SP 330

2019
EDITIONNIST Special Publication 330

The International System of Units (SI)David B. Newell and Eite Tiesinga, Editors

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https://doi.org/10.6028/NIST.SP.330-2019

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INSIDE FRONT COVER - BLANKNIST Special Publication 330
2019 EDITION

The International System of Units (SI)
United 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
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August 2019

U.S. Department of Commerce
Wilbur L. Ross, Jr., Secretary

National Institute of Standards and Technology
Walter Copan, NIST Director and Undersecretary of Commerce for Standards and Technology

Certain commercial entities, equipment, or materials may be identified in thisdocument 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 theentities, materials, or equipment are necessarily the best available for the purpose.

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National Institute of Standards and Technology Special Publication 330
Natl. Inst. Stand. Technol. Spec. Publ. 330, 122 pages (August 2019)
CODEN: NSPUE2This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019

Foreword
The 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 thepreferred system of weights and measures for United States trade and commerce.
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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 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 (themost 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.
The Secretary of Commerce acting through the Director of the NIST is authorized bystatute (§15 U.S.C. 272) under subsection (2) “to develop, maintain, and retain custody ofthe national standards of measurement, and provide the means and methods for making
measurements consistent with those standards” and under subsection (9) “to assure thecompatibility of United States national measurement standards with those of othernations.” 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 andagencies 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 of1988.
Like 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 mostrecent 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 = 103 kg is called“metric ton” rather than “tonne.”• Since the preferred unit symbol for the liter in the United States is L, only L isgiven 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

iii

•

A few very minor editorial changes are made in order to “Americanize” somephrases.

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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 byFederal 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 Useof the International System of Units (SI), by David B. Newell and Eite Tiesinga. NISTSP 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 areencouraged 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.
August 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 beendrafted with permission obtained from the BIPM. The only official text is the French textof the original document created by the BIPM.”
To make its work more widely accessible, the International Committee for Weights andMeasures (CIPM) has decided to publish an English version of its reports. Readers shouldnote 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.

iv

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.

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The BIPM has its headquarters near Paris, in the grounds (43 520 m2) of thePavillon de Breteuil (Parc de Saint-Cloud) placed at its disposal by the
French Government; its upkeep is financed jointly by the Member States ofthe Meter Convention.
The task of the BIPM is to ensure worldwide unification of measurements;
its objectives are to:• represent the world-wide measurement community, aiming tomaximize its uptake and impact,• be a center for scientific and technical collaboration between Member
States, providing capabilities for international measurementcomparisons 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 theauthority of the General Conference on Weights and Measures (CGPM) andreports 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 thepropagation 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 determinationsand various scientific resolutions of international scope;take all major decisions concerning the finance, organization anddevelopment 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 Member States of the Meter Convention. The principal task of the CIPM
is to ensure worldwide uniformity in units of measurement. It does this bydirect action or by submitting proposals to the CGPM.

v

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, RussianFederation, Saudi Arabia,
Serbia, Singapore, Slovakia,
Slovenia, South Africa,
Spain, Sweden, Switzerland,
Thailand, Tunisia, Turkey,
Ukraine, United ArabEmirates, United Kingdom,
United States of America and
Uruguay
Forty-two States andEconomies were Associatesof 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 Republicof), Viet Nam, Zambia, andZimbabwe

The activities of the BIPM, which in the beginning were limited to measurements oflength 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 thisend 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 thelaser work and in 1988 for a library and offices. In 2001, a new building for theworkshop, offices, and meeting rooms was opened.
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Some forty-five physicists and technicians work in the BIPM laboratories. They mainly
conduct metrological research, international comparisons of realizations of units andcalibrations of standards. An annual Director’s report gives details of the work inprogress.
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 withinformation 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 theirrespective fields and for proposing recommendations to the CIPM concerning units.
The Consultative Committees have common regulations (Document CIPM-D-01, Rulesof 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 andspecialized 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), newname given in 1997 to the Consultative Committee for Electricity (CCE) set
up in 1927;
2. The Consultative Committee for Photometry and Radiometry (CCPR), newname 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 namegiven 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 Ionizing Radiationvi

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 γ rays, electrons), Section II (Measurement of radionuclides),Section III (Neutron measurements), Section IV (α-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 thetitle 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 scientific 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 ofmeasurement, 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 9th 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
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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 .............................................................122.3.3 Dimensions of quantities ......................................................................13
2.3.4 Derived units .........................................................................................142.3.5 Units for quantities that describe biological andphysiological 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
Appendix 2. Practical realization of the definitions of some important units ................. 105
Appendix 3. Units for photochemical and photobiological quantities ............................ 106

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Appendix 4. Historical notes on the development of the International System ofUnits and its base units .............................................................................................. 107
Part 1. The historical development of the realization of SI units............................... 107
Part 2. The historical development of the International System ................................ 109
Part 3. Historical perspective on the base units ......................................................... 112
List of acronyms used in the present volume................................................................... 117
Index ................................................................................................................................ 119
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LIST OF TABLES
Table 1. The seven defining constants of the SI and the seven corresponding
units they define .................................................................................................................. 4
Table 2. SI base units .......................................................................................................... 6
Table 3. Base quantities and dimensions used in the SI ................................................... 13
Table 4. The 22 SI units with special names and symbols ............................................... 15
Table 5. Examples of coherent derived units in the SI expressed in terms ofbase units ........................................................................................................................... 17
Table 6. Examples of SI coherent derived units whose names and symbols
include SI coherent derived units with special names and symbols ................................. 18
Table 7. SI prefixes ........................................................................................................... 23
Table 8. Non-SI units accepted for use with the SI units.................................................. 25xPreface to the 9th edition
The International System of Units, the SI, has been used around the world as thepreferred system of units, the basic language for science, technology, industry and tradesince it was established in 1960 by a resolution at the 11th meeting of the Conférence
Générale des Poids et Mesures, the CGPM (known in English as the General Conferenceon Weights and Measures). 1

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This brochure is published by the Bureau International des Poids et Mesures, the BIPM
(known in English as the International Bureau of Weights and Measures) to promote andexplain the SI. It lists the most significant Resolutions of the CGPM and decisions of the
Comité International des Poids et Mesures, the CIPM (known in English as theInternational Committee on Weights and Measures) that concern the metric system goingback to the 1st meeting of the CGPM in 1889.
The SI has always been a practical and dynamic system that has evolved to exploit thelatest scientific and technological developments. In particular, the tremendous advancesin atomic physics and quantum metrology made over the last 50 years have enabled thedefinitions of the second, the meter, and the practical representation of the electrical units
to take advantage of atomic and quantum phenomena to achieve levels of accuracy forrealizing the respective units limited only by our technical capability and not by thedefinitions themselves. These advances in science together with developments inmeasurement technology have enabled changes to the SI which have been promoted andexplained in the previous editions of this brochure.
This 9th edition of the SI brochure has been prepared following the adoption by the 26th
meeting of the CGPM of a set of far-reaching changes. The meeting introduced a new
approach to articulating the definitions of the units in general, and of the seven base units
in particular, by fixing the numerical values of seven “defining” constants. Among them
are fundamental constants of nature such as the Planck constant and the speed of light, sothat the definitions are based on and represent our present understanding of the laws ofphysics. For the first time, a complete set of definitions is available that does not makereference to any artifact standards, material properties or measurement descriptions.
These changes enable the realization of all units with an accuracy that is ultimately
limited only by the quantum structure of nature and our technical abilities but not by thedefinitions themselves. Any valid equation of physics relating the defining constants to aunit can be used to realize the unit, thus creating opportunities for innovation, realization
everywhere with increasing accuracy as technology proceeds. Thus, this redefinition
marks a significant and historic step forward.
The changes were agreed by the CGPM in November 2018 with effect from May 20th
2019, a date chosen because it is World Metrology Day, the day when the Meter
Convention was signed in 1875. While the future impact of the changes will be far
reaching, great attention has been paid to ensure that these definitions are consistent withthose in place at the time the change was implemented.

1

Editors’ note: The 9th CGPM in 1948 initiated the study that led to the formal establishment of the SI by
the 11th CGPM in 1960.
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We draw attention to the fact that since its establishment in 1960, the International
System of Units has always been referred to as “the SI” in its shortened form. This
principle has been maintained in the eight previous editions of this brochure and was
reaffirmed in Resolution 1 adopted at the 26th meeting of the CGPM, which also
confirmed that the title of this brochure is simply “The International System of Units”.
This consistency of reference to the SI reflects the efforts of the CGPM and the CIPM toensure the continuity of the values of measurements expressed in SI units through eachchange that has been made.
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The text of this brochure has been prepared in order to provide a full description of the SI
and to provide some historical background. It also has four appendices:
Appendix 1 reproduces, in chronological order, all of 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 is only available in an electronic version (www.bipm.org). It outlines thepractical realization of the seven base units and other important units in each field.
This appendix will be updated regularly to reflect improvements in the experimental
techniques available for realizing the units.
Appendix 3 is only available in an electronic version (www.bipm.org). It discusses
units for photo-chemical and photo-biological quantities.
Appendix 4 provides some notes on the history of the development of the SI.
We conclude by expressing our thanks to the members of the Comité Consultatif desUnités of the CIPM, the CCU (known in English as the Consultative Committee for
Units), who were responsible for drafting this brochure. Both the CCU and the CIPM
have approved the final text.
March 2019

B. Inglis

J. Ullrich

M.J.T. Milton

President, CIPM

President, CCU

Director, BIPM

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Note on the text:

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The 22nd meeting of the CGPM decided, in 2003, following a decision of the CIPM in
1997, that “the symbol for the decimal marker shall be either the point on the line or thecomma on the line.” Following this decision, and following custom in the two languages,
in this edition the point on the line is used as a decimal marker in the English text, and acomma on the line is used in the French text. This has no implication for the translationof the decimal marker into other languages. Small spelling variations occur in thelanguage of the English speaking countries (for instance, “metre” and “meter,” “litre” and“liter”). In this respect, the English text presented here follows the ISO/IEC 80000 series
Quantities and units. 2 However, the symbols for SI units used in this brochure are thesame in all languages.
Readers should note that the official record of the meetings of the CGPM and thesessions of the CIPM is that of the French text. This brochure provides the text inEnglish, but when an authoritative reference is required or when there is doubt about theinterpretation of the text the French should be used.

2

Editors’ note: 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.
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1. Introduction
1.1 The SI and the defining constants

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This brochure presents information on the definition and use of the International System
of Units, universally known as the SI (from the French Système international d’unités),for which the General Conference on Weights and Measures (CGPM) has responsibility.
In 1960 the 11th CGPM formally defined and established the SI and has subsequently
revised it from time to time in response to the requirements of users and advances inscience and technology. The most recent and perhaps the most significant revision of the
SI since its establishment was made by the 26th CGPM (2018) and is documented in this
9th edition of the SI Brochure. The Meter Convention, the CGPM, the ComitéInternational des Poids et Mesures (CIPM), the Bureau International des Poids etMesures (BIPM), and the Consultative Committees are described in the text “The BIPM
and the Meter Convention” on page v. 3
The SI is a consistent system of units for use in all aspects of life, including international
trade, manufacturing, security, health and safety, protection of the environment, and in
the basic science that underpins all of these. The system of quantities underlying the SI
and the equations relating them are based on the present description of nature and arefamiliar to all scientists, technologists and engineers.
The definitions of the SI units are established in terms of a set of seven defining
constants. The complete system of units can be derived from the fixed values of thesedefining constants, expressed in the units of the SI. These seven defining constants are
the most fundamental feature of the definition of the entire system of units. These
particular constants were chosen after having been identified as being the best choice,taking into account the previous definition of the SI, which was based on seven baseunits, and progress in science.
A variety of experimental methods described by the CIPM Consultative Committees may
be used to realize the definitions. Descriptions of these realizations are also referred to as“mises en pratique.” Realizations may be revised whenever new experiments aredeveloped; for this reason advice on realizing the definitions is not included in thisbrochure but is available on the BIPM website.

1.2 Motivation for the use of defining constants to define the SI
Historically, SI units have been presented in terms of a set of – most recently seven –base units. All other units, described as derived units, are constructed as products ofpowers of the base units.
Different types of definitions for the base units have been used: specific properties ofartifacts such as the mass of the international prototype (IPK) for the unit kilogram; aspecific physical state such as the triple point of water for the unit kelvin; idealized3

Editors’ note: This sentence has been modified for clarity.
1

experimental prescriptions as in the case of the ampere and the candela; or constants ofnature such as the speed of light for the definition of the unit meter.

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To be of any practical use, these units not only have to be defined, but they also have tobe realized physically for dissemination. In the case of an artifact, the definition and therealization are equivalent – a path that was pursued by advanced ancient civilizations.
Although this is simple and clear, artifacts involve the risk of loss, damage or change.
The other types of unit definitions are increasingly abstract or idealized. Here, therealizations are separated conceptually from the definitions so that the units can, as amatter of principle, be realized independently at any place and at any time. In addition,
new and superior realizations may be introduced as science and technologies develop,
without the need to redefine the unit. These advantages – most obviously seen with thehistory of the definition of the meter from artifacts through an atomic reference transition
to the fixed numerical value of the speed of light – led to the decision to define all units
by using defining constants.
The choice of the base units was never unique, but grew historically and became familiar
to users of the SI. This description in terms of base and derived units is maintained in thepresent definition of the SI, but has been reformulated as a consequence of adoption of
the defining constants.

1.3 Implementation of the SI
The definitions of the SI units, as decided by the CGPM, represent the highest reference
level for measurement traceability to the SI.
Metrology institutes around the world establish the practical realizations of thedefinitions in order to allow for traceability of measurements to the SI. The Consultative
Committees provide the framework for establishing the equivalence of the realizations inorder to harmonize traceability world-wide.
Standardization bodies may specify further details for quantities and units and rules fortheir application, where these are needed by interested parties. Whenever SI units are
involved, these standards must refer to the definitions by the CGPM. Many suchspecifications are listed for example in the standards developed by the International
Organization for Standardization and the International Electrotechnical Commission(ISO/IEC 80000 series of international standards).
Individual countries have established rules concerning the use of units by national
legislation, 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 SI.
The International Organization of Legal Metrology (OIML) is charged with theinternational harmonization of the technical specifications of this legislation.

2

2. The International System of Units
2.1 Defining the unit of a quantity
The value of a quantity is generally expressed as the product of a number
and a unit. The unit is simply a particular example of the quantity concerned
which is used as a reference, and the number is the ratio of the value of thequantity to the unit.
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For a particular quantity different units may be used. For example, the valueof the speed v of a particle may be expressed as v = 25 m/s or v = 90 km/h,
where meter per second and kilometer per hour are alternative units for thesame value of the quantity speed.

For example, the speedof light in vacuum is aconstant of nature,
denoted by c, whose
value in SI units is givenby the relationc = 299 792 458 m/s
where the numericalvalue is 299 792 458
and the unit is m/s.

Before stating the result of a measurement, it is essential that the quantity
being presented is adequately described. This may be simple, as in the caseof the length of a particular steel rod, but can become more complex whenhigher accuracy is required and where additional parameters, such astemperature, need to be specified.
When a measurement result of a quantity is reported, the estimated value ofthe measurand (the quantity to be measured), and the uncertainty associatedwith that value, are necessary. Both are expressed in the same unit.

2.2 Definition of the SI
As for any quantity, the value of a fundamental constant can be expressed as
the product of a number and a unit.
The definitions below specify the exact numerical value of each constantwhen its value is expressed in the corresponding SI unit. By fixing the exact
numerical value the unit becomes defined, since the product of thenumerical value and the unit has to equal the value of the constant, which ispostulated to be invariant.

Quotients of SI units
may be expressed using
either a solidus (/) or anegative exponent (−)
For example,
m/s = m s−1
mol/mol = mol mol−1

The seven constants are chosen in such a way that any unit of the SI can be
written either through a defining constant itself or through products or
quotients of defining constants.
The International System of Units, the SI, is the system of units in which•

the unperturbed ground state hyperfine transition frequency of thecesium 133 atom ∆ν Cs is 9 192 631 770 Hz,•

the speed of light in vacuum c is 299 792 458 m/s,•

the Planck constant h is 6.626 070 15 × 10−34 J s,•

the elementary charge e is 1.602 176 634 × 10−19 C,•

the Boltzmann constant k is 1.380 649 × 10−23 J/K,

3

•

the Avogadro constant NA is 6.022 140 76 × 1023 mol−1,•

the luminous efficacy of monochromatic radiation of frequency
540 × 1012 Hz, Kcd, is 683 lm/W,

where the hertz, joule, coulomb, lumen, and watt, with unit symbols Hz, J, C, lm, and W,
respectively, are related to the units second, meter, kilogram, ampere, kelvin, mole, andcandela, with unit symbols s, m, kg, A, K, mol, and cd, respectively, according to
Hz = s–1, J = kg m2 s– 2, C = A s, lm = cd m2 m–2 = cd sr, and W = kg m2 s–3.
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The numerical values of the seven defining constants have no uncertainty.
Table 1. The seven defining constants of the SI and the seven corresponding units
they define
Defining constantSymbolNumerical value

Unithyperfine transition frequency of Cs∆ν Cs

9 192 631 770

Hzspeed of light in vacuumc299 792 458m s−1

Planck constanth6.626 070 15 × 10−34

Js

elementary chargee1.602 176 634 × 10−19C

Boltzmann constantk

1.380 649 × 10−23

J K−1

Avogadro constantNA

6.022 140 76 × 1023

mol−1luminous efficacy

Kcd

683

lm W−1

Preserving continuity, as far as possible, has always been an essential feature of any
changes to the International System of Units. The numerical values of the defining
constants have been chosen to be consistent with the earlier definitions in so far as
advances in science and knowledge allow.

