance with instructions given in Resolution 6 of the 18th

Confe ́ rence Ge ́ ne ́ rale des Poids et Mesures concerning the forthcoming

adjustment of the representations of the volt and the ohm,

considering

• that most existing laboratory reference standards of resistance

change significantly with time,

• that a laboratory reference standard of resistance based on the

quantum Hall effect would be stable and reproducible,

• that a detailed study of the results of the most recent determinations

leads to a value of 25 812.807 
 for the von Klitzing constant, RK, that

is to say, for the quotient of the Hall potential difference divided by

current corresponding to the plateau i = 1 in the quantum Hall effect,
58 • Appendix 2. Practical realization of the definitions of some important units

• that the quantum Hall effect, together with this value of RK, can

be used to establish a reference standard of resistance having a

one-standard-deviation uncertainty with respect to the ohm estimated

to be 2 parts in 107

, and a reproducibility which is significantly better,

recommends

• that 25 812.807 
 exactly be adopted as a conventional value,

denoted by RK-90, for the von Klitzing constant, RK,

• that this value be used from 1 January 1990, and not before, by all

laboratories which base their measurements of resistance on the

quantum Hall effect,

• that from this same date all other laboratories adjust the value of their

laboratory reference standards to agree with RK-90,

• that in the use of the quantum Hall effect to establish a laboratory

reference standard of resistance, laboratories follow the most recent

edition of the technical guidelines for reliable measurements of the

quantized Hall resistance drawn up by the Comite ́ Consultatif

d’E ́ lectricite ́ and published by the Bureau International des Poids et

Mesures, and

is of the opinion that no change in this recommended value of the von

Klitzing constant will be necessary in the foreseeable future.

At its meeting in 1988 the CCE carefully considered the way in which the

recommended conventional values KJ-90 and RK-90 should be used and made

additional statements to clarify the implications of the Recommendations.

These statements may be summarized as follows:

1. Recommendations 1 (CI-1988) and 2 (CI-1988) do not constitute a

redefinition of Sl units. The conventional values KJ-90 and RK-90 cannot be

used as bases for defining the volt and the ohm [meaning the present units

of electromotive force and electrical resistance in the Syste`me International

d’Unite ́s (SI)]. To do so would change the status of 0 from that of a

constant having an exactly defined value (and would therefore abrogate

the definition of the ampere) and would also produce electrical units which

would be incompatible with the definition of the kilogram and units

derived from it.

2. Concerning the use of subscripts on symbols for quantities or units, the

CCE considers that symbols for electromotive force (electric potential,

electric potential difference) and electric resistance, and for the volt and the

ohm, should not be modified by adding subscripts to denote particular

laboratories or dates.

These statements were subsequently endorsed by the CIPM. The 19th CGPM

(1991, Resolution 2) recommended the continuation of research into the basic

theory of the Josephson and the quantum-Hall effects.

5 Temperature

Direct measurements of thermodynamic temperature can only be made by

using one of a small number of so-called primary thermometers. These are

thermometers whose equation of state can be written down explicitly

without having to introduce unknown temperature-dependent constants.
Appendix 2. Practical realization of the definitions of some important units • 59

Primary thermometers that have been used to provide accurate values of

thermodynamic temperature include the constant-volume gas thermometer, the

acoustic gas thermometer, the spectral- and total-radiation thermometers and

the electronic-noise thermometer. Uncertainties of a few millikelvins have been

achieved with such thermometers up to about 373 K, beyond which the

uncertainties increase progressively. The use of such thermometers to high

accuracy is difficult and time-consuming and there exist secondary

thermometers, such as the platinum resistance thermometer, whose

reproducibility can be better by a factor of ten than that of any primary

thermometer. In order to allow the maximum advantage to be taken of

these secondary thermometers the CGPM has, in the course of time, adopted

successive versions of an international temperature scale. The first of these was

the International Temperature Scale of 1927 (ITS-27); this was replaced by the

International Practical Temperature Scale of 1948 (IPTS-48) which in turn was

replaced by the International Practical Temperature Scale of 1968 (IPTS- 68). In

1976 the CIPM adopted, for use at low temperatures, the 1976 Provisional 0.5 K

to 30 K Temperature Scale (EPT-76). On 1 January 1990 the IPTS-68 and the

EPT-76 were replaced by the International Temperature Scale of 1990 (ITS-90)

adopted by the CIPM in 1989 in its Recommendation 5 (CI-1989). The 19th

CGPM (1991, Resolution 3) recommended that national laboratories continue

their efforts to improve the world-wide uniformity and long-term stability of

temperature measurements by rapid implementation of the ITS-90.

