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NIST Special Publication 330

The International System of Units (SI)

2019

EDITION

SP 330

David B. Newell and Eite Tiesinga, Editors

This publication is available free of charge

https://doi.org/10.6028/NIST.SP.330-2019 ,16,'()5217&29(5%/$1.

NIST Special Publication 330

2019 EDITION

The International System of Units (SI)

U nited States version of the English text of the ninth edition (2019) of the International Bureau of Weights and Measures publication

Le Système

International d' Unités (SI)

(Supersedes NIST Special Publication 330, 2008 Edition)

Editors:

David B. Newell

Eite Tiesinga

Physical Measurement Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

Th is publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019 2019 U .S. Department of Commerce

Wilbur L. Ross, Jr., Secretary

N ational Institute of Standards and Technology Walter Copan, NIST Director and Undersecretary of Commerce for Standards and Technology This publication is available free of charge from: https://doi.org /10.6028/NIST.SP .330 2019
C ertain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose. National Institute of Standards and Technology Special Publication 330

Natl. Inst. Stand. Technol. Spec. Publ. 330, 122 pages ( 2019)

CODEN:

NS PUE2 This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019 iii This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 330
2019

Foreword

T he International System of Units, universally abbreviated SI (from the

French Le

Système International d'Unités), is the modern metric system of measurement. The SI is the dominant measurement system used in science and international commerce. In recognition of this fact, Congress has designated the metric system of measurement as the preferred system of weights and measures for United States trade and commerce. T he 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 Système International d'

Unités (SI), the booklet is in French followed by a text in English. This 2019 edition of the National Institute of Standards and Technology (NIST) Special Publication (SP) 330 is the United States version of the English text of the ninth edition of the Brochure (the most current) published in 2019. The 2019 edition of NIST SP 330 replaces its immediate predecessor, the 2008 edition, which was based on the eighth edition of the BIPM SI

Brochure published in 2006, updated in 2014.

T he Secretary of Commerce acting through the Director of the

NIST is authorized by

statute (§15 U.S.C. 272) under subsection (2) “to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for making measurements consistent with those standards" and under subsection (9) “to assure the compatibility of United States national measurement standards with those of other nations." Under this authority, the SI is interpreted or modified by the Director of NIST for use in the United States.

The Secretary of Commerce

acting through the NIST

Director

is designated to direct and coordinate efforts by Federal departments and agencies to implement Government metric usage in accordance the Metric Conversion Act (15 U.S.C. 205b), as amended by the Omnibus Trade and Competitiveness Act of 1988.
L ike its 2008 predecessor, the 2019 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. These differences include the following: 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," "deka ," and "cesium" are used rather than "metre," "litre," "deca " and " caesium" as in the original BIPM English text. The name of the unit with symbol t and defined according to 1 t = 10 3 kg is called "metric ton" rather than "tonne." Since the preferred unit symbol for the liter in the United States is L, only L is given as the symbol for the liter.

A number of "Editors' notes" are added in order to indicate such differenceswhere significant (except spelling differences) and to clarify the text; and

iv This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 330
2019
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 NIST (i) 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) provides official U.S. representation in the various international bodies established by the Meter Convention (see p.

1), and (iii) is responsible for interpreting and modifying the SI for use in the

United

States, NIST provides a number of other sources of information on the SI in addition to NIST SP 330. This includes NIST Special Publication 811, Guide for the Use of the International System of Units (SI), by David B. Newell and Eite Tiesinga. NIST SP 330, NIST SP 811, the aforementioned Federal Register notice are the essential elements of the U.S. interpretation of the SI. Users of this NIST publication are encouraged to take advantage of the resources, useful links, and other information available on the BIPM (www.bipm.org) and NIST Metric Program (www.nist.gov/metric) websites. 2019
David

B. Newell

Eite

Tiesinga

Note from

the BIPM on copyright and the use of the English text: "All BIPM's works are internationally protected by copyright. This document has been drafted with permission obtained from the BIPM. The only official text is the French text of the original document created by the BIPM." To make its work more widely accessible, the International Committee for Weights and