2.2.1 The nature of the seven defining constants
The nature of the defining constants ranges from fundamental constants of nature totechnical constants.
The use of a constant to define a unit disconnects definition from realization. This offers
the possibility that completely different or new and superior practical realizations can be
developed, as technologies evolve, without the need to change the definition.
A technical constant such as Kcd, the luminous efficacy of monochromatic radiation of
frequency 540 × 1012 Hz refers to a special application. In principle, it can be chosen
freely, such as to include conventional physiological or other weighting factors. In
contrast, the use of a fundamental constant of nature, in general, does not allow thischoice because it is related to other constants through the equations of physics.
The set of seven defining constants has been chosen to provide a fundamental, stable anduniversal reference that simultaneously allows for practical realizations with the smallest
4

uncertainties. The technical conventions and specifications also take historicaldevelopments into account.
Both the Planck constant h and the speed of light in vacuum c are properly described as
fundamental. They determine quantum effects and space-time properties, respectively,
and affect all particles and fields equally on all scales and in all environments.

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The elementary charge e corresponds to a coupling strength of the electromagnetic force
via the fine-structure constant α = e2/(2cε0h) where ε0 is the vacuum electric permittivity
or electric constant. Some theories predict a variation of α over time. The experimental
limits of the maximum possible variation in α are so low, however, that any effect onforeseeable practical measurements can be excluded.
The Boltzmann constant k is a proportionality constant between the quantities
temperature (with unit kelvin) and energy (with unit joule), whereby the numerical value
is obtained from historical specifications of the temperature scale. The temperature of asystem scales with the thermal energy, but not necessarily with the internal energy of asystem. In statistical physics the Boltzmann constant connects the entropy S with thenumber Ω of quantum-mechanically accessible states, S = k ln Ω.
The cesium frequency ∆ν Cs, the unperturbed ground-state hyperfine transition frequencyof the cesium-133 atom, has the character of an atomic parameter, which may be affectedby the environment, such as electromagnetic fields. However, the underlying transition iswell understood, stable and a good choice as a reference transition under practicalconsiderations. The choice of an atomic parameter like ∆ν Cs does not disconnect
definition and realization in the same way that h, c, e, or k do, but specifies the reference.
The Avogadro constant NA is a proportionality constant between the quantity amount of
substance (with unit mole) and the quantity for counting entities (with unit one, symbol
1). Thus, it has the character of a constant of proportionality similar to the Boltzmann
constant k.
The luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, is atechnical constant that gives an exact numerical relationship between the purely physicalcharacteristics of the radiant power stimulating the human eye (W) and its
photobiological response defined by the luminous flux due to the spectral responsivity ofa standard observer (lm) at a frequency of 540 × 1012 Hz.

2.3 Definitions of the SI units
Prior to the definitions adopted in 2018, the SI was defined through seven base units fromwhich the derived units were constructed as products of powers of the base units.
Defining the SI by fixing the numerical values of seven defining constants has the effectthat this distinction is, in principle, not needed, since all units, base as well as derived
units, may be constructed directly from the defining constants. Nevertheless, the conceptof base and derived units is maintained because it is useful and historically wellestablished, noting also that the ISO/IEC 80000 series of Standards specify base andderived quantities which necessarily correspond to the SI base and derived units definedhere.
52.3.1 Base units
The base units of the SI are listed in Table 2.
Table 2. SI base units
Base quantity

Base unit

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Name

Typical symbol Name

Symboltimetsecondslengthl, x, r, etc.

meter

m

mass

m

kilogram kg

electric current

I, iampereAthermodynamic temperature T

kelvinKamount of substance

n

mole

mol

luminous intensity

Iv

candelacd

The symbols for quantities
are generally single letters of
the Latin or Greek alphabets,
printed in an italic font, andare recommendations.
The symbols for units are
printed in an upright (roman)font and are mandatory, seechapter 5.

Starting from the definition of the SI in terms of fixed numerical values ofthe defining constants, definitions of each of the seven base units are
deduced by using, as appropriate, one or more of these defining constants togive the following set of definitions:
The second
The second, symbol s, is the SI unit of time. It is defined by taking the
fixed numerical value of the cesium frequency ∆ν Cs, the unperturbed
ground-state hyperfine transition frequency of the cesium 133 atom, tobe 9 192 631 770 when expressed in the unit Hz, which is equal to s−1.
This definition implies the exact relation ∆ν Cs = 9 192 631 770 Hz. Inverting this relation
gives an expression for the unit second in terms of the defining constant ∆ν Cs:
1 Hz =∆ν Cs
9 192 631 770

or

1s =

9 192 631 770
.
∆ν Cs

(1)

The effect of this definition is that the second is equal to the duration of 9 192 631 770
periods of the radiation corresponding to the transition between the two hyperfine levelsof the unperturbed ground state of the 133Cs atom.
The reference to an unperturbed atom is intended to make it clear that the definition of
the SI second is based on an isolated cesium atom that is unperturbed by any external
field, such as ambient black-body radiation.
6

The second, so defined, is the unit of proper time in the sense of the general theory of
relativity. To allow the provision of a coordinated time scale, the signals of different
primary clocks in different locations are combined, which have to be corrected for
relativistic cesium frequency shifts (see section 2.3.6).

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The CIPM has adopted various secondary representations of the second, based on aselected number of spectral lines of atoms, ions or molecules. The unperturbed
frequencies of these lines can be determined with a relative uncertainty not lower thanthat of the realization of the second based on the 133Cs hyperfine transition frequency, butsome can be reproduced with superior stability.
The meter
The meter, symbol m, is the SI unit of length. It is defined by taking the fixed
numerical value of the speed of light in vacuum c to be 299 792 458 when expressedin the unit m s−1, where the second is defined in terms of the cesium frequency ∆ν Cs.
This definition implies the exact relation c = 299 792 458 m s−1. Inverting this relation
gives an exact expression for the meter in terms of the defining constants c and ∆ν Cs:
9 192 631 770 ccc.
 s =
1 m = ≈ 30.663 319
299 792 458 ∆ν Cs∆ν Cs
 299 792 458 (2)The effect of this definition is that one meter is the length of the path travelled by light invacuum during a time interval with duration of 1/299 792 458 of a second.
The kilogram
The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed
numerical value of the Planck constant h to be 6.626 070 15 × 10−34 when expressedin the unit J s, which is equal to kg m2 s−1, where the meter and the second aredefined in terms of c and ∆ν Cs.
This definition implies the exact relation h = 6.626 070 15 × 10−34 kg m2 s−1. Inverting
this relation gives an exact expression for the kilogram in terms of the three defining
constants h, ∆ν Cs and c:

 −2
h
m s
1 kg = −34 
 6.626 070 15 × 10
(3)

which is equal to

1 kg =h ∆ν Csh ∆ν Cs(299 792 458)2≈ 1.475 5214 × 10 40
2−34(6.626 070 15 × 10 )(9 192 631 770) c
c2
7

(4)

The effect of this definition is to define the unit kg m2 s−1 (the unit of both the physicalquantities action and angular momentum). Together with the definitions of the second
and the meter this leads to a definition of the unit of mass expressed in terms of the
Planck constant h.

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The previous definition of the kilogram fixed the value of the mass of the international
prototype of the kilogram, m(K), to be equal to one kilogram exactly and the value of the
Planck constant h had to be determined by experiment. The present definition fixes thenumerical value of h exactly and the mass of the prototype has now to be determined byexperiment.
The number chosen for the numerical value of the Planck constant in this definition issuch that at the time of its adoption, the kilogram was equal to the mass of theinternational prototype, m(K) = 1 kg, with a relative standard uncertainty of 1 × 10−8,which was the standard uncertainty of the combined best estimates of the value of the
Planck constant at that time.
Note that with the present definition, primary realizations can be established, in principle,
at any point in the mass scale.
The ampere
The ampere, symbol A, is the SI unit of electric current. It is defined by taking the
fixed numerical value of the elementary charge e to be 1.602 176 634 × 10−19 when
expressed in the unit C, which is equal to A s, where the second is defined in termsof ∆ν Cs.
This definition implies the exact relation e = 1.602 176 634 × 10−19 A s. Inverting thisrelation gives an exact expression for the unit ampere in terms of the defining constants eand ∆ν Cs:

 −1
e
s
1 A = −19 
 1.602 176 634 × 10 

(5)which is equal to1A =1∆ν e ≈ 6.789 687 × 108 ∆ν Cs e
(9 192 631 770) 1.602 176 634 × 10 −19 Cs

(

)

(6)

The effect of this definition is that one ampere is the electric current corresponding to theflow of 1/(1.602 176 634 × 10−19) elementary charges per second.
The previous definition of the ampere was based on the force between two current
carrying conductors and had the effect of fixing the value of the vacuum magnetic
8

permeability μ0 (also known as the magnetic constant) to be exactly
4π × 10−7 H m−1 = 4π × 10−7 N A−2, where H and N denote the coherent derived units
henry and newton, respectively. The new definition of the ampere fixes the value of e
instead of μ0. As a result, μ0 must be determined experimentally.

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It also follows that since the vacuum electric permittivity ε0 (also known as the electric
constant), the characteristic impedance of vacuum Z0, and the admittance of vacuum Y0
are equal to 1/μ0c2, μ0c, and 1/μ0c, respectively, the values of ε0, Z0, and Y0 must now also
be determined experimentally, and are affected by the same relative standard uncertainty
as μ0 since c is exactly known. The product ε0μ0 = 1/c2 and quotient Z0/μ0 = c remain
exact. At the time of adopting the present definition of the ampere, µ0 was equal to
4π × 10−7 H/m with a relative standard uncertainty of 2.3 × 10−10.
The kelvin
The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined bytaking the fixed numerical value of the Boltzmann constant k to be 1.380 649 × 10−23
when expressed in the unit J K−1, which is equal to kg m2 s−2 K−1, where thekilogram, meter and second are defined in terms of h, c and ∆ν Cs.
This definition implies the exact relation k = 1.380 649 × 10−23 kg m2 s−2 K−1. Inverting
this relation gives an exact expression for the kelvin in terms of the defining constants k,
h and ∆ν Cs:

 1.380 649 
2 −2
− 23
1K = 
 × 10 kg m s
k



(7)

which is equal to1K =1.380 649 × 10 −23(6.626 070 15 × 10 )−34

∆ν Cs h∆ν Cs h≈ 2.266 6653
k
(9 192 631 770) k(8)The effect of this definition is that one kelvin is equal to the change of thermodynamic
temperature that results in a change of thermal energy kT by 1.380 649 × 10−23 J.
The previous definition of the kelvin set the temperature of the triple point of water,
TTPW, to be exactly 273.16 K. Due to the fact that the present definition of the kelvin fixes
the numerical value of k instead of TTPW, the latter must now be determined
experimentally. At the time of adopting the present definition TTPW was equal to 273.16
K with a relative standard uncertainty of 3.7 × 10−7 based on measurements of k madeprior to the redefinition.
As a result 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 the9reference temperature T0 = 273.15 K, close to the ice point. This difference is called theCelsius temperature, symbol t, which is defined by the quantity equationt = T − T0.

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The unit of Celsius temperature is the degree Celsius, symbol ○C, which is by definition
equal in magnitude to the unit kelvin. A difference or interval of temperature may be
expressed in kelvin or in degrees Celsius, the numerical value of the temperature
difference being the same in either case. However, the numerical value of a Celsius
temperature expressed in degrees Celsius is related to the numerical value of thethermodynamic temperature expressed in kelvin by the relationt/○C = T/K − 273.15(10)(see 5.4.1 for an explanation of the notation used here).
The kelvin and the degree Celsius are also units of the International Temperature Scale of1990 (ITS-90) adopted by the CIPM in 1989 in Recommendation 5 (CI-1989, PV, 57,
115). Note that the ITS-90 defines two quantities T90 and t90 which are close
approximations to the corresponding thermodynamic temperatures T and t.
Note that with the present definition, primary realizations of the kelvin can, in principle,
be established at any point of the temperature scale.
The mole
The mole, symbol mol, is the SI unit of amount of substance. One mole contains
exactly 6.022 140 76 × 1023 elementary entities. This number is the fixed numericalvalue of the Avogadro constant, NA, when expressed in the unit mol−1 and is called
the Avogadro number.
The amount of substance, symbol n, of a system is a measure of the number of
specified elementary entities. An elementary entity may be an atom, a molecule, anion, an electron, any other particle or specified group of particles.
This definition implies the exact relation NA = 6.022 140 76 × 1023 mol−1. Inverting thisrelation gives an exact expression for the mole in terms of the defining constant NA: 6.022 140 76 × 10 23 
1 mol = 
NA



(11)

The effect of this definition is that the mole is the amount of substance of a system that
contains 6.022 140 76 × 1023 specified elementary entities.

10

The previous definition of the mole fixed the value of the molar mass of carbon-12,
M(12C), to be exactly 0.012 kg/mol. According to the present definition M(12C) is nolonger known exactly and must be determined experimentally. The value chosen for NA issuch that at the time of adopting the present definition of the mole, M(12C) was equal to0.012 kg/mol with a relative standard uncertainty of 4.5 × 10−10.
The molar mass of any atom or molecule X may still be obtained from its relative atomic
mass from the equation
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M(X) = Ar(X) [M(12C)/12] = Ar(X) Mu(12)

and the molar mass of any atom or molecule X is also related to the mass of theelementary entity m(X) by the relation(13)

M(X) = NA m(X) = NA Ar(X) mu .

In these equations Mu is the molar mass constant, equal to M(12C)/12 and mu is the unified
atomic mass constant, equal to m(12C)/12. They are related to the Avogadro constantthrough the relation(14)

Mu = NA mu .

In the name “amount of substance,” the word “substance” will typically be replaced bywords to specify the substance concerned in any particular application, for example“amount of hydrogen chloride, HCl,” or “amount of benzene, C6H6.” It is important togive a precise definition of the entity involved (as emphasized in the definition of themole); this should preferably be done by specifying the molecular chemical formula ofthe material involved. Although the word “amount” has a more general dictionary
definition, the abbreviation of the full name “amount of substance” to “amount” may be
used for brevity. This also applies to derived quantities such as “amount-of-substanceconcentration,” which may simply be called “amount concentration.” In the field ofclinical chemistry, the name “amount-of-substance concentration” is generally
abbreviated to “substance concentration.”
The candela
The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It isdefined by taking the fixed numerical value of the luminous efficacy of
monochromatic radiation of frequency 540 × 1012 Hz, Kcd, to be 683 when expressedin the unit lm W−1, which is equal to cd sr W−1, or cd sr kg−1 m−2 s3, where thekilogram, meter and second are defined in terms of h, c and ∆ν Cs.

11

This definition implies the exact relation Kcd = 683 cd sr kg−1 m−2 s3 for monochromaticradiation of frequency ν = 540 × 1012 Hz. Inverting this relation gives an exact expression
for the candela in terms of the defining constants Kcd, h and ∆ν Cs:
K 
1 cd =  cd  kg m 2 s − 3 sr −1
 683 (15)

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which is equal to

1 cd =

1(6.626 070 15 × 10 ) (9 192 631 770) 683−342≈ 2.614 830 × 10 10 (∆ν Cs ) 2 h K cd(∆ν Cs ) 2 h K cd

(16)

(17)

The effect of this definition is that one candela is the luminous intensity, in a given
direction, of a source that emits monochromatic radiation of frequency 540 × 1012 Hz andhas a radiant intensity in that direction of (1/683) W/sr. The definition of the steradian isgiven below Table 4.

2.3.2 Practical realization of SI units
The highest-level experimental methods used for the realization of units using theequations of physics are known as primary methods. The essential characteristic of a
primary method is that it allows a quantity to be measured in a particular unit by using only
measurements of quantities that do not involve that unit. In the present formulation of theSI, the basis of the definitions is different from that used previously, so that new methods
may be used for the practical realization of SI units.
Instead of each definition specifying a particular condition or physical state, which sets afundamental limit to the accuracy of realization, a user is now free to choose any
convenient equation of physics that links the defining constants to the quantity intended
to be measured. This is a much more general way of defining the basic units ofmeasurement. It is not limited by today’s science or technology; future developments
may lead to different ways of realizing units to a higher accuracy. When defined thisway, there is, in principle, no limit to the accuracy with which a unit might be realized.
The exception remains the definition of the second, in which the original microwave
transition of cesium must remain, for the time being, the basis of the definition. For a
more comprehensive explanation of the realization of SI units see Appendix 2.

12

2.3.3 Dimensions of quantities
Physical quantities can be organized in a system of dimensions, where the system used isdecided by convention. Each of the seven base quantities used in the SI is regarded ashaving its own dimension. The symbols used for the base quantities and the symbols used
to denote their dimension are shown in Table 3.
Table 3. Base quantities and dimensions used in the SI
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Base quantity

Typical symbol for quantity

Symbol for dimension

time

t

T

lengthl, x, r, etc.