■ CIPM, 1989, Recommendation 5 (PV, 57, 115 and Metrologia, 1990,

27, 13): the International Temperature Scale of 1990

The Comite ́ International des Poids et Mesures (CIPM) acting in

accordance with Resolution 7 of the 18th Confe ́ rence Ge ́ ne ́ rale des Poids

et Mesures (1987) has adopted the International Temperature Scale of

1990 (ITS-90) to supersede the International Practical Temperature Scale

of 1968 (IPTS-68).

The CIPM notes that, by comparison with the IPTS-68, the ITS-90

• extends to lower temperatures, down to 0.65 K, and hence also

supersedes the EPT-76,

• is in substantially better agreement with corresponding

thermodynamic temperatures,

• has much improved continuity, precision and reproducibility

throughout its range and

• has subranges and alternative definitions in certain ranges which

greatly facilitate its use.

The CIPM also notes that, to accompany the text of the ITS-90 there will

be two further documents, the Supplementary Information for the ITS-90

and Techniques for Approximating the ITS-90. These documents will be

published by the BIPM and periodically updated.

The CIPM recommends

• that on 1 January 1990 the ITS-90 come into force and

• that from this same date the IPTS-68 and the EPT-76 be abrogated.
60 • Appendix 2. Practical realization of the definitions of some important units

The ITS-90 extends upwards from 0.65 K to the highest temperature

measurable using an optical pyrometer. The scale is based on 1) a set of

defining fixed points and 2) specified methods of interpolating between them.

The defining fixed points are the temperatures assigned by agreement to

a number of experimentally realizable thermodynamic states and the

interpolations are defined in terms of the helium vapor-pressure equations from

0.65 K to 5 K, interpolating constant-volume gas thermometers from 3 K to

24.5561 K, platinum resistance thermometers from 13.8033 K to 961.78 C and

the Planck radiation law at higher temperatures. In several ranges of

temperature more than one definition of T90, the temperature defined by the

Scale, exists. The various definitions have equal validity.

Advice on the realization and implementation of the ITS-90 is given in two

documents, Supplementary Information for the ITS-90 and Techniques for

Approximating the ITS-90, which are approved and updated periodically by the

CCT and published by the BIPM.

6 Amount of substance

All quantitative results of chemical analyses or of dosages can be expressed in

units of amount of substance of the elementary entities, for which the base unit

is the mole. The principle of physical measurement based on this unit is

explained below.

The simplest case is that of a sample of a pure substance that is considered to be

formed of atoms; call X the chemical symbol of these atoms. A mole of atoms

X contains by definition as many atoms as there are 12C atoms in 0.012 kg of

carbon 12. As neither the mass m(

12C) of an atom of carbon 12 nor the mass

m(X) of an atom X can be measured accurately, we use the ratio of these

masses, m(X)/m(

12C), which can be determined accurately, for example by

means of a Penning trap. The mass corresponding to 1 mol of X is then

[m(X)/m(12C)] 0.012 kg, which is expressed by the statement that the molar

mass M(X) of X (quotient of mass by amount of substance) is

M(X) = [m(X)/m(

12C)] 0.012 kg/mol.

For example, the atom of fluorine 19F and the atom of carbon 12C have

masses which are in the approximate ratio 18.9984/12. The molar mass of the

molecular gas F2 is:

M(F2) = 2 18.9984

12 0.012 kg/mol = 0.037 996 8 kg/mol,

and the amount of substance corresponding to a given mass, for example

0.0500 kg of F2 is:

0.0500 kg

0.037 996 8 kg  mol–1 = 1.316 mol.
Appendix 2. Practical realization of the definitions of some important units • 61

In the case of a pure substance that is supposed made up of molecules B, which

are combinations of atoms X, Y, ... according to the chemical formula

B=X Y
..., the mass of one molecule is m(B) = m(X) + 
m(Y) + .... This

mass is not known precisely but the ratio m(B)/m(

12C) can be determined

accurately. The molar mass of a molecular substance B is then:

M(B) = m(B)

m(

12C)0.12 kg/mol=

m(X)

m(

12C)+
 m(Y)

m(

12C)+...0.012 kg/mol.