Measures

(CIPM) 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. v This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 330
2019

The BIPM and the Meter Convention

The International Bureau of Weights and Measures (BIPM) was set up by the Meter Convention 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 m 2 ) 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 worldwide unification of measurements; it s objectives are to: represent the world-wide measurement community, aiming to maximize its uptake and impact, be a center for scientific and technical collaboration between Member States, providing capabilities for international measurement comparisons on a shared-cost basis, be the coordinator of the world-wide measurement system, ensuring it gives comparable and internationally accepted measurement results. The BIPM operates under the exclusive supervision of the International

Committee for

Weights and Measures (CIPM) which itself comes under the authority of the General Conference on Weights and Measures (CGPM) and reports to it on the work accomplished by the BIPM. Delegates from all Member States attend the General Conference which normally 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 CIPM has eighteen members, each from a different State: at present, it meets every year. The officers of this committee present an annual report on the administrative and financial position of the BIPM to the Governments of the Me mber States of the Meter Convention. The principal task of the CIPM is to ensure worldwide uniformity in units of measurement. It does this by direct action or by submitting proposals to the CGPM.

As of 20 May 2019 there

were fifty nine Member

States: Argentina, Australia,

Austria, Belgium, Brazil,

Bulgaria, Canada, Chile,

China, Colombia, Croatia,

Czech Republic, Denmark,

Egypt, Finland, France,

Germany, Greece, Hungary,

India, Indonesia, Iran

(Islamic Rep. of), Iraq,

Ireland, Israel, Italy, Japan,

Kazakhstan, Kenya, Korea

(Republic of), Lithuania,

Malaysia, Mexico,

Montenegro, Netherlands,

New Zealand, Norway,

Pakistan, Poland, Portugal,

Romania, Russian

Federation, Saudi Arabia,

Serbia, Singapore, Slovakia,

Slovenia, South Africa,

Spain, Sweden, Switzerland,

Thailand, Tunisia, Turkey,

Ukraine, United Arab

Emirates, United Kingdom,

United States of America and

Uruguay

Forty-two States and

Economies were Associates

of the General Conference:

Albania, Azerbaijan,

Bangladesh, Belarus, Bolivia,

Bosnia and Herzegovina,

Botswana, CARICOM,

Chinese Taipei, Costa Rica,

Cuba, Ecuador, Estonia,

Ethiopia, Georgia, Ghana,

Hong Kong (China), Jamaica,

Kuwait, Latvia, Luxembourg,

Malta, Mauritius, Moldova

(Republic of),

Mongolia, Namibia, North

Macedonia, Oman, Panama,

Paraguay, Peru, Philippines,

Qatar, Seychelles, Sri Lanka,

Sudan, Syrian Arab Republic,

Tanzania (United Republic

of), Viet Nam, Zambia, and

Zimbabwe

vi This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 330
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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), time scales (1988), and to chemistry (2000). To this end the original laboratories, built in 1876 to 1878, were enlarged in 1929; new buildings were constructed in 1963 - 1964 for the ionizing radiation laboratories, in 1984 for the laser work and in 1988 for a library and offices. In 2001, a new building for the workshop, offices, and meeting rooms was opened. Some forty-five physicists and technicians work in the BIPM laboratories. They mainly conduct metrological research, international comparisons of realizations of units and calibrations of standards. An annual

Director"s report 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, 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 coordinating the international work carried out in their respective fields and for proposing recommendations to the CIPM concerning units. The Consultative Committees have common regulations (Document CIPM-D-01, Rules of procedure for the Consultative Committees (CCs) created by the CIPM, CC working groups and CC workshops). They meet at irregular intervals. The president 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 by the CIPM, which send delegates of their choice. In addition, there are individual members appointed by the CIPM, and a representative of the BIPM (Document CIPM-D-01, Rules of procedure for the Consultative Committees (CCs) created by the CIPM, CC working groups and CC workshops). At present, there are ten such committees: 1. The Consultative Committee for Electricity and Magnetism (CCEM), new name given in 1997 to the Consultative Committee for Electricity (CCE) set up in 1927; 2.