L

mass

m

M

electric current

I, i

I

thermodynamic temperatureTΘ

amount of substancenNluminous intensity

Iv

J

All other quantities, with the exception of counts, are derived quantities, which may be
written in terms of base quantities according to the equations of physics. The dimensionsof the derived quantities are written as products of powers of the dimensions of the basequantities using the equations that relate the derived quantities to the base quantities.
In general, the dimension of any quantity Q is written in the form of a dimensional
product,

dim Q = Tα LβM γ Iδ Θε Nζ Jη

(18)

where the exponents α, β, γ, δ, ε, ζ and η, which are generally small integers, which canbe positive, negative, or zero, are called the dimensional exponents.
There are quantities Q for which the defining equation is such that all of the dimensional
exponents in the equation for the dimension of Q are zero. This is true in particular for
any quantity that is defined as the ratio of two quantities of the same kind. For example,
the refractive index is the ratio of two speeds and the relative permittivity is the ratio of
the permittivity of a dielectric medium to that of free space. Such quantities are simply
numbers. The associated unit is the unit one, symbol 1, although this is rarely explicitly
written (see 5.4.7).

13

There are also some quantities that cannot be described in terms of the seven basequantities of the SI, but have the nature of a count. Examples are a number of molecules,
a number of cellular or biomolecular entities (for example copies of a particular nucleic
acid sequence), or degeneracy in quantum mechanics. Counting quantities are also
quantities with the associated unit one.

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The unit one is the neutral element of any system of units – necessarily and present
automatically. There is no requirement to introduce it formally by decision. Therefore, aformal traceability to the SI can be established through appropriate, validated
measurement procedures.
Plane and solid angles, when expressed in radians and steradians respectively, are ineffect also treated within the SI as quantities with the unit one (see section 5.4.8). The
symbols rad and sr are written explicitly where appropriate, in order to emphasize that,for radians or steradians, the quantity being considered is, or involves the plane angle orsolid angle respectively. For steradians it emphasizes the distinction between units of fluxand intensity in radiometry and photometry for example. However, it is a longestablished practice in mathematics and across all areas of science to make use of rad = 1
and sr = 1. For historical reasons the radian and steradian are treated as derived units, as
described in section 2.3.4.
It is especially important to have a clear description of any quantity with unit one (seesection 5.4.7) that is expressed as a ratio of quantities of the same kind (for example
length ratios or amount fractions) or as a count (for example number of photons or
decays).

2.3.4 Derived units
Derived units are defined as products of powers of the base units. When the numericalfactor of this product is one, the derived units are called coherent derived units. The baseand coherent derived units of the SI form a coherent set, designated the set of coherent SI
units. The word “coherent” here means that equations between the numerical values ofquantities take exactly the same form as the equations between the quantities themselves.
Some of the coherent derived units in the SI are given special names. Table 4 lists 22 SI
units with special names. Together with the seven base units (Table 2) they form the coreof the set of SI units. All other SI units are combinations of some of these 29 units.
It is important to note that any of the seven base units and 22 SI units with special names
can be constructed directly from the seven defining constants. In fact, the units of theseven defining constants include both base and derived units.
The CGPM has adopted a series of prefixes for use in forming the decimal multiples andsub-multiples of the coherent SI units (see chapter 3). They are convenient for expressing
the values of quantities that are much larger than or much smaller than the coherent unit.
However, when prefixes are used with SI units, the resulting units are no longer coherent,
because the prefix introduces a numerical factor other than one. Prefixes may be usedwith any of the 29 SI units with special names with the exception of the base unit
kilogram, which is further explained in chapter 3.

14

Table 4. The 22 SI units with special names and symbols
Unit expressed interms of other
SI units

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Derived quantity

Special nameof unit

Unit expressed interms of base units (a)plane angle

radian (b)rad = m/m

solid angle

steradian (c)sr = m2/m2

frequency

hertz (d)Hz = s−1

force

newtonN = kg m s−2

pressure, stresspascalPa = kg m−1 s−2energy, work,
amount of heatjoule

J = kg m2 s−2Nmpower, radiant fluxwatt

W = kg m2 s−3

J/selectric charge

coulomb

C=Aselectric potential
difference (e)volt

V = kg m2 s−3 A−1

W/A

capacitancefarad

F = kg−1 m−2 s4 A2

C/V

electric resistanceohm

Ω = kg m2 s−3 A−2

V/Aelectric conductancesiemens

S = kg−1 m−2 s3 A2

A/V

magnetic flux

weber

Wb = kg m2 s−2 A−1

Vs

magnetic flux density

tesla

T = kg s−2 A−1

Wb/m2

inductancehenry

H = kg m2 s−2 A−2

Wb/A

Celsius temperature

degree Celsius (f)oluminous flux

lumen

lm = cd sr (g)cd srilluminancelux

lx = cd sr m−2

lm/m2

activity referred to aradionuclide (d,h)

becquerel

Bq = s−1

absorbed dose, kerma

grayGy = m2 s−2

J/kg

dose equivalentsievert (i)Sv = m2 s−2

J/kg

catalytic activity

katalkat = mol s−1

C=K

15

(a) The order of symbols for base units in this Table is different from that in the 8thedition following a decision by the CCU at its 21st meeting (2013) to return to theoriginal order in Resolution 12 of the 11th CGPM (1960) in which newton was
written kg m s−2, the joule as kg m2 s−2 and J s as kg m−2 s−1. The intention was toreflect the underlying physics of the corresponding quantity equations although forsome more complex derived units this may not be possible.

This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019(b) The radian is the coherent unit for plane angle. One radian is the angle subtended at
the center of a circle by an arc that is equal in length to the radius. It is also the unit
for phase angle. For periodic phenomena, the phase angle increases by 2π rad in one
period. The radian was formerly an SI supplementary unit, but this category wasabolished in 1995.
(c) The steradian is the coherent unit for solid angle. One steradian is the solid angle
subtended at the center of a sphere by an area of the surface that is equal to thesquared radius. Like the radian, the steradian was formerly an SI supplementary unit.
(d) The hertz shall only be used for periodic phenomena and the becquerel shall only be
used for stochastic processes in activity referred to a radionuclide.
(e) Electric potential difference is also called “voltage” in the United States and in many
countries, as well as “electric tension” or simply “tension” in some countries.
(f) The degree Celsius is used to express Celsius temperatures. The numerical value of atemperature difference or temperature interval is the same when expressed in either
degrees Celsius or in kelvin.
(g) In photometry the name steradian and the symbol sr are usually retained in
expressions for units(h) Activity referred to a radionuclide is sometimes incorrectly called radioactivity.
(i) See CIPM Recommendation 2 on the use of the sievert (PV, 2002, 70, 205).
The seven base units and 22 units with special names and symbols may be used in
combination to express the units of other derived quantities. Since the number ofquantities is without limit, it is not possible to provide a complete list of derived
quantities and derived units. Table 5 lists some examples of derived quantities and thecorresponding coherent derived units expressed in terms of base units. In addition, Table
6 lists examples of coherent derived units whose names and symbols also include derived
units. The complete set of SI units includes both the coherent set and the multiples andsub-multiples formed by using the SI prefixes.

16

Table 5. Examples of coherent derived units in the SI expressed in terms of baseunits

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Derived quantity

Typical symbol ofquantity

Derived unit expressedin terms of base units

area

A

m2

volumeVm3

speed, velocity

v

m s−1

acceleration

a

m s−2

wavenumberσm−1

density, mass density

ρkg m−3surface density

ρA

kg m−2

specific volumev

m3 kg−1current density

j

A m−2

magnetic field strength

H

A m−1

amount of substance concentrationc

mol m−3

mass concentration

ρ, γ

kg m−3luminance

Lv

cd m−217

Table 6. Examples of SI coherent derived units whose names and symbols include SI
coherent derived units with special names and symbols

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Derived quantity

Name of coherent derived
unit

SymbolDerived unit expressedin terms of base units

dynamic viscosity

pascal second

Pa s

kg m−1 s−1

moment of force

newton meterNm

kg m2 s−2

surface tension
angular velocity,
angular frequency
angular acceleration
heat flux density,
irradianceheat capacity, entropy
specific heat
capacity, specificentropyspecific energy

newton per meter

N m−1

kg s−2

radian per second

rad s−1

s−1

radian per second squared

rad/s2s−2watt per square meter

W/m2

kg s−3joule per kelvin

J K−1

kg m2 s−2 K−1joule per kilogram kelvin

J K−1 kg−1

m2 s−2 K−1joule per kilogram

J kg−1m2 s−2

thermal conductivity

watt per meter kelvin

W m−1 K−1

kg m s−3 K−1energy density

joule per cubic meter

J m−3

kg m−1 s−2electric field strength
electric charge
densitysurface charge
densityelectric flux density,
electric displacement
permittivity

volt per meter

V m−1

kg m s−3 A−1

coulomb per cubic meter

C m−3

A s m−3coulomb per square meter

C m−2

A s m−2

coulomb per square meter

C m−2

A s m−2

farad per meter

F m−1

kg−1 m−3 s4 A2

permeability

henry per meter

H m−1

kg m s−2 A−2molar energy
molar entropy, molar
heat capacity
exposure (x- and γrays)
absorbed dose ratejoule per mole

J mol−1

kg m2 s−2 mol−1joule per mole kelvin

J K−1 mol−1

kg m2 s−2 mol−1 K−1coulomb per kilogram

C kg−1A s kg−1

gray per second

Gy s−1m2 s−3

radiant intensity

watt per steradianwatt per square meter
steradian

W sr−1

kg m2 s−3

W sr−1 m−2

kg s−3katal per cubic meterkat m−3mol s−1 m−3

radiance
catalytic activity
concentration18

It is important to emphasize that each physical quantity has only one
coherent SI unit, even though this unit can be expressed in different forms
by using some of the special names and symbols.

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The converse, however, is not true, because in general several different
quantities may share the same SI unit. For example, for the quantity heat
capacity as well as for the quantity entropy the SI unit is joule per kelvin.
Similarly, for the base quantity electric current as well as the derived
quantity magnetomotive force the SI unit is the ampere. It is therefore
important not to use the unit alone to specify the quantity. This applies not
only to technical texts, but also, for example, to measuring instruments (i.e.
the instrument read-out needs to indicate both the unit and the quantity
measured).
In practice, with certain quantities, preference is given to the use of certain
special unit names to facilitate the distinction between different quantities
having the same dimension. When using this freedom, one may recall theprocess by which this quantity is defined. For example, the quantity torqueis the cross product of a position vector and a force vector. The SI unit isnewton meter. Even though torque has the same dimension as energy (SIunit joule), the joule is never used for expressing torque.
The SI unit of frequency is hertz, the SI unit of angular velocity and angularfrequency is radian per second, and the SI unit of activity is becquerel,
implying decays per second. Although it is formally correct to write all threeof these units as the reciprocal second, the use of the different names
emphasizes the different nature of the quantities concerned. It is especially
important to carefully distinguish frequencies from angular frequencies,
because by definition their numerical values differ by a factor 4 of 2π.
Ignoring this fact may cause an error of 2π. Note that in some countries,
frequency values are conventionally expressed using “cycle/s” or “cps”
instead of the SI unit Hz, although “cycle” and “cps” are not units in the SI.
Note also that it is common, although not recommended, to use the term
frequency for quantities expressed in rad/s. Because of this, it isrecommended that quantities called “frequency,” “angular frequency,” and“angular velocity” always be given explicit units of Hz or rad/s and not s−1.
In the field of ionizing radiation, the SI unit becquerel rather than thereciprocal second is used. The SI units gray and sievert are used forabsorbed dose and dose equivalent, respectively, rather than joule perkilogram. The special names becquerel, gray and sievert were specificallyintroduced because of the dangers to human health that might arise frommistakes involving the units reciprocal second and joule per kilogram, incase the latter units were incorrectly taken to identify the different quantities
involved.
Special care must be taken when expressing temperatures or temperature
differences, respectively. A temperature difference of 1 K equals that of4

see ISO 80000-3 for details.

19

The International
ElectrotechnicalCommission (IEC) has
introduced the var(symbol: var) as a specialname for the unit ofreactive power. In termsof SI coherent units, thevar is identical to the volt
ampere.

1 oC, but for an absolute temperature the difference of 273.15 K must be taken into
account. The unit degree Celsius is only coherent when expressing temperature
differences.

2.3.5 Units for quantities that describe biological and physiological effects
Four of the SI units listed in tables 2 and 4 include physiological weighting factors:
candela, lumen, lux, and sievert.
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Lumen and lux are derived from the base unit candela. Like the candela, they carryinformation about human vision. The candela was established as a base unit in 1954,
acknowledging the importance of light in daily life. Further information on the units andconventions used for defining photochemical and photobiological quantities is in
Appendix 3.
Ionizing radiation deposits energy in irradiated matter. The ratio of deposited energy tomass is termed absorbed dose D. As decided by the CIPM in 2002, the quantity dose
equivalent H = Q D is the product of the absorbed dose D and a numerical quality factor
Q that takes into account the biological effectiveness of the radiation and is dependent on
the energy and type of radiation.
There are units for quantities that describe biological effects and involve weighting
factors which are not SI units. Two examples are given here:
Sound causes pressure fluctuations in the air, superimposed on the normal atmosphericpressure, that are sensed by the human ear. The sensitivity of the ear depends on thefrequency of the sound, but it is not a simple function of either the pressure changes or
the frequency. Therefore, frequency-weighted quantities are used in acoustics toapproximate the way in which sound is perceived. They are used, for example, formeasurements concerning protection against hearing damage. The effect of ultrasonicacoustic waves poses similar concerns in medical diagnosis and therapy.
There is a class of units for quantifying the biological activity of certain substances usedin medical diagnosis and therapy that cannot yet be defined in terms of the units of the SI.
This lack of definition is because the mechanism of the specific biological effect of thesesubstances is not yet sufficiently well understood for it to be quantifiable in terms ofphysico-chemical parameters. In view of their importance for human health and safety,
the World Health Organization (WHO) has taken responsibility for defining WHO
International Units (IU) for the biological activity of such substances.

2.3.6 SI units in the framework of the general theory of relativity
The practical realization of a unit and the process of comparison require a set of
equations within a framework of a theoretical description. In some cases, these equations
include relativistic effects.
For frequency standards it is possible to establish comparisons at a distance by means ofelectromagnetic signals. To interpret the results, the general theory of relativity isrequired, since it predicts, among other things, a relative frequency shift between
20

standards of about 1 part in 1016 per meter of altitude difference at the surface of theearth. Effects of this magnitude must be corrected for when comparing the best frequency
standards.
When practical realizations are compared locally, i.e. in a small space-time domain,
effects due to the space-time curvature described by the general theory of relativity canbe neglected. When realizations share the same space-time coordinates (for example thesame motion and acceleration or gravitational field), relativistic effects may be neglected
entirely.
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22

3. Decimal multiples and sub-multiples of SI units
Decimal multiples and submultiples ranging from 1024 to 10−24 are provided
for use with the SI units. The names and symbols of these multiple and submultiple prefixes are presented in Table 7.

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Prefix symbols are printed in upright typeface, as are unit symbols,
regardless of the typeface used in the surrounding text and are attached tounit symbols without a space between the prefix symbol and the unit
symbol. With the exception of da (deka), h (hecto) and k (kilo), all multiple
prefix symbols are upper-case letters and all sub-multiple prefix symbols arelowercase letters. All prefix names are printed in lowercase letters, except at
the beginning of a sentence.

Table 7. SI prefixes
FactorName

SymbolFactorName

Symbol

101

deka

da

10−1

deci

d

102

hecto

h

10−2

centi

c

103

kilo

k

10−3

milli

m

106

mega

M

10−6

micro

µ

109

giga

G

10−9

nano

n

1012

tera

T

10−12

pico

p

1015

peta

P

10−15

femto

f

1018

exa

E

10−18

atto

a

1021

zetta

Z

10−21

zepto

z

1024

yotta

Y

10−24

yocto

y

The SI prefixes referstrictly to powers of 10.
They should not be used
to indicate powers of 2(for example, one kilobit
represents 1000 bits andnot 1024 bits). The
names and symbols forprefixes to be used withpowers of 2 arerecommended as follows:
kibi
mebi
gibi
tebi
pebi
exbi
zebi
yobi

Ki
Mi
Gi
Ti
Pi
Ei
Zi
Yi

The grouping formed by a prefix symbol attached to a unit symbol constitutes a new
inseparable unit symbol (forming a multiple or sub-multiple of the unit concerned) thatcan be raised to a positive or negative power and that can be combined with other unit
symbols to form compound unit symbols.
Examples:pm (picometer), mmol (millimole), GΩ (gigaohm), THz (terahertz)
2.3 cm3 = 2.3 (cm)3 = 2.3 (10−2 m)3 = 2.3 ×10−6 m3
1 cm−1 = 1 (cm)−1 = 1 (10−2 m)−1 = 102 m−1 = 100 m−1 .

Similarly prefix names are also inseparable from the unit names to which they areattached. Thus, for example, millimeter, micropascal and meganewton are single words.
23

210
220
230
240
250
260
270
280

Compound prefix symbols, i.e. prefix symbols formed by the juxtaposition of two or
more prefix symbols, are not permitted. This rule also applies to two or more compound
prefix names.
Prefix symbols can neither stand alone nor be attached to the number 1, the symbol forthe unit one. Similarly, prefix names cannot be attached to the name of the unit one, thatis, to the word “one.”

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The kilogram is the only coherent SI unit whose name and symbol, for historical reasons,
include a prefix. Names and symbols for decimal multiples and sub-multiples of the unitof mass are formed by attaching prefix names and symbols to the unit name “gram” andthe unit symbol “g” respectively. For example, 10−6 kg is written as milligram, mg, not as
microkilogram, µkg.

24

4. Non-SI units that are accepted for use with the SI
The SI provides the internationally agreed reference in terms of which all other units aredefined. The coherent SI units have the important advantage that unit conversions are notrequired when inserting particular values for quantities into quantity equations.