The same procedure is used in the more general case when the composition of

substance B is specified as X Y
 even if , 
... are not integers. If we denote

the mass ratios m(X)/m(

12C), m(Y)/m(12C), ... by r(X), r(Y), ... , the

molar mass of substance B is given by the formula:

M(B) = [r(X) + 
r(Y) + ... ] 0.012 kg/mol.

Other methods for the measurement of amount of substance are based on the

laws of physics and physical chemistry. Three examples are:

1. With perfect gases, 1 mol of particles of any gas occupies the same

volume at a temperature T and a pressure p (approximately 0.0224 m3

at T = 273.15 K and p = 101 325 Pa): this provides a method of

measuring the ratio of amounts of substance for any two gases (the

corrections to apply if the gases are not perfect are well known).

2. For quantitative electrolytic reactions the ratio of amounts of substance

can be obtained by measuring quantities of electricity. For example,

1 mol of Ag and (1/2) mol of Cu are deposited on a cathode by the

same quantity of electricity (approximately 96 485 C).

3. Application of the laws of extremely dilute solutions is yet another

method of determining ratios of amounts of substance.

7 Photometric quantities

The definition of the candela given on page 9 is expressed in strictly physical

terms. The objective of photometry, however, is to measure light in such a way

that the result of the measurement correlates closely with the visual sensation

experienced by a human observer of the same radiation. For this purpose, the

International Commission on Illumination (CIE) introduced two special

functions V() and V'(), referred to as spectral luminous efficiency functions,

which describe, respectively, the relative spectral responsivity of the average

human eye for photopic (light adapted) and scotopic (dark adapted) vision. The

more important of these two, the light-adapted function V(), is expressed

relative to its value for the monochromatic radiation to which the eye is most

sensitive when adapted to high levels of illuminance. That is, it is defined relative

to radiation at 540 1012 Hz which corresponds to a wavelength of 555.016 nm

in standard air.

The CIPM has approved the use of these functions with the effect that the

corresponding photometric quantities are defined in purely physical terms as

See

“Principles governing

photometry,”

Monographie BIPM,

1983, 31 p.
62 • Appendix 2. Practical realization of the definitions of some important units

quantities proportional to the integral of a spectral power distribution, weighted

according to a specified function of wavelength.

Since the inception of the SI, the candela has been one of its base units: it

remained a base unit even after being linked, in 1979, to the derived SI unit of

power, the watt. The original photometric standards were light sources,

the earliest ones being candles, hence the name candela as the name of the

photometric base unit. From 1948 to 1979 the radiation from a black body,

Planck radiation, at the temperature of freezing platinum was used to define the

candela. Today the definition is given in terms of monochromatic radiation

rather than the broadband radiation implied by the black-body definition. The

value 1/683 watt per steradian which appears in the present definition was

chosen in 1979 so as to minimize any change in the mean representations of the

photometric units maintained by the national standards laboratories.

The definition gives no indication as to how the candela should be realized,

which has the great advantage that new techniques to realize the candela can be

adopted without changing the definition of the base unit. Today, national

metrology institutes realize the candela by radiometric methods. Standard

lamps are still used, however, to maintain the photometric units: they provide

either a known luminous intensity in a given direction, or a known luminous

flux.
63

Appendix 3. The BIPM and the Meter Convention†

The International Bureau of Weights and Measures (BIPM, Bureau International des

Poids et Mesures) was set up by the Meter Convention (Convention du Me`tre , often

called the Treaty of the Meter in the United States) signed in Paris on 20 May 1875 by

seventeen States during the final session of the diplomatic Conference of the Meter.

This Convention was amended in 1921.

The BIPM has its headquarters near Paris, in the grounds (43 520 m2

) of the Pavillon de

Breteuil (Parc de Saint-Cloud) placed at its disposal by the French Government; its

upkeep is financed jointly by the Member States of the Meter Convention.

The task of the BIPM is to ensure world-wide unification of physical measurements; its

function is thus to:

• establish fundamental standards and scales for the measurement of the principal

physical quantities and maintain the international prototypes;

• carry out comparisons of national and international standards;

• ensure the coordination of corresponding measuring techniques;

• carry out and coordinate measurements of the fundamental physical constants

relevant to these activities.