The Consultative Committee for Photometry and Radiometry (CCPR), new name given in 1971 to the Consultative Committee for Photometry (CCP) set up in 1933 (between 1930 and 1933 the CCE dealt with matters concerning

photometry); 3. The Consultative Committee for Thermometry (CCT), set up in 1937; 4.

The Consultative Committee for Length (CCL), new name given in 1997 to the Consultative Committee for the Definition of the Meter (CCDM), set up in

1952;
5. The Consultative Committee for Time and Frequency (CCTF), new name given in 1997 to the Consultative Committee for the Definition of the Second (CCDS) set up in 1956; 6. The Consultative Committee for Ionizing Radiation (CCRI), new name given in 1997 to the Consultative Committee for Standards of Io nizing Radiation vii This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 330
2019
(CCEMRI) set up in 1958 (in 1969 this committee established four sections: Section I (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), 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), set up in 1980; 9. The Consultative Committee for Amount of Substance: Metrology in

Chemistry and Biology (CCQM), set up in 1993;

10. The Consultative Committee for Acoustics, Ultrasound and Vibration (CCAUV), set up in 1999. The proceedings of the General Conference and the CIPM are published by the BIPM in the following series: Report of the meeting of the General Conference on Weights and Measures; Report of the meeting of the International Committee for Weights and Measures. The CIPM decided in 2003 that the reports of meetings of the Consultative Committees should no longer be printed, but would be placed on the BIPM website, in their original language. The BIPM also publishes monographs on special metrological subjects and, under the title The International System of Units (SI), a brochure, periodically updated, in which are collected all the decisions and recommendations concerning units.

The collection of the

Travaux et

Mémoires 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 sc

ientific work of the BIPM is published in the open scientific literature.

Since 1965

Metrologia

, an international journal published under the auspices of the CIPM, has printed articles dealing with scientific metrology, improvements in methods of measureme nt, work on standards and units, as well as reports concerning the activities, decisions and recommendations of the various bodies created under the Meter

Convention.

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Table of Contents

Preface to the 9

th edition ........................................................................ ............................. xi

1. Introduction

.............................................. 1

1.1 The SI and the defining constants ............................................................................ 1

1.2 Motivation for the use of defining constants to define the SI .................................. 1

1.3 Implementation of the SI ......................................................................................... 2

2. The International System of Units ................................................................................... 3

2.1 Defining the unit of a quantity ................................................................................. 3

2.2 Definition of the SI ........................................................................

.......................... 3

2.3 Definitions of the SI units ........................................................................................ 5

2.3.1 Base units ........................................................................

........................6

2.3.2 Practical realization of SI units .............................................................12

2.3.3 Dimensions of quantities ......................................................................13

2.3.4 Derived units ........................................................................

.................14

2.3.5 Units for quantities that describe biological and

physiological effects........................................................................ ............20

2.3.6 SI units in the framework of the general theory of relativity ...............20

3. Decimal multiples and sub-multiples of SI units ........................................................... 23

4. Non-SI units that are accepted for use with the SI ......................................................... 25

5. Writing unit symbols and names, and expressing the values of quantities .................... 29

5.1 The use of unit symbols and names .......................................................................

29

5.2 Unit symbols ........................................................................

.................................. 29

5.3 Unit names ........................................................................

..................................... 30

5.4 Rules and style conventions for expressing values of quantities ........................... 30

5.4.1 Value and numerical value of a quantity, and the use of quantity

calculus ........................................................................ ................................30

5.4.2 Quantity symbols and unit symbols ......................................................31

5.4.3 Formatting the value of a quantity ........................................................32

5.4.4 Formatting numbers, and the decimal marker ......................................32

5.4.5 Expressing the measurement uncertainty in the value of a quantity.....33

5.4.6 Multiplying or dividing quantity symbols, the values of quantities,

or numbers ........................................................................ ...........................33

5.4.7 Stating quantity values being pure numbers .........................................33

5.4.8 Plane angles,

solid angles and phase angles .........................................34

Appendix 1. Decisions of the CGPM and the CIPM ......................................................... 37

Appendi

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