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Nonetheless it is recognized that some non-SI units are widely used and are expected tocontinue to be used for many years. Therefore, the CIPM has accepted some non-SI units
for use with the SI; these are listed in Table 8. If these units are used it should beunderstood that some advantages of the SI are lost. The SI prefixes can be used withseveral of these units, but not, for example, with the non-SI units of time.
Table 8. Non-SI units accepted for use with the SI units

Quantitytime

Name of unit

Symbolfor unit

Value in SI units

minutemin

1 min = 60 s

hour

h

1 h = 60 min = 3600 s

dayd

1 d = 24 h = 86 400 s
1 au = 149 597 870 700 m

astronomical unit (a) au
lengthplane andphase angle

degreeo

1o = (π/180) radminute′1′ = (1/60)o = (π/ 10 800) radsecond (b)″1″ = (1/60)′ = (π/ 648 000) radarea

hectare (c)ha

1 ha = 1 hm2 = 104 m2

volumeliter (d)L

1 L = 1 dm3 = 103 cm3 = 10−3 m3

metric ton (e)t

1 t = 103 kg

dalton (f)Da

1 Da = 1.660 539 040 (20) × 10−27 kg

electronvolt (g)eV

1 eV = 1.602 176 634 × 10−19 J

neper (h)Npbel (h)Bdecibel (h)

dB

mass
energylogarithmic
ratio
quantities

see text

25

(a)As decided at the XXVIII General Assembly of the International
Astronomical Union (Resolution B2, 2012).
(b)For some applications such as in astronomy, small angles are measured inarcseconds (i.e. seconds of plane angle), denoted as or ″, milliarcseconds,
microarcseconds and picoarcseconds, denoted mas, μas and pas,
respectively, where arcsecond is an alternative name for second of planeangle.
This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019(c) The unit hectare and its symbol ha, were adopted by the CIPM in 1879
(PV, 1879, 41). The hectare is used to express land area.
(d)The liter and the symbol lower-case l, were adopted by the CIPM in 1879
(PV, 1879, 41). The alternative symbol, capital L, was adopted by the
16th CGPM (1979, Resolution 6; CR, 101 and Metrologia, 1980, 16, 5657) in order to avoid the risk of confusion between the letter l (el) and thenumeral 1 (one). Editors’ note: Since the preferred unit symbol for theliter in the United States is L, only L is given in the table; see the Federal
Register notice of July 28, 1998, “Metric System of Measurement:Interpretation of the International System of Units for the United States”(FR 40334-4030).
(e) Editors’ note: Metric ton is the name to be used for this unit in the
United States; see the Federal Register notice of May 16, 2008,“Interpretation of the International System of Units (the Metric System of
Measurement) for the United States” (FR 28432-28433). The original
English text in the BIPM SI Brochure uses the CGPM adopted name“tonne” and footnote (e) reads as follows: The tonne and its symbol t,were adopted by the CIPM in 1879 (PV, 1879, 41). This unit issometimes referred to as “metric ton” in some English-speaking
countries.
(f) The dalton (Da) and the unified atomic mass unit (u) are alternative
names (and symbols) for the same unit, equal to 1/12 of the mass of afree carbon 12 atom, at rest and in its ground state. This value of thedalton is the value recommended in the CODATA 2014 adjustment. It
will be updated in the CODATA 2018 adjustment to take into accountthe, now fixed, 2017 value of the Planck constant h. This will reduce the2014 uncertainty by an order of magnitude. Editors’ note: The
CODATA 2018 recommended values are available online athttps://physics.nist.gov/cuu/Constants/.
(g)The electronvolt is the kinetic energy acquired by an electron in passing
through a potential difference of one volt in vacuum. The electronvolt isoften combined with the SI prefixes.
(h)In using these units it is important that the nature of the quantity be
specified and that any reference value used be specified.

26

The gal (symbol: Gal) is
a non SI unit ofacceleration employed ingeodesy and geophysics
to express acceleration
due to gravity.
1 Gal = 1 cm s−2= 10−2 m s−2

Table 8 also includes the units of logarithmic ratio quantities, the neper, bel and decibel.
They are used to convey information on the nature of the logarithmic ratio quantity
concerned. The neper, Np, is used to express the values of quantities whose numericalvalues are based on the use of the neperian (or natural) logarithm, ln = loge. The bel andthe decibel, B and dB, where 1 dB = (1/10) B, are used to express the values oflogarithmic ratio quantities whose numerical values are based on the decadic logarithm,
lg = log10. The statement LX = m dB = (m/10) B (where m is a number) is interpreted tomean that m = 10 lg(X/X0). The units neper, bel and decibel have been accepted by the
CIPM for use with the International System, but are not SI units.
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There are many more non-SI units, which are either of historical interest, or are still usedin specific fields (for example, the barrel of oil) or in particular countries (the inch, footand yard). The CIPM can see no case for continuing to use these units in modern
scientific and technical work. However, it is clearly a matter of importance to be able torecall the relation of these units to the corresponding SI units and this will continue to betrue for many years. 5

5
Editors’ note: For a more thorough listing of non-SI units commonly used in the United States, see NIST Special
Publication 811, Guide for the Use of the International System of Units (SI).

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5. Writing unit symbols and names, and expressing the valuesof quantities
5.1 The use of unit symbols and names

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General principles for the writing of unit symbols and numbers were first given by the
9th CGPM (1948, Resolution 7). These were subsequently elaborated by ISO, IEC andother international bodies. As a consequence, there now exists a general consensus on
how unit symbols and names, including prefix symbols and names as well as quantity
symbols should be written and used, and how the values of quantities should be
expressed. Compliance with these rules and style conventions, the most important of
which are presented in this chapter, supports the readability of scientific and technicalpapers.

5.2 Unit symbols
Unit symbols are printed in upright type regardless of the type used in the surrounding
text. They are printed in lower-case letters unless they are derived from a proper name, inwhich case the first letter is a capital letter.
An exception, adopted by the 16th CGPM (1979, Resolution 6), is that either capital L orlower-case l is allowed for the liter, in order to avoid possible confusion between the
numeral 1 (one) and the lower-case letter l (el). 6
A multiple or sub-multiple prefix, if used, is part of the unit and precedes the unit symbol
without a separator. A prefix is never used in isolation and compound prefixes are neverused.
Unit symbols are mathematical entities and not abbreviations. Therefore, they are notfollowed by a period except at the end of a sentence, and one must neither use the plural
nor mix unit symbols and unit names within one expression, since names are notmathematical entities.
In forming products and quotients of unit symbols the normal rules of algebraic
multiplication or division apply. Multiplication must be indicated by a space or a halfhigh (centered) dot (⋅), since otherwise some prefixes could be misinterpreted as a unit
symbol. Division is indicated by a horizontal line, by a solidus (oblique stroke, /) or by
negative exponents. When several unit symbols are combined, care should be taken to
avoid ambiguities, for example by using brackets or negative exponents. A solidus mustnot be used more than once in a given expression without brackets to remove
ambiguities.
It is not permissible to use abbreviations for unit symbols or unit names, such as sec (foreither s or second), sq. mm (for either mm2 or square millimeter), cc (for either cm3 or
cubic centimeter), or mps (for either m/s or meter per second). The use of the correct
symbols for SI units, and for units in general, as listed in earlier chapters of this brochure,
6

Editors’ note: the unit symbol L is preferred in the United States; see footnote (d) of Table 8.
29

is mandatory. In this way ambiguities and misunderstandings in the values of quantities
are avoided.

5.3 Unit names

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Unit names are normally printed in upright type and they are treated like ordinary nouns.
In English, the names of units start with a lower-case letter (even when the symbol for theunit begins with a capital letter), except at the beginning of a sentence or in capitalizedmaterial such as a title. In keeping with this rule, the correct spelling of the name of theunit with the symbol °C is “degree Celsius” (the unit degree begins with a lower-case dand the modifier Celsius begins with an upper-case C because it is a proper name).
Although the values of quantities are normally expressed using symbols for numbers andsymbols for units, if for some reason the unit name is more appropriate than the unit
symbol, the unit name should be spelled out in full.
When the name of a unit is combined with the name of a multiple or sub-multiple prefix,
no space or hyphen is used between the prefix name and the unit name. The combinationof prefix name and unit name is a single word (see chapter 3).
When the name of a derived unit is formed from the names of individual units byjuxtaposition, either a space or a hyphen is used to separate the names of the individual
units.

5.4 Rules and style conventions for expressing values ofquantities
5.4.1 Value and numerical value of a quantity, and the use of quantity
calculus
Symbols for quantities are generally single letters set in an italic font, although they may
be qualified by further information in subscripts or superscripts or in brackets. For
example, C is the recommended symbol for heat capacity, Cm for molar heat capacity,
Cm, p for molar heat capacity at constant pressure, and Cm,V for molar heat capacity atconstant volume.
Recommended names and symbols for quantities are listed in many standard references,such as the ISO/IEC 80000 series Quantities and units, the IUPAP SUNAMCO RedBook Symbols, Units and Nomenclature in Physics and the IUPAC Green Book
Quantities, Units and Symbols in Physical Chemistry. However, symbols for quantities
are recommendations (in contrast to symbols for units, for which the use of the correct
form is mandatory). In certain circumstances authors may wish to use a symbol of theirown choice for a quantity, for example to avoid a conflict arising from the use of thesame symbol for two different quantities. In such cases, the meaning of the symbol must
be clearly stated. However, neither the name of a quantity, nor the symbol used to denoteit, should imply any particular choice of unit.

30Symbols for units are treated as mathematical entities. In expressing the value of aquantity as the product of a numerical value and a unit, both the numerical value and theunit may be treated by the ordinary rules of algebra. This procedure is described as theuse of quantity calculus, or the algebra of quantities. For example, the equation p = 48
kPa may equally be written as p/kPa = 48. It is common practice to write the quotient of aquantity and a unit in this way for a column heading in a table, so that the entries in thetable are simply numbers. For example, a table of the velocity squared versus pressure
may be formatted as shown below.
ν2/(m/s)2

48.73

94766

72.87

94771

135.42

94784

The axes of a graph may also be labelled in this way, so that the tick marks are labelled
only with numbers, as in the graph below.

94790

2

94780

94770

2

v / (m/s)

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p/kPa

94760

94750
0

50

100

150

p / kPa

5.4.2 Quantity symbols and unit symbols
Unit symbols must not be used to provide specific information about thequantity and should never be the sole source of information on the quantity.
Units are never qualified by further information about the nature of thequantity; any extra information on the nature of the quantity should be
attached to the quantity symbol and not to the unit symbol.
31

For example:
The maximum electric
potential difference is
Umax = 1000 V
but not U = 1000 Vmax.
The mass fraction of copperin the sample of silicon isw(Cu) = 1.3 × 10−6 but not
1.3 × 10−6 w/w.

5.4.3 Formatting the value of a quantity

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The numerical value always precedes the unit and a space is always used toseparate the unit from the number. Thus the value of the quantity is the
product of the number and the unit. The space between the number and theunit is regarded as a multiplication sign (just as a space between units
implies multiplication). The only exceptions to this rule are for the unit
symbols for degree, minute and second for plane angle, °, ′ and ″,respectively, for which no space is left between the numerical value and theunit symbol.
This rule means that the symbol °C for the degree Celsius is preceded by aspace when one expresses values of Celsius temperature t.

m = 12.3 g where m is used
as a symbol for the quantity
mass, but φ = 30° 22′ 8″,
where φ is used as a symbol
for the quantity plane angle.

t = 30.2 oC,
but not t = 30.2oC,
nort = 30.2o C
a 10 kΩ resistor
a 35-millimeter film

Even when the value of a quantity is used as an adjective, a space is left
between the numerical value and the unit symbol. Only when the name of
the unit is spelled out would the ordinary rules of grammar apply, so that inEnglish a hyphen would be used to separate the number from the unit.
In any expression, only one unit is used. An exception to this rule is inexpressing the values of time and of plane angles using non-SI units.
However, for plane angles it is generally preferable to divide the degree
decimally. It is therefore preferable to write 22.20° rather than 22° 12′,
except in fields such as navigation, cartography, astronomy, and in themeasurement of very small angles.

l = 10.234 m, but not
l = 10 m 23.4 cm

5.4.4 Formatting numbers, and the decimal marker
The symbol used to separate the integral part of a number from its decimal
part is called the decimal marker. Following a decision by the 22nd CGPM
(2003, Resolution 10), the decimal marker “shall be either the point on theline or the comma on the line.” The decimal marker chosen should be thatwhich is customary in the language and context concerned.
If the number is between +1 and −1, then the decimal marker is always
preceded by a zero.
Following the 9th CGPM (1948, Resolution 7) and the 22nd CGPM (2003,
Resolution 10), for numbers with many digits the digits may be divided into
groups of three by a space, in order to facilitate reading. Neither dots nor
commas are inserted in the spaces between groups of three. However, when
there are only four digits before or after the decimal marker, it is customary
not to use a space to isolate a single digit. The practice of grouping digits inthis way is a matter of choice; it is not always followed in certain
specialized applications such as engineering drawings, financial statements
and scripts to be read by a computer.
For numbers in a table, the format used should not vary within one column.

32−0.234, but not −.234

43 279.168 29,
but not 43,279.168,29

either 3279.1683
or
3 279.168 3

5.4.5 Expressing the measurement uncertainty in the value ofa quantity
The uncertainty associated with an estimated value of a quantity should be
evaluated and expressed in accordance with the document JCGM 100:2008(GUM 1995 with minor corrections), Evaluation of measurement data Guide to the expression of uncertainty in measurement. The standard
uncertainty associated with a quantity x is denoted by u(x). One convenient
way to represent the standard uncertainty is given in the following example:
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mn = 1.674 927 471 (21) × 10−27 kg,
where mn is the symbol for the quantity (in this case the mass of a neutron)and the number in parentheses is the numerical value of the standard
uncertainty of the estimated value of mn referred to the last digits of thequoted value; in this case u(mn) = 0.000 000 021 × 10−27 kg. If an expanded
uncertainty U(x) is used in place of the standard uncertainty u(x), then the
coverage probability p and the coverage factor k must be stated.

5.4.6 Multiplying or dividing quantity symbols, the values ofquantities, or numbers
When multiplying or dividing quantity symbols any of the followingamethods may be used: ab, a b, a⋅ b, a × b, a/b, b , a b−1.

When multiplying the value of quantities either a multiplication sign × or
brackets should be used, not a half-high (centered) dot. When multiplying
numbers only the multiplication sign × should be used.
When dividing the values of quantities using a solidus, brackets are used to
avoid ambiguity.

Examples:F = ma for force equals mass
times acceleration(53 m/s) × 10.2 sor (53 m/s)(10.2 s)
25 × 60.5
but not 25 ⋅ 60.5
(20 m)/(5 s) = 4 m/s(a/b)/c, not a/b/c

5.4.7 Stating quantity values being pure numbers
As discussed in Section 2.3.3, values of quantities with unit one areexpressed simply as numbers. The unit symbol 1 or unit name “one” are notexplicitly shown. SI prefix symbols can neither be attached to the symbol 1
nor to the name “one,” therefore powers of 10 are used to express
particularly large or small values.

33

n = 1.51,
but not n = 1.51 × 1,
where n is the quantity
symbol for refractive index.

Quantities that are ratios of quantities of the same kind (for example length
ratios and amount fractions) have the option of being expressed with units(m/m, mol/mol) to aid the understanding of the quantity being expressed andalso allow the use of SI prefixes, if this is desirable (µm/m, nmol/mol).
Quantities relating to counting do not have this option, they are just
numbers.

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The internationally recognized symbol % (percent) may be used with the SI.
When it is used, a space separates the number and the symbol %. The
symbol % should be used rather than the name “percent”. In written text,
however, the symbol % generally takes the meaning of “parts per hundred”.
Phrases such as “percentage by mass”, “percentage by volume”, or“percentage by amount of substance” shall not be used; the extra
information on the quantity should instead be conveyed in the description
and symbol for the quantity.
The term “ppm”, meaning 10−6 relative value, or 1 part in 106, or parts per
million, is also used. This is analogous to the meaning of percent as parts
per hundred. The terms “parts per billion” and “parts per trillion” and theirrespective abbreviations “ppb” and “ppt”, are also used, but their meanings
are language dependent. For this reason the abbreviations ppb and ppt
should be avoided. 7

5.4.8 Plane angles, solid angles and phase angles
The coherent SI unit for the plane angle and the phase angle is radian, unit
symbol rad, and that for the solid angle is steradian, unit symbol sr.
The plane angle, expressed in radian, between two lines originating from acommon point is the length of circular arc s, swept out between the lines by
a radius vector of length r from the common point divided by the length of
the radius vector, θ = s/r rad. The phase angle (often just referred to as the“phase”) is the argument of any complex number. It is the angle between thepositive real axis and the radius of the polar representation of the complex
number in the complex plane.

When the SI was adopted
by the 11th CGPM in 1960,
a category of“supplementary units” wascreated to accommodate theradian and steradian.
Decades later, the CGPM
decided:(1) “to interpret the
supplementary units in theSI, namely the radian andthe steradian, as
dimensionless derived
units, the names andsymbols of which may, butneed not, be used in
expressions for other SI
derived units, as isconvenient”, and(2) to eliminate the separate
class of supplementary
units (Resolution 8 of the20th CGPM (1995)).

One radian corresponds to the angle for which s = r, thus 1 rad = 1. The
measure of the right angle is exactly equal to the number π/2.
A historical convention is the degree. The conversion between radians anddegrees follows from the relation 360° = 2π rad. Note that the degree, withthe symbol °, is not a unit of the SI.