The BIPM operates under the exclusive supervision of the International Committee for

Weights and Measures (CIPM, Comite ́ International des Poids et Mesures) which itself

comes under the authority of the General Conference on Weights and Measures

(CGPM, Confe ́rence Ge ́ne ́rale des Poids et Mesures) and reports to it on the work

accomplished by the BIPM.

Delegates from all Member States of the Meter Convention attend the General

Conference which, at present, meets every four years. The function of these meetings

is to :

• discuss and initiate the arrangements required to ensure the propagation and

improvement of the International System of Units (SI), which is the modern form of

the metric system;

• confirm the results of new fundamental metrological determinations and various

scientific resolutions of international scope;

• take all major decisions concerning the finance, organization and development of the

BIPM.

The International Committee has eighteen members each from a different State:

at present, it meets every year. The officers of this committee present an Annual

† Editor’s note: In the original BIPM text, this material appeared before the Contents under the title “The

BIPM and the Convention du Me`tre.” Further, the names of organizations and the name of the Meter

Convention were in French only.

As of 31 December 1997,

forty-eight States were

members of this

Convention: Argentina,

Australia, Austria,

Belgium, Brazil, Bulgaria,

Cameroon, Canada, Chile,

China, Czech Republic,

Denmark, Dominican

Republic, Egypt, Finland,

France, Germany,

Hungary, India, Indonesia,

Iran (Islamic Rep. of),

Ireland, Israel, Italy,

Japan, Korea (Dem.

People’s Rep. of), Korea

(Rep. of), Mexico,

Netherlands,

New Zealand, Norway,

Pakistan, Poland,

Portugal, Romania,

Russian Federation,

Singapore, Slovakia,

South Africa, Spain,

Sweden, Switzerland,

Thailand, Turkey, United

Kingdom, United States,

Uruguay, Venezuela.

Editor’s note: Greece

joined the Meter

Convention at the

beginning of 2001,

bringing the number

of Member States

to forty-nine.
64 • Appendix 3. The BIPM and the Meter Convention

Report on the administrative and financial position of the BIPM to the Governments of

the Member States of the Meter Convention. The principal task of the CIPM is to ensure

world-wide uniformity in units of measurement. It does this by direct action or by

submitting proposals to the CGPM.

The activities of the BIPM, which in the beginning were limited to measurements of

length and mass, and to metrological studies in relation to these quantities, have been

extended to standards of measurement of electricity (1927), photometry and radiometry

(1937), ionizing radiation (1960) and to time scales (1988). To this end, the original

laboratories, built in 1876-1878, were enlarged in 1929; new buildings were

constructed in 1963-1964 for the ionizing radiation laboratories and in 1984 for the

laser work. In 1988 a new building for a library and offices was opened.

Some forty-five physicists and technicians work in the BIPM laboratories. They mainly

carry out metrological research, international comparisons of realizations of units and

calibrations of standards. An annual report, published in the Proce`s-Verbaux des

Se ́ances du Comite ́ International des Poids et Mesures, gives details of the work in

progress.

Following the extension of the work entrusted to the BIPM in 1927, the CIPM has set up

bodies, known as Consultative Committees (Comite ́s Consultatifs), whose function is to

provide it with information on matters that it refers to them for study and advice. These

Consultative Committees, which may form temporary or permanent working groups to

study special topics, are responsible for co-ordinating the international work carried out

in their respective fields and for proposing recommendations to the CIPM concerning

units.

The Consultative Committees have common regulations (PV, 1963, 31, 97). They meet

at irregular intervals. The chairman of each Consultative Committee is designated by

the CIPM and is normally a member of the CIPM. The members of the Consultative

Committees are metrology laboratories and specialized institutes, agreed to by the

CIPM, which send delegates of their choice (Criteria for membership of Consultative

Committees, PV, 1996, 64, 124). In addition, there are individual members appointed

by the CIPM, and a representative of the BIPM. At present, there are ten such

committees:

1. The Consultative Committee for Electricity and Magnetism (CCEM, Comite ́

Consultatif d’E ́lectricite ́ et Magne ́tisme ), a new name given in 1997 to the

Consultative Committee for Electricity (CCE, Comite ́ Consultatif d’E ́lectricite ́ ) set

up in 1927.

2. The Consultative Committee for Photometry and Radiometry (CCPR, Comite ́

Consultatif de Photome ́trie et Radiome ́trie ), new name given in 1971 to the

Consultative Committee for Photometry set up in 1933 [between 1930 and 1933 the

preceding Committee (CCE) dealt with matters concerning photometry].

3. The Consultative Committee for Thermometry (CCT, Comite ́ Consultatif de

Thermome ́trie), which for a time was called Consultative Committee for

Thermometry and Calorimetry (CCTC) set up in 1937.

4. The Consultative Committee for Length (CCL, Comite ́ Consultatif des Longueurs),

new name given in 1997 to the Consultative Committee for the Definition of the

Meter (CCDM, Comite ́ Consultatif pour la De ́finition du Me`tre ), set up in 1952.
Appendix 3. The BIPM and the Meter Convention • 65

5. The Consultative Committee for Time and Frequency (CCTF, Comite ́ Consultatif

du Temps et des Fre ́quences), new name given in 1997 to the Consultative

Committee for the Definition of the Second (CCDS, Comite ́ Consultatif pour la

De ́finition de la Seconde) set up in 1956.

6. The Consultative Committee for Ionizing Radiation (CCRI, Comite ́ des

Rayonnements Ionisants), new name given in 1997 to the Consultative Committee

for the Standards of Measurement of Ionizing Radiation (CCEMRI, Comite ́

Consultatif pour les E ́talons de Mesure des Rayonnements Ionisants) set up in

1958. In 1969 this committee established four sections: Section I (Measurement of

x and  rays, electrons); Section II (Measurement of radionuclides); Section III

(Neutron measurements); Section IV (-energy standards). In 1975 this last section

was dissolved and Section II was made responsible for its field of activity.

7. The Consultative Committee for Units (CCU, Comite ́ Consultatif des Unite ́s), set

up in 1964 (this committee replaced the “Commission for the System of Units” set

up by the CIPM in 1954).

8. The Consultative Committee for Mass and Related Quantities (CCM, Comite ́

Consultatif pour la Masse et les grandeurs apparente ́es), set up in 1980;

9. The Consultative Committee for Amount of Substance (CCQM, Comite ́ Consultatif

pour la Quantite ́ de Matie`re ), set up in 1993.

10. The Consultative Committee for Acoustics, Ultrasound and Vibration (CCAUV,

Comite ́ Consultatif de l’Acoustique, des Ultrasons et des Vibrations), set up in

September 1998.†

The proceedings of the General Conferences, the International Committee and the

Consultative Committees are published by the BIPM in the following series:

• Comptes Rendus des Se ́ances de la Confe ́rence Ge ́ne ́rale des Poids et Mesures (CR);

• Proce ́s-Verbaux des Se ́ ances du Comite ́ International des Poids et Mesures (PV);

• Sessions des Comite ́s Consultatifs.

The Bureau International also publishes monographs on special metrological subjects

and, under the title Le Syste`me International d’Unite ́s (SI), this brochure, periodically

updated, in which are collected all the decisions and recommendations concerning units.

The collection of the Travaux et Me ́moires du Bureau International des Poids et Mesures

(22 volumes published between 1881 and 1966) and the Recueil de Travaux du Bureau

International des Poids et Mesures (11 volumes published between 1966 and 1988)

ceased by a decision of the CIPM.

The scientific work of the BIPM is published in the open scientific literature and an

annual list of publications appears in the Proce`s-Verbaux of the CIPM.

Since 1965 Metrologia, an international journal published under the auspices of the

CIPM, has printed articles dealing with scientific metrology, improvements in methods

of measurement and work on standards and units, as well as reports concerning the

activities, decisions and recommendations of the various bodies created under the Meter

Convention.

† Editor’s note: This entry has been added to the origninal BIPM text.
67

Index†

A

absorbed dose (see gray)

accelaration due to gravity, standard

value of (gn), 29

amount of substance, 8, 35, 60-61

ampere, 6-7, 32-33

ångstrom, 17

are, 17

astronomical unit, 17

atmosphere, standard, 19, 34

atomic mass unit, unified, 17

B

bar, 17

barn, 17

becquerel, 11, 37

bel, 16

Bureau International des Poids et

Mesures (BIPM), 63

C

candela, 8-9, 36-37

candle, new, 35, 42

coherent system of units, 2, 15, 25

Comite ́ International des Poids et

Mesures (CIPM), 63

Consultative Committees, 64-65

Confe ́rence Ge ́ne ́rale des Poids et

Mesures (CGPM), 63

Convention du Me`tre, 63

coulomb, 11, 33

cubic decimeter, 43

curie, 17, 19, 37

D

day, 16

definitions of units, practical

realization of the, 45-62

degree, 16

degree Celsius, 7, 34, 35

dimensionless quantities, 13

dose equivalent (see sievert)