7

Editors’ note: The NIST policy on the proper way to employ the International System of Units to express
the values of quantities does not allow the use of parts per million, parts per billion, or parts per trillion, nor
the abbreviations ppm, ppb, or ppt. Further, it only allows the use of the word “percent” and the symbol %to mean the number 0.01 in the expression of the value of a quantity. See NIST Special Publication 811.
34

The solid angle, expressed in steradian, corresponds to the ratio between an area A of thesurface of a sphere of radius r and the squared radius, Ω = A/r2 sr. One steradiancorresponds to the solid angle for which A = r2, thus 1 sr = 1.
The units rad and sr correspond to ratios of two lengths and two squared lengths,
respectively. However, it shall be emphasized that rad and sr must only be used toexpress angles and solid angles, but not to express ratios of lengths and squared lengths ingeneral.
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36

Appendix 1. Decisions of the CGPM and the CIPM

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This appendix lists those decisions of the CGPM and the CIPM that bear directly upondefinitions of the units of the SI, prefixes defined for use as part of the SI, andconventions 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 Séances de la Conférence Générale des Poids etMesures (CR) and Procès-Verbaux des Séances du Comité International des Poids etMesures (PV) or, for recent decisions, to Metrologia.
Since the SI is not a static convention, but evolves following developments in the scienceof measurement, some decisions have been abrogated or modified; others have beenclarified by additions. Decisions that have been subject to such changes are identified byan 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 (sansserif) of normal weight to distinguish it from the main text. The asterisks and notes wereadded by the BIPM to make the text more understandable. They do not form part of theoriginal text.
The decisions of the CGPM and CIPM are listed in this appendix in strict chronologicalorder, from 1889 to 2018, in order to preserve the continuity with which they were taken.
However in order to make it easy to locate decisions related to particular topics a table ofcontents is included below, ordered by subject, with page references to the particular
meetings at which decisions relating to each subject were taken.

37

Table of Contents of Appendix 1
Decisions relating to the establishment of the SI

Page

9th CGPM, 1948:
10th CGPM, 1954:
CIPM 1956:

49
52
53

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decision to establish the SI
decision on the first six base units
decision to adopt the name “Système Internationald’Unités”
11th CGPM, 1960:
confirms the name and the abbreviation “SI”,
names prefixes from tera to pico, establishes the
supplementary units rad and sr, lists some derived
units
CIPM, 1969:declarations concerning base, supplementary,derived and coherent units, and the use of prefixes
CIPM, 2001:“SI units” and “units of the SI”
23rd CGPM, 2007:
possible redefinition of certain base units of theInternational System of Units, the SI
24th CGPM, 2011:
possible future revision of the International
System of Units, the SI
25th CGPM, 2014:
future revision of the International System ofUnits, the SI
26th CGPM, 2018:
revision of the International System of Units, theSI (to enter into force on 20 May 2019)
Decisions relating to the base units of the SI
Length
1st CGPM, 1889:
sanction of the prototype meter7th CGPM, 1927:
definition and use of the prototype meter10th CGPM, 1954:
meter adopted as a base unit
11th CGPM, 1960:
redefinition of the meter in terms of krypton 86
radiation
15th CGPM, 1975:
recommends value for the speed of light
17th CGPM, 1983:
redefinition of the meter using the speed of light,
realization of the definition of the meter
CIPM, 2002:
specifies the rules for the practical realization of
the definition of the meter
CIPM, 2003:
revision of the list of recommended radiations
CIPM, 2005:
revision of the list of recommended radiations
CIPM, 2007:
revision of the list of recommended radiations
23th CGPM, 2007:
revision of the mise en pratique of the definition of
the meter and development of new opticalfrequency standards
38

54

62
77
86
89
97
101

45
47
52
54
65
70
78
81
83
85
86

CIPM, 2009:24th CGPM, 2011:
24th CGPM, 2011:

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CIPM, 2013:
26th CGPM, 2018:
Mass
1st CGPM, 1889:
3rd CGPM, 1901:
10th CGPM, 1954:
CIPM, 1967:
21st CGPM, 1999:
23rd CGPM, 2007:
24th CGPM, 2011:
25th CGPM, 2014:
26th CGPM, 2018:
Time
CIPM, 1956:
10th CGPM, 1954:
11th CGPM, 1960:
CIPM, 1964:
12th CGPM, 1964:
13th CGPM, 1967/68:
CCDS, 1970:
14th CGPM, 1971:
15th CGPM, 1975:

updates to the list of standard frequencies
possible future revision of the International
System of Units, the SI.
revision of the mise en pratique of the definition of
the meter and development of new opticalfrequency standards
updates to the list of standard frequencies
revision of the International System of Units, theSI(to enter into force on 20 May 2019)sanction of the prototype kilogram
declaration on distinguishing mass and weight, andon the conventional value of gn
kilogram adopted as a base unit
declaration on applying prefixes to the gramfuture redefinition of the kilogram
possible redefinition of certain base units of theInternational System of Units (SI)possible future revision of the International
System of Units, the SI
future revision of the International System ofUnits, the SI
revision of the International System of Units, theSI (to enter into force on 20 May 2019)
definition of the second as a fraction of the tropicalyear 1900
second adopted as a base unit
ratifies the CIPM 1956 definition of the second
declares the cesium 133 hyperfine transition to be
the recommended standard
empowers CIPM to investigate atomic andmolecular frequency standards
defines the second in terms of the cesiumtransition
defines International Atomic Time, TAI
requests the CIPM to define and establish
International Atomic Time, TAI
endorses the use of Coordinated Universal Time,
UTC
39

89
89
89

96
101

45
46
52
59
76
86
89
97
101

53
52
54
57
58
59
63
63
65

CIPM, 2006:
23rd CGPM, 2007:

CIPM, 2009:24th CGPM, 2011:
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24th CGPM, 2011:

CIPM, 2013:
CIPM, 2015:
26th CGPM, 2018:secondary representations of the secondon the revision of the mise en pratique of thedefinition of the meter and the development of
new optical frequency standards
updates to the list of standard frequencies
possible future revision of the International
System of Units, the SI
revision of the mise en pratique of the meter andthe development of new optical frequency
standards
updates to the list of standard frequencies
updates to the list of standard frequencies
revision of the International System of Units, theSI (to enter into force on 20 May 2019)

Electrical Units
CIPM, 1946:

definitions of coherent electrical units in themeter-kilogram-second (MKS) system of units(toenter into force on 1 January 1948)
10th CGPM, 1954:
ampere adopted as a base unit
14th CGPM, 1971:
adopts the name siemens, symbol S, for electricalconductance
18th CGPM, 1987:
forthcoming adjustment to the representations of
the volt and of the ohm
CIPM, 1988:
conventional value of the Josephson constantdefined (to enter into force on 1 January 1990)
CIPM, 1988:
conventional value of the von Klitzing constantdefined (to enter into force on 1 January 1990)
23rd CGPM, 2007:
possible redefinition of certain base units of theInternational System of Units (SI)24th CGPM, 2011:
possible future revision of the International
System of Units, the SI
25th CGPM, 2014:
future revision of the International System ofUnits, the SI
26th CGPM, 2018:
revision of the International System of Units, theSI (to enter into force on 20 May 2019)
Thermodynamic temperature
9th CGPM, 1948:
adopts the triple point of water as thethermodynamic reference point,
adopts the zero of Celsius temperature to be
0.01 degree below the triple point

40

84
86

89
89
89

96
99
101

47

52
63
72
73
73
86
89
97
101

49
49

CIPM, 1948:
10th CGPM, 1954:
10th CGPM, 1954:

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13th CGPM, 1967/68:
CIPM, 1989:
CIPM, 2005:
23rd CGPM, 2007:
23rd CGPM, 2007:
24th CGPM, 2011:
25th CGPM, 2014:
26th CGPM, 2018:
Amount of substance
14th CGPM, 1971:
21st CGPM, 1999:
23rd CGPM, 2007:
24th CGPM, 2011:
25th CGPM, 2014:
26th CGPM, 2018:
Luminous intensity
CIPM, 1946:
10th CGPM, 1954:
13th CGPM, 1967/68:
16th CGPM, 1979:

adopts the name degree Celsius for the Celsius
temperature scaledegree Kelvin adopted as a base unit
defines thermodynamic temperature such that the
triple point of water is 273.16 degrees Kelvinexactly, defines standard atmospheredecides formal definition of the kelvin, symbol K
the International Temperature Scale of 1990, ITS90
note added to the definition of the kelvinconcerning the isotopic composition of water
clarification of the definition of the kelvin, unit ofthermodynamic temperature
possible redefinition of certain base units of theInternational System of Units (SI)possible future revision of the International
System of Units, the SI
future revision of the International System ofUnits, the SI
revision of the International System of Units, theSI (to enter into force on 20 May 2019)
definition of the mole, symbol mol, as a seventhbase unit, and rules for its use
adopts the special name katal, katon the possible redefinition of certain base units of
the International System of Units (SI)possible future revision of the International
System of Units, the SI
future revision of the International System ofUnits, the SI
revision of the International System of Units, theSI (to enter into force on 20 May 2019)
definition of photometric units, new candle andnew lumen (to enter into force on 1 January 1948)
candela adopted as a base unit
defines the candela, symbol cd, in terms of a black
body radiator
redefines the candela in terms of monochromaticradiation
41

49
52
52

59
75
83
86
86
89
97
101

63
76
86
89
97
101

47
52
59
67

24th CGPM, 2011:

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possible future revision of the International
89
System of Units, the SI
26th CGPM, 2018:
revision of the International System of Units, the101
SI (to enter into force on 20 May 2019)
Decisions relating to SI derived and supplementary units
SI derived units
12th CGPM, 1964:
accepts the continued use of the curie as a non-SI
58
unit
13th CGPM, 1967/68:
lists some examples of derived units
59
15th CGPM, 1975:
adopts the special names becquerel, Bq, and gray,65
Gy
16th CGPM, 1979:
adopts the special name sievert, Sv
67
CIPM, 1984:
decides to clarify the relationship between
71
absorbed dose (SI unit gray) and dose equivalent(SI unit sievert)
CIPM, 2002:
modifies the relationship between absorbed dose78
and dose equivalent
Supplementary units
CIPM, 1980:
decides to interpret supplementary units as
69
dimensionless derived units
20th CGPM, 1995:
decides to abrogate the class of supplementary
76
units, and confirms the CIPM interpretation thatthey are dimensionless derived units
Decisions concerning terminology and the acceptance of units for use with the SI
SI prefixes
12th CGPM, 1964:
decides to add femto and atto to the list of prefixes
58
15th CGPM, 1975:
decides to add peta and exa to the list of prefixes
65
19th CGPM, 1991:
decides to add zetta, zepto, yotta, and yocto to the75
list of prefixes
Unit symbols and numbers
9th CGPM, 1948:
decides rules for printing unit symbols
49
Unit names
13th CGPM, 1967/68:
abrogates the use of the micron and new candle as59
units accepted for use with the SI
The decimal marker
22nd CGPM, 2003:
decides to allow the use of the point or the comma81
on the line as the decimal marker
Units accepted for use with the SI: an example, the liter
3rd CGPM, 1901:
defines the liter as the volume of 1 kg of water46

42

11th CGPM, 1960:
CIPM, 1961:
12th CGPM, 1964:

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16th CGPM, 1979:

requests the CIPM to report on the difference
between the liter and the cubic decimeterrecommends that volume be expressed in SI units
and not in liters
abrogates the former definition of the liter,recommends that liter may be used as a specialname for the cubic decimeter
decides, as an exception, to allow both l and L as
symbols for the liter

43

54
57
58

67

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44

1st CGPM, 1889
 Sanction of the international prototypes of the meter and thekilogram (CR, 34 - 38)*
The Conférence Générale des Poids et Mesures,considering• the “Compte rendu of the President of the Comité International des Poids
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•
•
•

•
•

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 theinternational 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 thekilogram are made of an alloy of platinum with 10 per cent iridium, towithin 0.0001;
the equality in length of the international Meter and the equality in massof the international Kilogram with the length of the Meter and the massof 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 ahydrogen thermometer scale which can always be reproduced thanks tothe 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 andKilograms 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 thetemperature of melting ice, shall henceforth represent the metric unit oflength.
2. The Prototype of the kilogram adopted by the CIPM. This prototype shallhenceforth be considered as the unit of mass.
3. The hydrogen thermometer centigrade scale in terms of which theequations of the prototype Meters have been established.
B. As regards national prototypes:…

45* The definition of the meter
was abrogated in 1960 by the
11th CGPM (Resolution 6,
see p. 54).

3rd CGPM, 1901
 Declaration concerning the definition of the liter (CR, 38-39)*…
The Conference declares* This definition was
abrogated in 1964 by the
12th CGPM (Resolution 6,
see p. 58).

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”.
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2. …
 Declaration on the unit of mass and on the definition of weight8;
conventional value of gn (CR, 70)*
Taking into account the decision of the Comité International des Poids etMesures of 15 October 1887, according to which the kilogram has been
defined as unit of mass;* This definition was
abrogated in 2018 by the
26th CGPM (Resolution 1,
See p. 101).

Taking into account the decision contained in the sanction of the
prototypes of the Metric System, unanimously accepted by the Conférence
Générale 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 theinternational 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 togravity; in particular, the standard weight of a body is the product of its
mass and the standard acceleration due to gravity;

This value of gn was theconventional reference forcalculating the now obsolete
unit kilogram force.

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.

8

Editors’ note: In the United States the term “weight” is used to mean both force and mass. In science andtechnology this declaration 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 often (but incorrectly) used asa synonym for mass, the SI unit of which is the kilogram (kg).
46

7th CGPM, 1927
 Definition of the meter by the international Prototype (CR, 49)*

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The unit of length is the meter, defined by the distance, at 0°, between theaxes 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 themeter by the 1st Conférence Générale des Poids et Mesures, this bar being
subject to standard atmospheric pressure and supported on two cylinders ofat least one centimeter diameter, symmetrically placed in the same
horizontal plane at a distance of 571 mm from each other.

* This definition was
abrogated in 1960 by the
11th CGPM (Resolution 6,
see p. 54).

CIPM, 1946
 Definitions of photometric units (PV, 20, 119-122)*
Resolution…
4. The photometric units may be defined as follows:
New candle (unit of luminous intensity). — The value of the new candle issuch that the brightness of the full radiator at the temperature ofsolidification of platinum is 60 new candles per square centimeter.
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 aluminous intensity of 1 new candle.

* The two definitions
contained in thisResolution were ratified in1948 by the 9th CGPM,
which also approved thename candela given to the“new candle” (CR, 54).
For the lumen the qualifier“new” was later
abandoned.
This definition was
modified in 1967 by the
13th CGPM (Resolution 5,
see p. 61).

5. …
 Definitions of electric units (PV, 20, 132-133)
Resolution 2...
4. (A) Definitions of the mechanical units which enter the definitions ofelectric 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 accelerationof 1 meter per second, per second.

47

The definitions contained inthis Resolution were ratified
in 1948 by the 9th CGPM
(CR, 49), which also adopted
the name newton(Resolution 7, see p. 50) for
the MKS unit of force.

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.

In 1954, the 10th CGPM
(Resolution 6, see p. 52)
established a practical systemof units of measurement forinternational use. The ampere
was designated as a base unitof this system.

(B) Definitions of electric units. The Comité International des Poids etMesures (CIPM) accepts the following propositions which define thetheoretical value of the electric units:
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Ampere (unit of electric current). — The ampere is that constant current
which, if maintained in two straight parallel conductors of infinite length,of negligible circular cross-section, and placed 1 meter apart in vacuum,
would produce between these conductors a force equal to 2 × 107 MKS
unit of force [newton] per meter of length.*
Volt (unit of potential difference and of electromotive force). — The volt isthe potential difference between two points of a conducting wire carrying
a constant current of 1 ampere, when the power dissipated between thesepoints 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 differenceof 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 ofelectricity 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 aclosed circuit in which an electromotive force of 1 volt is produced whenthe 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 forceof 1 volt if it were reduced to zero at a uniform rate in 1 second.

48* This definition of theampere was abrogated in2018 by the 26th CGPM
(Resolution 1, See p. 101).

9th CGPM, 1948
 Triple point of water; thermodynamic scale with a single fixed point;
unit of quantity of heat (joule) (CR, 55 and 63)
Resolution 3
1. With present-day techniques, the triple point of water is capable ofproviding a thermometric reference point with an accuracy higher thancan be obtained from the melting point of ice.
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In consequence the Comité Consultatif de Thermométrie et Calorimétrie(CCTC) considers that the zero of the centesimal thermodynamic scalemust 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 witha single fundamental fixed point, at present provided by the triple pointof 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.
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 notpossible to avoid using the calorie), the information necessary forconversion 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).
 Adoption of “degree Celsius” [CIPM, 1948 (PV, 21, 88) and 9th
CGPM, 1948
(CR, 64)]
From three names (“degree centigrade”, “centesimal degree”, “degree
Celsius”) proposed to denote the degree of temperature, the CIPM haschosen “degree Celsius” (PV, 21, 88).
This name is also adopted by the 9th CGPM (CR, 64).

49

The kelvin was redefined by
the 26th CGPM in 2018
(Resolution 1, See p. 101).