E

electric current (see ampere)

electrical quantities, 55-58

electronvolt, 17

F

farad, 11, 25, 33

force, 7

frequency standard, 30, 53

G

gn, 29

general relativity, 4

gray, 11, 37-38

H

Hall effect, quantum, 56-58

hectare, 17

henry, 11, 25, 33, 42

hertz, 11, 25, 42

hour, 16

I

International System of Units

(SI), 22-26

J

jansky, 19

joule, 11, 25, 32, 33-34

Josephson effect, 56-57

K

katal, 11, 39

kelvin, 7, 34-35

kilogram, 6, 14, 26, 29, 52

kilogram, multiples of the, 14, 29

knot, 17

L

legislation on units, 4

length, 5, 26-28, 45-52

liter, 16, 43-44;

symbols for the, 43-44

logarithmic quantities

(neper, bel), 16

lumen, 11, 25, 42; new, 36

luminous intensity, 8-9, 35-37

lux, 11, 25, 42

M

mass, 5, 29, 52

mass and weight, 29

meter, 5, 26-28, 45-52

Meter Convention, 63

Numbers in boldface

indicate the pages

where the definitions

of the units are to be

found.

† Editor’s note: This Index contains minor changes to the Index in the original BIPM text.
68 • Index

metric ton, 16, 42

Metrologia, 65

micron, 19, 42

minute, 16

mole, 8, 35, 60-61

N

names, writing of SI unit, 20-21

nautical mile, 17

neper, 16

newton, 7, 11, 25, 32

numbers, writing and printing, 41-42

O

ohm, 11, 25, 33, 42, 55-58

P

pascal, 11, 33

photometric quantities, 61-62

prefixes, SI, 3, 14, 24, 41

prefixes, SI, rules for using, 21

Q

quantities of dimension one, 13

quantities, system of, 4

quantity of heat, unit for (see joule)

quantum Hall effect, 56-58

R

rad, 17, 19

radian, 11, 24, 39-40

realization of the definitions of some

important units, practical, 45-62

rem, 17, 19

roentgen, 17, 19

S

second, 6, 16, 29-32, 53-55

SI units, multiples and submultiples

of, 3, 14, 24, 41

siemens, 11, 33

sievert, 11, 13, 38

speed of light (recommended value), 5, 27

standard atmosphere, 19, 34

steradian, 11, 24, 39-40

substance, amount of, 8, 35,

60-61

symbols for base units, 9

symbols for derived units with

special names, 11

symbols for the liter, 16, 43-44

symbols, writing of SI unit, 20-21

system of quantities, 4

System of Units (SI), International,

22-26

system of units, proposal for

establishing a practical, 22-23

T

TAI, 31-32, 54-55

temperature, 33-35, 58-60

temperature, Celsius, 7, 34, 35

temperature, thermodynamic, 7, 33-35

tesla, 11, 25

thermodynmic scale, 33-34

time, 6, 29-32, 53-55

Time (TAI), International Atomic,

31-32, 54-55

Time (UTC), Coordinated Universal,

32, 55

tonne, 16, 42

triple point of water, 7, 33

U

unit for quantity of heat (see joule)

unit of force, 7, 11, 32

units, electric, 32-33, 55-58

units, examples of other non-SI, 19

units, legislation on, 4

units, photometric, 35-37, 62

units, SI, multiples and submultiples

of, 3, 14, 24, 41

units, SI, the two classes of, 3

units, SI base, 5-9, 26-37;

symbols for, 9

units, SI derived, 9-13, 37-40

units, SI supplementary, 39-40

units, accepted for use with SI, non-SI,

16-17

units currently accepted for use with SI,

other non-SI, 17

units with special names, derived CGS,

18

units with special names, SI derived, 11

UTC, 32, 55

V

volt, 11, 25, 33, 42, 55-58

W

watt, 11, 25, 32, 42

weber, 11, 25, 33

weight (see mass)