 Proposal for establishing a practical system of units of measurement(CR, 64)
Resolution 6
The Conférence Générale des Poids et Mesures (CGPM),
considering

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that the Comité International des Poids et Mesures (CIPM) has beenrequested by the International Union of Physics to adopt forinternational use a practical Système International d’Unités; that theInternational Union of Physics recommends the MKS system and one
electric unit of the absolute practical system, but does not recommendthat the CGS system be abandoned by physicists;•that the CGPM has itself received from the French Government asimilar request, accompanied by a draft to be used as basis of discussion
for the establishment of a complete specification of units ofmeasurement;

instructs the CIPM:• to seek by an energetic, active, official enquiry 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 ofmeasurement, suitable for adoption by all countries adhering to theMeter Convention.
 Writing and printing of unit symbols and of numbers (CR, 70)*
Resolution 7
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 isused. These symbols are not followed by a full stop.
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.

50* The CGPM abrogatedcertain decisions on units andterminology, in particular:
micron, degree absolute, andthe terms “degree”, and“deg”, 13th CGPM, 1967/68(Resolutions 7 and 3,
see pp. 62 and60,
respectively), and the liter;
16th CGPM, 1979
(Resolution 6, see p. 68).

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Unit

SymbolUnit

Symbol• metermampereA• square meter

m2

volt

V

• cubic meter

m3

watt

W

• micron

µ

ohm

Ω

• liter 9lcoulombC• gram

g

farad

F

• tonne 10

t

henry

H

second

s

hertz

Hz

erg

erg

poise

P

dyne

dyn

newtonNdegree 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.

9

Editors’ note: The preferred unit symbol for the liter in the United States is L, not lowercase l (el)represented in the table. See the Federal Register notice of July 28, 1998, “Metric System of Measurement:Interpretation of the International System of Units for the United States” (FR 40334-4030).
10 Editors’ note: The name “tonne” appears in the original text, not “metric ton.” The unit name “metricton” is used in the United States rather than “tonne.” See footnote (e) of Table 8.
51

10th CGPM, 1954
 Definition of the thermodynamic temperature scale (CR, 79)*
Resolution 3
The 10th Conférence Générale des Poids et Mesures decides to define thethermodynamic 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.

* The 13th CGPM in 1967
explicitly defined the kelvin(Resolution 4, see p. 61).
* The kelvin was redefinedby the 26th CGPM in 2018
(Resolution 1, See p. 101).

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 Definition of the standard atmosphere (CR, 79)
Resolution 4
The 10th Conférence Générale des Poids et Mesures (CGPM), having notedthat the definition of the standard atmosphere given by the 9th CGPM whendefining the International Temperature Scale led some physicists to believethat 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.
 Practical system of units (CR, 80)*
Resolution 6
In accordance with the wish expressed by the 9th Conférence Générale desPoids et Mesures (CGPM) in its Resolution 6 concerning the establishmentof 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

kilogramtime

secondelectric current

amperethermodynamic temperature

degree Kelvinluminous intensity

candela52* The unit name “degreekelvin” was changed to“kelvin” in 1967 by the
13th CGPM (Resolution 3,
see p. 60).

CIPM, 1956
 Definition of the unit of time (second) (PV, 25, 77)*
Resolution 1
In virtue of the powers invested in it by Resolution 5 of the 10th Conférence
Générale des Poids et Mesures, the Comité International des Poids etMesures,considering
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1. that the 9th General Assembly of the International Astronomical Union(Dublin, 1955) declared itself in favour of linking the second to thetropical year,
2. that, according to the decisions of the 8th General Assembly of theInternational Astronomical Union (Rome, 1952), the second of ephemeris
time (ET) is the fraction
12 960 276 813
× 10−9 of the tropical year for 1900 January 0 at 12 h ET,
408 986 496

decides“The second is the fraction 1/31 556 925.9747 of the tropical year for 1900
January 0 at 12 hours ephemeris time.”
 Système International d’Unités (PV, 25, 83)
Resolution 3
The Comité International des Poids et Mesures,considering•

the task entrusted to it by Resolution 6 of the 9th Conférence Générale
des Poids et Mesures (CGPM) concerning the establishment of apractical 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 theenquiry requested by the 9th CGPM,•

Resolution 6 of the 10th CGPM, fixing the base units of the system tobe established,recommends
1. that the name “Système International d’Unités” be given to the systemfounded 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)].

53* This definition was
abrogated in 1967 by the
13th CGPM (Resolution 1,
see p. 59).

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)].
* This definition was
abrogated in 1983 by the17th CGPM (Resolution 1,
see p. 70).

11th CGPM, 1960
 Definition of the meter (CR, 85)*
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Resolution 6
The 11th Conférence Générale des Poids et Mesures (CGPM),
considering• that the international Prototype does not define the meter with anaccuracy 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 and5d5 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.
 Definition of the unit of time (second) (CR, 86)*
Resolution 9
The 11th Conférence Générale des Poids et Mesures (CGPM),
considering• the powers given to the Comité 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:

54* This definition was
abrogated in 1967 by the
13th CGPM (Resolution 1,
see p. 59).

“The second is the fraction 1/31 556 925.9747 of the tropical year for 1900
January 0 at 12 hours ephemeris time.”
 Système International d’Unités (CR, 87)*

* The CGPM later abrogatedcertain of its decisions andextended the list of prefixes,
see notes below.

Resolution 12
The 11th Conférence Générale des Poids et Mesures (CGPM),
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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

kilogramkg

time

secondselectric current

ampereAthermodynamic temperature

degree Kelvin°Kluminous intensity

candelacd

The name and symbol for theunit of thermodynamic
temperature was modified by
the 13th CGPM in 1967
(Resolution 3, see p. 60).

•

Resolution 3 adopted by the Comité International des Poids et Mesures(CIPM) in 1956,•

the recommendations adopted by the CIPM in 1958 concerning anabbreviation 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 “SystèmeInternational d’Unités”;
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:

Multiplying factor

PrefixSymbol1 000 000 000 000 = 1012

tera

T

1 000 000 000 = 109

giga

1 000 000 = 106

Multiplying factor

A seventh base unit, themole, was adopted by the
14th CGPM in 1971
(Resolution 3, see p. 65).
Further prefixes wereadopted by the 12th CGPM
in 1964 (Resolution 8,
see p. 59),
the 15th CGPM in 1975
(Resolution 10, see p. 66)
and the 19th CGPM in 1991
(Resolution 4, see p. 75).

PrefixSymbol

0.1 = 10−1

deci

d

G

0.01 = 10−2

centi

c

mega

M

0.001 = 10−3

milli

m

1 000 = 103

kilo

k

0.000 001 = 10−6

micro

µ

100 = 102

hecto

h

0.000 000 001 = 10−9

nano

n

10 = 101dekada0.000 000 000 001 = 10−12

pico

p

55

4. the units listed below are used in the system, without excluding others
which might be added later.

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Supplementary units
plane angle
solid angle
Derived units
area
volumefrequency
mass density(density)
speed, velocity
angular velocity
acceleration
angular acceleration
force
pressure (mechanicalstress)kinematic viscosity
dynamic viscosity
work, energy,
quantity of heat
power
quantity of electricity
tension (voltage),potential difference,electromotive force
electric field strength
electric resistancecapacitancemagnetic flux
inductancemagnetic flux density
magnetic fieldstrengthmagnetomotive force
luminous flux
luminance
illuminanceradiansteradianradsrsquare metercubic meter
hertz

m2
m3
Hz

kilogram per cubic meter

kg/m3

meter per second
radian per second
meter per second squared
radian per second
squarednewton

m/s
rad/s
m/s2

newton per square meterN/m2

square meter per second
newton-second per
square meter

m2/s

joule

J

N·m

watt
coulomb

W
C

J/s
A·s

volt

V

W/A

volt per meter
ohm
farad
weber
henry
tesla

V/m
Ω
F
Wb
H
T

V/A
A · s/VV·s
V · s/AWb/m2

ampere per meterA/mamperelumen
candela per square meter
lux

A
lm
cd/m2
lx

56

1/s

The 20th CGPM in 1995
abrogated the class of
supplementary units in the SI(Resolution 8, see p. 76).
These are now considered as
derived units.

The 13th CGPM in 1967
(Resolution 6, see p. 62)
specified other units whichshould be added to the list. In
principle, this list of derived
units is without limit.

rad/s2N

kg · m/s2

N · s/m2

cd · srlm/m2

Modern practice is to use thephrase “amount of heat”
rather than “quantity of heat”,
because the word quantity
has a different meaning in
metrology.

Modern practice is to use thephrase “amount ofelectricity” rather than“quantity of electricity” (seenote above).

 Cubic decimeter and liter (CR, 88)
Resolution 13
The 11th Conférence Générale des Poids et Mesures (CGPM),
considering• that the cubic decimeter and the liter are unequal and differ by about 28 parts in 106,

This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019• that determinations of physical quantities which involve measurements of volume arebeing made more and more accurately, thus increasing the risk of confusion between
the cubic decimeter and the liter,
requests the Comité International des Poids et Mesures to study the problem and submit
its conclusions to the 12th CGPM.
CIPM, 1961
 Cubic decimeter and liter (PV, 29, 34)
Recommendation
The Comité International des Poids et Mesures recommends that the results of accurate
measurements of volume be expressed in units of the International System and not inliters.
CIPM, 1964
 Atomic and molecular frequency standards (PV, 32, 26)
Declaration
The Comité International des Poids et Mesures,
empowered by Resolution 5 of the 12th Conférence Générale des Poids et Mesures toname 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 2S1/2 of the cesium 133 atom,
unperturbed by external fields, and that the frequency of this transition is assigned thevalue 9 192 631 770 hertz.

57

12th CGPM, 1964
 Atomic standard of frequency (CR, 93)
Resolution 5
The 12th Conférence Générale des Poids et Mesures (CGPM),
considering

This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019• that the 11th CGPM noted in its Resolution 10 the urgency, in theinterests 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 Système International d’Unités,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 timemeasurements in physics are based on atomic or molecular frequency
standards,
empowers the Comité International des Poids et Mesures to name theatomic 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.
 Liter (CR, 93)
Resolution 6
The 12th Conférence Générale des Poids et Mesures (CGPM),
considering Resolution 13 adopted by the 11th CGPM in 1960 and the
Recommendation adopted by the Comité International des Poids et Mesuresin 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 theresults of high-accuracy volume measurements.
 Curie (CR, 94)*
Resolution 7
The 12th Conférence Générale des Poids et Mesures,

58* The name “becquerel” (Bq)
was adopted by the
15th CGPM in 1975
(Resolution 8, see p. 66) for
the SI unit of activity:
1 Ci = 3.7 × 1010 Bq.

considering that the curie has been used for a long time in many countries
as unit of activity for radionuclides,
recognizing that in the Système International d’Unités (SI), the unit of thisactivity 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 thevalue 3.7 × 1010 s−1. The symbol for this unit is Ci.
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 SI prefixes femto and atto (CR, 94)*
Resolution 8
The 12th Conférence Générale 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:
Multiplying factor

PrefixSymbol

10−15

femto

f

10−18

atto

a

CIPM, 1967
 Decimal multiples and submultiples of the unit of mass (PV, 35, 29
and Metrologia, 1968, 4, 45)
Recommendation 2
The Comité International des Poids et Mesures,considering that the rule for forming names of decimal multiples andsubmultiples of the units of paragraph 3 of Resolution 12 of the 11th
Conférence Générale des Poids et Mesures (CGPM) (1960) might beinterpreted in different ways when applied to the unit of mass,declares that the rules of Resolution 12 of the 11th CGPM apply to thekilogram in the following manner: the names of decimal multiples andsubmultiples of the unit of mass are formed by attaching prefixes to theword “gram”.
13th CGPM, 1967/68
 SI unit of time (second) (CR, 103 and Metrologia, 1968, 4, 43)
Resolution 1
The 13th Conférence Générale des Poids et Mesures (CGPM),

59* New prefixes were addedby the 15th CGPM in 1975
(Resolution 10, see p. 66).

considering• that the definition of the second adopted by the Comité International desPoids 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 CIPM, empowered by Resolution 5 of the
12th CGPM (1964), recommended, in order to fulfil these requirements,
a cesium atomic frequency standard for temporary use,
This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019• that this frequency standard has now been sufficiently tested and foundsufficiently accurate to provide a definition of the second fulfillingpresent requirements,• that the time has now come to replace the definition now in force of theunit of time of the Système International d’Unités 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 theground 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.

At its 1997 meeting, the
CIPM affirmed that thisdefinition refers to a cesium
atom at rest at athermodynamic temperatureof 0 K.

The wording of the definitionof the second was modified
by the 26th CGPM in 2018
(Resolution 1, See p. 101).

 SI unit of thermodynamic temperature (kelvin) (CR, 104 andMetrologia, 1968, 4, 43)*
Resolution 3
The 13th Conférence Générale 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 Comité International des Poids et Mesures in 1962 (PV,30, 27),•that the unit of thermodynamic temperature and the unit of temperatureinterval are one and the same unit, which ought to be denoted by asingle name and a single symbol,

60* At its 1980 meeting, the
CIPM approved the report of
the 7th meeting of the CCU,
which requested that the useof the symbols “°K” and“deg” no longer be permitted.

decides1. 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 temperatureinterval;** See Recommendation 2(CI-2005) of the CIPM on theisotopic composition of water
entering in the definition of
the kelvin, p. 83.

3. a temperature interval may also be expressed in degrees Celsius;
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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 areabrogated, but the usages which derive from these decisions remain
permissible for the time being.
 Definition of the SI unit of thermodynamic temperature (kelvin) (CR,104 and Metrologia, 1968, 4, 43)*
Resolution 4* See Recommendation 5(CI-1989) of the CIPM on theInternational Temperature
Scale of 1990, p. 75.

The 13th Conférence Générale 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),

The kelvin was redefined by
the 26th CGPM in 2018
(Resolution 1, See p. 101).

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.” SI unit of luminous intensity (candela) (CR, 104 and Metrologia, 1968,
4, 43-44)*
Resolution 5
The 13th Conférence Générale 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 ofphotometric units” adopted by the Comité International des Poids etMesures 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, butthat its wording may be open to criticism,

decides to express the definition of the candela as follows:61* This definition was
abrogated by the 16th CGPM
in 1979 (Resolution 3, seep. 67).

“The candela is the luminous intensity, in the perpendicular direction, of asurface of 1/600 000 square meter of a black body at the temperature offreezing platinum under a pressure of 101 325 newtons per square meter.”* The unit of activity was
given a special name andsymbol by the 15th CGPM
in 1975 (Resolution 8, see
p. 66).

 SI derived units (CR, 105 and Metrologia, 1968, 4, 44)*
Resolution 6
The 13th Conférence Générale des Poids et Mesures (CGPM),
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considering that it is useful to add some derived units to the list ofparagraph 4 of Resolution 12 of the 11th CGPM (1960),
decides to add:
wave number

1 per meterm−1

entropyjoule 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 steradianW/sractivity (of a radioactive source)

1 per seconds− 1 Abrogation of earlier decisions (micron and new candle) (CR, 105 andMetrologia, 1968, 4, 44)
Resolution 7
The 13th Conférence Générale des Poids et Mesures (CGPM),
considering that subsequent decisions of the General Conference
concerning the Système International d’Unités are incompatible with partsof 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 “µ” which had been given to that
unit but which has now become a prefix;
2. the unit name “new candle”.
CIPM, 1969
 Système International d’Unités, Rules for application of Resolution
12 of the 11th CGPM (1960) (PV, 37, 30 and Metrologia, 1970, 6, 66)*
Recommendation 1
The Comité International des Poids et Mesures,

62* The 20th CGPM in 1995
decided to abrogate the classof supplementary units in the
SI (Resolution 8, see p. 76).

considering that Resolution 12 of the 11th Conférence Générale des Poids
et Mesures (CGPM) (1960), concerning the Système International d’Unités,has provoked discussions on certain of its aspects,
declares1. the base units, the supplementary units and the derived units of the
Système International d’Unités, which form a coherent set, are denotedby the name “SI units”;**
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2. the prefixes adopted by the CGPM for the formation of decimal multiples
and submultiples of SI units are called “SI prefixes”;** The CIPM approved in2001 a proposal of the CCU
to clarify the definition of« SI units » and « units of the
SI », see p. 77.

and recommends
3. the use of SI units and of their decimal multiples and submultiples whosenames 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 forwhich the General Conference declines to state whether they are base units
or derived units.
CCDS, 1970 (In CIPM, 1970)
 Definition of TAI (PV, 38, 110-111 and Metrologia, 1971, 7, 43)
Recommendation S 2
International Atomic Time (TAI) is the time reference coordinate
established by the Bureau International de l'Heure on the basis of thereadings of atomic clocks operating in various establishments in accordancewith the definition of the second, the unit of time of the International System
of Units.
In 1980, the definition of TAI was completed as follows (declaration of the
CCDS, BIPM Com. Cons. Déf. Seconde, 1980, 9, S 15 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.
14th CGPM, 1971
 Pascal and siemens (CR, 78)
The 14th Conférence Générale des Poids et Mesures adopted the specialnames “pascal” (symbol Pa), for the SI unit newton per square meter, and“siemens” (symbol S), for the SI unit of electric conductance [reciprocal
ohm].

63

This definition was further
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, isTerrestrial Time (TT), itself
related to the time coordinateof the geocentric reference
frame, Geocentric Coordinate
Time (TCG), by a constantrate.”(see Proc. 21st General
Assembly of the IAU, IAU
Trans., 1991, vol. XXIB,
Kluwer.) International Atomic Time, function of CIPM (CR, 77-78 andMetrologia, 1972, 8, 35)
Resolution 1
The 14th Conférence Générale des Poids et Mesures (CGPM),
considering

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that the second, unit of time of the Système International d’Unités, hassince 1967 been defined in terms of a natural atomic frequency, and nolonger in terms of the time scales provided by astronomical motions,•that the need for an International Atomic Time (TAI) scale is aconsequence 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 ComitéInternational des Poids et Mesures (CIPM) helped by a Consultative
Committee, and that the unit interval of the International Atomic Timescale must be the second realized according to its atomic definition,•that all the competent international scientific organizations and thenational 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 internationalorganizations concerned, to ensure that available scientific competence
and existing facilities are used in the best possible way to realize theInternational Atomic Time scale and to satisfy the requirements of usersof International Atomic Time.

64

The definition of TAI was
given by the CCDS in 1970(now the CCTF), see CCDS
report p. 63.

 SI unit of amount of substance (mole) (CR, 78 and Metrologia, 1972,
8, 36)*
Resolution 3
The 14th Conférence Générale des Poids et Mesures (CGPM),

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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 todefine a unit of amount of substance,* At its 1980 meeting, the
CIPM approved the report of
the 7th meeting of the CCU(1980) specifying that, in thisdefinition, it is understoodthat unbound atoms of carbon
12, at rest and in their groundstate, are referred to.

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”.

The mole was redefined by
the 26th CGPM in 2018
(Resolution 1, See p. 101).

2. When the mole is used, the elementary entities must be specified andmay be atoms, molecules, ions, electrons, other particles, or specified
groups of such particles.
3. The mole is a base unit of the Système International d’Unités.
15th CGPM, 1975
 Recommended value for the speed of light (CR, 103 and Metrologia,
1975, 11, 179-180)
Resolution 2
The 15th Conférence Générale 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 themeter,
considering also the concordant measurements of the frequencies of severalof these radiations,recommends the use of the resulting value for the speed of propagation ofelectromagnetic waves in vacuum c = 299 792 458 meters per second.
 Coordinated Universal Time (UTC) (CR, 104 and Metrologia, 1975,
11, 180)
Resolution 5
The 15th Conférence Générale 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,
65

The relative uncertainty
given here corresponds tothree standard deviations in
the data considered.

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.
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 SI units for ionizing radiation (becquerel and gray) (CR, 105 andMetrologia, 1975, 11, 180)*
Resolutions 8 and 9
The 15th Conférence Générale des Poids et Mesures,by reason of the pressing requirement, expressed by the International
Commission on Radiation Units and Measurements (ICRU), to extend theuse of the Système International d’Unités to radiological research andapplications,* 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 specificenergy imparted, kerma andabsorbed dose index.

by reason of the need to make as easy as possible the use of the units fornonspecialists,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),
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 be used with other physical quantities also expressedin joules per kilogram: the Comité Consultatif des Unités has responsibility
for studying this matter in collaboration with the competent internationalorganizations.
 SI prefixes peta and exa (CR, 106 and Metrologia, 1975, 11, 180-181)*
Resolution 10
The 15th Conférence Générale 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:

66* New prefixes were addedby the 19th CGPM in 1991
(Resolution 4, see p. 75).

Multiplying factor

PrefixSymbol

1015

peta

P

1018

exa

E

16th CGPM, 1979
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 SI unit of luminous intensity (candela) (CR, 100 and Metrologia, 1980,
16, 56)
Resolution 3
The 16th Conférence Générale des Poids et Mesures (CGPM),
considering

Photopic vision is detected by
the cones on the retina of theeye, which are sensitive to ahigh level of luminance(L > ca. 10 cd/m2) and areused in daytime vision.

•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,

Scotopic vision is detected by
the rods of the retina, which
are sensitive to low level
luminance(L < ca. 10−3 cd/m2),
used in night vision.

•that radiometric techniques are developing rapidly, allowing precisions
that are already equivalent to those of photometry and that thesetechniques are already in use in national laboratories to realize thecandela without having to construct a black body,In the domain between theselevels of luminance bothcones and rods are used, andthis is described as mesopic
vision.

•that the relation between luminous quantities of photometry andradiometric quantities, namely the value of 683 lumens per watt for the
spectral luminous efficacy of monochromatic radiation of frequency
540 × 1012 hertz, has been adopted by the Comité International desPoids et Mesures (CIPM) in 1977,•

that this value has been accepted as being sufficiently accurate for thesystem 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 ofphotometric standards, and that applies to both photopic and scotopic
photometric quantities and to quantities yet to be defined in the mesopic
field,

decides
1. The candela is the luminous intensity, in a given direction, of a sourcethat emits monochromatic radiation of frequency 540 × 1012 hertz andthat 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.
67

The wording of the definitionof the candela was modified
by the 26th CGPM in 2018
(Resolution 1, See p. 101).

 Special name for the SI unit of dose equivalent (sievert) (CR, 100 andMetrologia, 1980, 16, 56)*
Resolution 5
The 16th Conférence Générale des Poids et Mesures,* The CIPM, in 1984,
decided to accompany
this Resolution with an
explanation(Recommendation 1,
see p. 71).

considering
This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019• 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
Système International d’Unités 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.
 Symbols for the liter (CR, 101 and Metrologia, 1980, 16, 56-57)
Resolution 6
The 16th Conférence Générale des Poids et Mesures (CGPM),
recognizing the general principles adopted for writing the unit symbols in
Resolution 7 of the 9th CGPM (1948),
considering that the symbol l for the unit liter was adopted by the ComitéInternational des Poids et Mesures (CIPM) in 1879 and confirmed in thesame Resolution of 1948,
considering also that, in order to avoid the risk of confusion between theletter 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 SystèmeInternational d’Unités, 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.
68

The CIPM, in 1990,
considered that it was still too
early to choose a single
symbol for the liter.

CIPM, 1980
 SI supplementary units (radian and steradian) (PV, 48, 24 andMetrologia, 1981, 17, 72)*
Recommendation 1
The Comité International des Poids et Mesures (CIPM),

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taking into consideration Resolution 3 adopted by ISO/TC 12 in 1978 andRecommendation U 1 (1980) adopted by the Comité Consultatif des Unités
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 inphotometry where the steradian plays an important role indistinguishing between units corresponding to different quantities,•

that in the equations used one generally expresses plane angle as theratio of two lengths and solid angle as the ratio between an area and thesquare 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 thatnone exists which is at the same time coherent and convenient and inwhich the quantities plane angle and solid angle might be considered asbase 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 Conférence
Générale des Poids et Mesures (CGPM) in 1960 allows the freedom oftreating 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.

69* The class of SI
supplementary units wasabrogated by decision of the20th CGPM in 1995
(Resolution 8, see p. 76).

17th CGPM, 1983
 Definition of the meter (CR, 97 and Metrologia, 1984, 20, 25)
Resolution 1

The wording of the definitionof the meter was modified by
the 26th CGPM in 2018
(Resolution 1, See p. 101).

The 17th Conférence Générale des Poids et Mesures (CGPM),
considering

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that the present definition does not allow a sufficiently precise
realization of the meter for all requirements,•that progress made in the stabilization of lasers allows radiations tobe obtained that are more reproducible and easier to use than thestandard radiation emitted by a krypton 86 lamp,•that progress made in the measurement of the frequency andwavelength 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 agiven value for the speed of light have a reproducibility superior tothat 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, inmaintaining 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 anexact value, equal to the recommended value, and that thisintroduces 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 pathtravelled by light in a specified time interval or to the wavelength ofa radiation of measured or specified frequency, have been the objectof consultations and deep discussions, have been recognized as being
equivalent and that a consensus has emerged in favour of the first
form,

•

that the Comité Consultatif pour la Définition du Mètre (CCDM) is
now in a position to give instructions for the practical realization ofsuch a definition, instructions which could include the use of theorange radiation of krypton 86 used as standard up to now, andwhich may in due course be extended or revised,70

The relative uncertainty
given here corresponds tothree standard deviations in
the data considered.

decides1. The meter is the length of the path travelled by light in vacuum during atime 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.

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 On the realization of the definition of the meter (CR, 98 andMetrologia, 1984, 20, 25-26)
Resolution 2

See Recommendation 1(CI-2002) of the CIPM on therevision of the practicalrealization of the definitionof the meter, p. 78.

The 17th Conférence Générale des Poids et Mesures,
invites the Comité International des Poids et Mesures• to draw up instructions for the practical realization of the new definitionof the meter,• to choose radiations which can be recommended as standards ofwavelength for the interferometric measurement of length and to draw up
instructions for their use,
• to pursue studies undertaken to improve these standards.
CIPM, 1984
 Concerning the sievert (PV, 52, 31 and Metrologia, 1985, 21, 90)*
Recommendation 1
The Comité International des Poids et Mesures,considering the confusion which continues to exist on the subject ofResolution 5, approved by the 16th Conférence Générale des Poids etMesures (1979),
decides to introduce the following explanation in the brochure “Le SystèmeInternational d'Unités (SI)”:
The quantity dose equivalent H is the product of the absorbed dose D ofionizing 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 valuesof 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

71* The CIPM, in 2002,
decided to change theexplanation of thequantity dose equivalent
in the SI Brochure(Recommendation 2,
see p. 80).

kilogram for the unit of absorbed dose D and the name sievert instead of joules per
kilogram for the unit of dose equivalent H.
18th CGPM, 1987
 Forthcoming adjustment to the representations of the volt and of the ohm (CR,
100 and Metrologia, 1988, 25, 115)
Resolution 6
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The 18th Conférence Générale des Poids et Mesures,considering• that worldwide uniformity and long-term stability of national representations of theelectrical units are of major importance for science, commerce and industry from boththe technical and economic points of view,• that many national laboratories use the Josephson effect and are beginning to use thequantum Hall effect to maintain, respectively, representations of the volt and of theohm, as these offer the best guarantees of long-term stability,• that because of the importance of coherence among the units of measurement of thevarious 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 theirresults without delay to the Comité International des Poids et Mesures, andinstructs the Comité 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 tobe put into practice simultaneously in all countries; these values should be announced atleast one year in advance and would be adopted on 1 January 1990.

72

CIPM, 1988
 Representation of the volt by means of the Josephson effect (PV, 56,
44 and Metrologia, 1989, 26, 69)
Recommendation 1
The Comité International des Poids et Mesures,This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019

acting in accordance with instructions given in Resolution 6 of the 18th
Conférence Générale 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, thatis 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 toestablish a reference standard of electromotive force having a onestandard-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, toreplace 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 theirlaboratory reference standards to agree with the new adopted value,

is of the opinion that no change in this recommended value of theJosephson constant will be necessary in the foreseeable future, anddraws the attention of laboratories to the fact that the new value is greaterby 3.9 GHz/V, or about 8 parts in 106, than the value given in 1972 by the
Comité Consultatif d'Électricité in its Declaration E-72.

73

The 26th CGPM in 2018
(Resolution 1, See p. 101)
abrogated the adoption of aconventional value for KJ.

 Representation of the ohm by means of the quantum Hall effect (PV,56, 45 and Metrologia, 1989, 26, 70)
Recommendation 2
The Comité International des Poids et Mesures,
acting in accordance with instructions given in Resolution 6 of the 18th
Conférence Générale des Poids et Mesures concerning the forthcoming
adjustment of the representations of the volt and the ohm,
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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 Ω for the von Klitzing constant, RK, thatis to say, for the quotient of the Hall potential difference divided bycurrent corresponding to the plateau i = 1 in the quantum Hall effect,•that the quantum Hall effect, together with this value of RK, can be used
to establish a reference standard of resistance having a one-standarddeviation 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 Ω exactly be adopted as a conventional value, denotedby RK-90, for the von Klitzing constant, RK,•

that this value be used from 1 January 1990, and not before, by alllaboratories which base their measurements of resistance on thequantum Hall effect,•that from this same date all other laboratories adjust the value of theirlaboratory reference standards to agree with RK-90,•

that in the use of the quantum Hall effect to establish a laboratoryreference standard of resistance, laboratories follow the most recent
edition of the technical guidelines for reliable measurements of thequantized Hall resistance drawn up by the Comité Consultatifd'Électricité and published by the Bureau International des Poids etMesures, andis of the opinion that no change in this recommended value of the vonKlitzing constant will be necessary in the foreseeable future.

74

At its 89th meeting in 2000,
the CIPM approved thedeclaration of the
22nd meeting of the CCEM
on the use of the value of the
von Klitzing constant.

The 26th CGPM in 2018
(Resolution 1, See p. 101)
abrogated the adoption of aconventional value for RK.

CIPM, 1989 The International Temperature Scale of 1990 (PV, 57, 115 andMetrologia, 1990, 27, 13)

The kelvin was redefined by
the 26th CGPM in 2018
(Resolution 1, See p. 101).

Recommendation 5This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019

The Comité International des Poids et Mesures (CIPM) acting in accordancewith Resolution 7 of the 18th Conférence Générale 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 alsosupersedes 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 andTechniques 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.
19th CGPM, 1991
 SI prefixes zetta, zepto, yotta and yocto (CR, 185 and Metrologia,
1992, 29, 3)
Resolution 4
The 19th Conférence Générale des Poids et Mesures (CGPM)
decides to add to the list of SI prefixes to be used for multiples andsubmultiples of units, adopted by the 11th CGPM, Resolution 12, paragraph
3, the 12th CGPM, Resolution 8 and the 15th CGPM, Resolution 10, thefollowing prefixes:

75

The names zepto and zetta
are derived from septo
suggesting the number seven(the seventh power of 103)
and the letter “z” issubstituted 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); theletter “y” is added to avoid
the use of the letter “o” as asymbol because it may be
confused with the number
zero.

Multiplying factor

PrefixSymbol

1021

zetta

Z

10−21

zepto

z

1024

yotta

Y

10−24

yocto

y

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20th CGPM, 1995
 Elimination of the class of supplementary units in the SI (CR, 223 and Metrologia,
1996, 33, 83)
Resolution 8
The 20th Conférence Générale des Poids et Mesures (CGPM),
considering• that the 11th Conférence Générale in 1960 in its Resolution 12, establishing the
Système International d’Unités, SI, distinguished between three classes of SI units:
the base units, the derived units, and the supplementary units, the last of thesecomprising 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 Comité 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 Comité 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.

21st CGPM, 1999
 The definition of the kilogram (CR, 331 and Metrologia, 2000, 37, 94)
Resolution 7
The 21st Conférence Générale des Poids et Mesures,considering•

the need to assure the long-term stability of the International System of Units (SI),

76

•
•
•
•

the intrinsic uncertainty in the long-term stability of the artifact defining the unit ofmass, one of the base units of the SI,
the consequent uncertainty in the long-term stability of the other three base units of
the SI that depend on the kilogram, namely, the ampere, the mole and the candela,
the progress already made in a number of different experiments designed to link theunit of mass to fundamental or atomic constants,
the desirability of having more than one method of making such a link,

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recommends that national laboratories continue their efforts to refine experiments thatlink the unit of mass to fundamental or atomic constants with a view to a future
redefinition of the kilogram.
 Special name for the SI derived unit mole per second, the katal, for the
expression of catalytic activity (CR, 334-335 and Metrologia, 2000, 37, 95)
Resolution 12
The 21st Conférence Générale des Poids et Mesures,considering
•
•
•
•
•
•

the importance for human health and safety of facilitating the use of SI units in thefields of medicine and biochemistry,that a non-SI unit called “unit”, symbol U, equal to 1 µmol ∙ min–1, which is notcoherent with the International System of Units (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 represents 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 forover 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 tothe measurement procedure; the measurement procedure must identify the indicator
reaction.
CIPM, 2001
 “SI units” and “units of the SI” (PV, 69, 120)
The CIPM approved in 2001 the following proposal of the CCU regarding “SI units” and“units of the SI”:
77

“We suggest that “SI units” and “units of the SI” should be regarded as names that
include both the base units and the coherent derived units, and also all units obtained by
combining these with the recommended multiple and sub-multiple prefixes.
We suggest that the name “coherent SI units” should be used when it is desired to restrict
the meaning to only the base units and the coherent derived units.”
CIPM, 2002
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 Revision of the practical realization of the definition of the meter (PV, 70, 194204 and Metrologia, 40, 103-133)
Recommendation 1
The International Committee for Weights and Measures,
recalling• that in 1983 the 17th General Conference (CGPM) adopted a new definition of themeter;• that in the same year the CGPM invited the International Committee (CIPM)• to draw up instructions for the practical realization of the meter,• to choose radiations which can be recommended as standards of wavelength forthe interferometric measurement of length and draw up instructions for their use,
• to pursue studies undertaken to improve these standards and in due course toextend 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 planeelectromagnetic wave in a time t; this length is obtained from the measured timet, 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 λ of a plane electromagnetic wave of
frequency f; this wavelength is obtained from the measured frequency f using therelation λ = 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 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 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
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small that the effects of the non-uniformity of the gravitational field can beignored (note that, at the surface of the Earth, this effect in the vertical direction
is about 1 part in 1016 per meter). In this case, the effects to be taken into
account are those of special relativity only. The local methods for the realizationof the meter recommended in (b) and (c) provide the proper meter but notnecessarily 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 theinterpretation of measurements in which this is not the case, see the report of theConsultative Committee for Time and Frequency (CCTF) Working Group on the
Application of General Relativity to Metrology (Application of general relativity
to metrology, Metrologia, 1997, 34, 261-290);• that the CIPM had already recommended a list of radiations for this purpose;
recalling also that in 1992 and in 1997 the CIPM revised the practical realization of thedefinition of the meter;
considering• that science and technology continue to demand improved accuracy in the realizationof the meter;• that since 1997 work in national laboratories, in the BIPM and elsewhere has
identified new radiations and methods for their realization which lead to lower
uncertainties;• that there is an increasing move towards optical frequencies for time-related activities,
and that there continues to be a general widening of the scope of application of therecommended radiations of the mise en pratique to cover not only dimensional
metrology and the realization of the meter, but also high-resolution spectroscopy,
atomic and molecular physics, fundamental constants and telecommunication;• that a number of new frequency values with reduced uncertainties for radiations ofhigh-stability cold atom and ion standards already listed in the recommended
radiations list are now available, that the frequencies of radiations of several new cold
atom and ion species have also recently been measured, and that new improved values
with substantially reduced uncertainties for a number of optical frequency standards
based on gas cells have been determined, including the wavelength region of interest
to optical telecommunications;• that new femtosecond comb techniques have clear significance for relating thefrequency of high-stability optical frequency standards to that of the frequency
standard realizing the SI second, that these techniques represent a convenientmeasurement technique for providing traceability to the International System of Units(SI) and that comb technology also can provide frequency sources as well as ameasurement technique;recognizes comb techniques as timely and appropriate, and recommends further research
to fully investigate the capability of the techniques;79welcomes validations now being made of comb techniques by comparison
with other frequency chain techniques;
urges national metrology institutes and other laboratories to pursue thecomb technique to the highest level of accuracy achievable and also to seek
simplicity so as to encourage widespread application;
recommends
This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019• that the list of recommended radiations given by the CIPM in 1997
(Recommendation 1 (CI-1997)) be replaced by the list of radiations given
below*, including•

updated frequency values for cold Ca atom, H atom and the trapped
Sr+ ion,•frequency values for new cold ion species including trapped Hg+ion, trapped In+ ion and trapped Yb+ ion,•

updated frequency values for Rb-stabilized lasers, I2-stabilized
Nd:YAG and He-Ne lasers, CH4-stabilized He-Ne lasers and OsO4stabilized CO2 lasers at 10 µm,•

frequency values for standards relevant to the opticalcommunications bands, including Rb- and C2H2-stabilized lasers.

* The list of recommended
radiations,
Recommendation 1(CI-2002), is given in PV, 70,
197-204 and Metrologia,
2003, 40, 104-115.
See also J. Radiol. Prot.,
2005, 25, 97-100.

...
 Dose equivalent (PV, 70, 205)
Recommendation 2
The International Committee for Weights and Measures,considering that•the current definition of the SI unit of dose equivalent (sievert) includes
a factor “N ” (product of any other multiplying factors) stipulated by theInternational Commission on Radiological Protection (ICRP), and•both the ICRP and the International Commission on Radiation Units andMeasurements (ICRU) have decided to delete this factor N as it is nolonger deemed to be necessary, and•the current SI definition of H including the factor N is causing some confusion,

decides to change the explanation in the brochure “Le Système International d'Unités(SI)” to the following:
The quantity dose equivalent H is the product of the absorbed dose D of ionizing
radiation and the dimensionless factor Q (quality factor) defined as a function of linear
energy transfer by the ICRU:
H = Q · 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 on the value of Q.
80

The Committee further decides to maintain the final sentence in the explanation as
follows:
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 namegray should be used instead of joules per kilogram for the unit of absorbed dose D andthe name sievert instead of joules per kilogram for the unit of dose equivalent H.

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CIPM, 2003
 Revision of the Mise en Pratique list of recommended radiations (PV, 71, 146 andMetrologia, 2004, 41, 99-100)
Recommendation 1
The International Committee for Weights and Measures,considering that•

improved frequency values for radiations of some high-stability cold ion standards
already documented in the recommended radiations list have recently become
available;•

improved frequency values for the infra-red gas-cell-based optical frequency standard
in the optical telecommunications region, already documented in the recommended
radiations list, have been determined;•

femtosecond comb-based frequency measurements for certain iodine gas-cellstandards on the subsidiary recommended source list have recently been made for the
first time, leading to significantly reduced uncertainty;
proposes that the recommended radiation list be revised to include the following:•

updated frequency values for the single trapped 88Sr+ ion quadrupole transition andthe single trapped 171Yb+ octupole transition;•

an updated frequency value for the C2H2-stabilized standard at 1.54 µm;•

updated frequency values for the I2-stabilized standards at 543 nm and 515 nm.

22nd CGPM, 2003
 Symbol for the decimal marker (CR, 381 and Metrologia, 2004, 41, 104)
Resolution 10
The 22nd General Conference,
considering that•a principal purpose of the International System of Units (SI) is to enable values ofquantities to be expressed in a manner that can be readily understood throughout theworld,

81

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the value of a quantity is normally expressed as a number times a unit,•

often the number in the expression of the value of a quantity contains multiple digits
with an integral part and a decimal part,•in Resolution 7 of the 9th General Conference, 1948, it is stated that “In numbers, thecomma (French practice) or the dot (British practice) is used only to separate theintegral part of numbers from the decimal part”,•

following a decision of the International Committee made at its 86th meeting (1997),
the International Bureau of Weights and Measures now uses the dot (point on theline) as the decimal marker in all the English language versions of its publications,
including the English text of the SI Brochure (the definitive international reference on
the SI), with the comma (on the line) remaining the decimal marker in all of its
French language publications,•however, some international bodies use the comma on the line as the decimal marker
in their English language documents,•

furthermore, some international bodies, including some international standards
organizations, specify the decimal marker to be the comma on the line in all
languages,•

the prescription of the comma on the line as the decimal marker is in many languages
in conflict with the customary usage of the point on the line as the decimal marker inthose languages,•

in some languages that are native to more than one country, either the point on theline or the comma on the line is used as the decimal marker depending on the country,
while in some countries with more than one native language, either the point on theline or comma on the line is used depending on the language,

declares that the symbol for the decimal marker shall be either the point on the line or thecomma on the line,
reaffirms that “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,” as stated in
Resolution 7 of the 9th CGPM, 1948.

82

CIPM, 2005
 Clarification of the definition of the kelvin, unit of thermodynamic
temperature (PV, 73, 235 and Metrologia, 2006, 43, 177-178)
Recommendation 2
The International Committee for Weights and Measures (CIPM),
considering
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that the kelvin, unit of thermodynamic temperature, is defined as thefraction 1/273.16 of the thermodynamic temperature of the triple pointof water,•that the temperature of the triple point depends on the relative amount ofisotopes of hydrogen and oxygen present in the sample of water used,•that this effect is now one of the major sources of the observed
variability between different realizations of the water triple point,

decides•that the definition of the kelvin refer to water of a specified isotopic
composition,•that this composition be:
0.000 155 76 mole of 2H per mole of 1H,
0.000 379 9 mole of 17O per mole of 16O, and
0.002 005 2 mole of 18O per mole of 16O,

which is the composition of the International Atomic Energy Agency
reference material Vienna Standard Mean Ocean Water (VSMOW), as
recommended by IUPAC in “Atomic Weights of the Elements: Review
2000”.
•

that this composition be stated in a note attached to the definition of thekelvin in the SI brochure as follows:“This definition refers to water having the isotopic composition definedexactly by the following amount of substance ratios: 0.000 155 76 moleof 2H per mole of 1H, 0.000 379 9 mole of 17O per mole of 16O and 0.002
005 2 mole of 18O per mole of 16O”.

 Revision of the Mise en pratique list of recommended radiations (PV,73, 236 and Metrologia, 2006, 43, 178)
Recommendation 3
The International Committee for Weights and Measures (CIPM),

83

The kelvin was redefined by
the 26th CGPM in 2018
(Resolution 1, See p. 101).

considering that:•••
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improved frequency values for radiations of some high-stability cold ion and cold
atom standards already documented in the recommended radiations list have recently
become available;
improved frequency values for the infra-red gas-cell-based optical frequency
standard in the optical telecommunications region, already documented in therecommended radiations list, have been determined;
improved frequency values for certain iodine gas-cell standard, already documented
in the subsidiary recommended source list, have been determined;
frequencies of new cold atoms, of atoms in the near-infrared region and of moleculesin the optical telecommunications region have been determined by femtosecond
comb-based frequency measurements for the first time;

decides that the list of recommended radiations be revised to include the following:
•

•
•
•
•
•
•

updated frequency values for the single trapped 88Sr+ ion quadrupole transition, thesingle trapped 199Hg+ quadrupole transition and the single trapped 171Yb+ quadrupoletransition;
an updated frequency value for the Ca atom transition;
an updated frequency value for the C2H2-stabilized standard at 1.54 µm;
an updated frequency value for the I2-stabilized standard at 515 nm;
the addition of the 87Sr atom transition at 698 nm;
the addition of the 87Rb atom two-photon transitions at 760 nm;
the addition of the 12C2H2 (ν1 + ν3) band and the 13C2H2 (ν1 + ν3) and(ν1 + ν3 + ν4 + ν5) bands at 1.54 µm.

CIPM, 2006
 Concerning secondary representations of the second (PV, 74, 249 and Metrologia,
2007, 44, 97)
Recommendation 1
The International Committee for Weights and Measures (CIPM),
considering that•••a common list of “Recommended values of standard frequencies for applications
including the practical realization of the meter and secondary representations of thesecond” shall be established,
the CCL/CCTF Joint Working Group (JWG) on the Mise en Pratique of theDefinition of the Meter and the Secondary Representations of the Second in its
meeting at the International Bureau of Weights and Measures (BIPM) in September
2005 discussed possible candidates to be included in this list for secondary
representations of the second,
the CCL/CCTF JWG reviewed and updated the values for the Hg ion, Sr ion, Yb ion,and the Sr neutral atom transition frequencies in its session in September 2006,84•

the CCTF in its Recommendation CCTF 1 (2004) already recommended theunperturbed ground-state hyperfine quantum transition frequency of 87Rb as asecondary representation of the second;

recommends that the following transition frequencies shall be used as secondary
representations of the second and be included into the new list of “Recommended valuesof standard frequencies for applications including the practical realization of the meterand secondary representations of the second”
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•

•
•
•
•
•

•

the unperturbed ground-state hyperfine quantum transition of 87Rb with a frequency
of f87Rb = 6 834 682 610.904 324 Hz and an estimated relative standard uncertainty of
3 × 10−15,
the unperturbed optical 5s 2S1/2 – 4d 2D5/2 transition of the 88Sr+ ion with a frequency
of f88Sr+ = 444 779 044 095 484 Hz and a relative uncertainty of 7 × 10−15,
the unperturbed optical 5d10 6s 2S1/2 (F = 0) – 5d9 6s2 2D5/2 (F = 2) transition of the199
Hg+
ion with a frequency of f199Hg+ = 1 064 721 609 899 145 Hz and a relative standard
uncertaintyof 3 × 10−15,
the unperturbed optical 6s 2S1/2 (F = 0) – 5d 2D3/2 (F = 2) transition of the 171Yb+ ion
with a frequency of f171Yb+ = 688 358 979 309 308 Hz and a relative standard
uncertainty of 9 × 10−15,
the unperturbed optical transition 5s2 1S0 – 5s 5p 3P0 of the 87Sr neutral atom with afrequency of f87Sr = 429 228 004 229 877 Hz and a relative standard uncertainty of
1.5 × 10−14.

CIPM, 2007
 Revision of the Mise en pratique list of recommended radiations (PV, 75, 185)
Recommendation 1
The International Committee for Weights and Measures,considering that:•••

improved frequency values of molecules in the optical telecommunications region,
already documented in the list of standard frequencies, have been determined byfemtosecond comb-based frequency measurements;
frequencies of molecules in the optical telecommunications region have been
determined by femtosecond comb-based frequency measurements for the first time;
frequencies of certain iodine gas-cell absorptions close to the 532 nm opticalfrequency standard have been determined by femtosecond comb-based frequency
measurements for the first time;

proposes that the list of standard frequencies be revised to include the following:•••

an updated list of frequency values for the 12C2H2 (ν1 + ν3) band at 1.54 µm;
the addition of frequency values for the 12C2HD (2ν1) band at 1.54 µm;
the addition of frequency values for the hyperfine components of the P(142) 37-0,
R(121) 35-0 and R(85) 33-0 iodine transitions at 532 nm.

85

23rd CGPM, 2007
 On the revision of the mise en pratique of the definition of the meterand the development of new optical frequency standards (CR, 431)
Resolution 9
The 23rd General Conference,
considering that:
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•
•
•
•

there have been rapid and important improvements in the performanceof optical frequency standards,
femtosecond comb techniques are now used routinely for relating
optical and microwave radiations at a single location,
National Metrology Institutes (NMIs) are working on comparison
techniques for optical frequency standards over short distances,remote comparison techniques need to be developed at an international
level so that optical frequency standards can be compared,

welcomes•••

the activities of the Joint Working Group of the Consultative
Committee for Length and the Consultative Committee for Time andFrequency to review the frequencies of optically-based representationsof the second,
the additions to the mise en pratique of the definition of the meter andto the list of recommended radiations made by the International
Committee in 2002, 2003, 2005, 2006, and 2007,
the initiative taken by the International Bureau of Weights andMeasures (BIPM) to raise the issue of how to compare opticalfrequency standards,

recommends that:••

NMIs commit resources to the development of optical frequency
standards and their comparison,
the BIPM works toward the coordination of an international projectwith the participation of NMIs, oriented to the study of the techniques
which could serve to compare optical frequency standards.

 Clarification of the definition of the kelvin, unit of thermodynamic
temperature (CR, 432)
Resolution 10
The 23rd General Conference,
considering•that the kelvin, unit of thermodynamic temperature, is defined as thefraction 1/273.16 of the thermodynamic temperature of the triple pointof water,
86

The kelvin was redefined by
the 26th CGPM in 2018
(Resolution 1, See p. 101).

•that the temperature of the triple point depends on the relative amountof isotopes of hydrogen and oxygen present in the sample of water used,•that this effect is now one of the major sources of the observed
variability between different realizations of the water triple point,notes and welcomes the decision by the International Committee for
Weights and Measures in October 2005, on the advice of the Consultative
Committee for Thermometry, that
This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019• the definition of the kelvin refers to water of a specified isotopic

composition,• this composition be:

0.000 155 76 mole of 2H per mole of 1H,
0.000 379 9 mole of 17O per mole of 16O, and
0.002 005 2 mole of 18O per mole of 16O,
which is the composition of the International Atomic Energy Agency
reference material Vienna Standard Mean Ocean Water (VSMOW), as
recommended by the International Union of Pure and Applied Chemistry in"Atomic Weights of the Elements: Review 2000,"• this composition be stated in a note attached to the definition of thekelvin in the SI Brochure as follows:"This definition refers to water having the isotopic composition
defined by the following amount-of-substance ratios: 0.000 155 76
mole of 2H per mole of 1H, 0.000 379 9 mole of 17O per mole of 16O
and 0.002 005 2 mole of 18O per mole of 16O".
 On the possible redefinition of certain base units of the International
System of Units (SI) (CR, 434)
Resolution 12
The 23rd General Conference,
considering•

that, for many years, National Metrology Institutes (NMIs) as well as
the International Bureau of Weights and Measures (BIPM) have madeconsiderable efforts to advance and improve the International System ofUnits (SI) by extending the frontiers of metrology so that the SI baseunits could be defined in terms of the invariants of nature - thefundamental physical constants,•

that, of the seven base units of the SI, only the kilogram is still definedin terms of a material artifact - the international prototype of thekilogram (2nd CGPM, 1889, 3rd CGPM, 1901) and that the definitionsof the ampere, mole and candela depend on the kilogram,
87

The 26th CGPM in 2018
(Resolution 1, See p. 101)
finally approved the revisionof the SI.

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Resolution 7 of the 21st General Conference (1999) which recommended that"national laboratories continue their efforts to refine experiments that link the unit ofmass to fundamental or atomic constants with a view to a future redefinition of thekilogram,"•

the many advances, made in recent years, in experiments which relate the mass of theinternational prototype to the Planck constant h or the Avogadro constant NA,•

initiatives to determine the value of a number of relevant fundamental constants,
including work to redetermine the Boltzmann constant kB,•

that as a result of recent advances, there are significant implications for, and potential
benefits from, redefinitions of the kilogram, the ampere, the kelvin and the mole,•

Recommendation 1 of the International Committee (C1-2005) at its meeting in
October 2005, and various Recommendations of Consultative Committees on thesubject of a redefinition of one or more of the base units of the SI,

noting• that any changes in definitions of units of the SI must be constrained by self-consistency,• that it is desirable that definitions of the base units should be easily understood,• the work of the International Committee and the Consultative Committees,• the need to monitor the results of relevant experiments,• the importance of soliciting comments and contributions from the wider scientificand user communities, and• the decision of the International Committee in 2005 to approve, in principle, thepreparation of new definitions of the kilogram, ampere, kelvin and the possibility ofredefining the mole,
recommends that National Metrology Institutes and the BIPM
• pursue the relevant experiments so that the International Committee can come to aview on whether it may be possible to redefine the kilogram, the ampere, the kelvin,
and the mole using fixed values of the fundamental constants at the time of the 24th
General Conference (2011),• should, together with the International Committee, its Consultative Committees, andappropriate working groups, work on practical ways of realizing any new definitions
based on fixed values of the fundamental constants, prepare a mise en pratique foreach of them, and consider the most appropriate way of explaining the new
definitions to users,• initiate awareness campaigns to alert user communities to the possibility ofredefinitions and that the technical and legislative implications of such redefinitions
and their practical realizations be carefully discussed and considered,and requests the International Committee to report on these issues to the 24th General
Conference in 2011 and to undertake whatever preparations are considered necessary sothat, if the results of experiments are found to be satisfactory and the needs of users met,88

formal proposals for changes in the definitions of the kilogram, ampere, thekelvin and mole can be put to the 24th General Conference.
CIPM, 2009
 Updates to the list of standard frequencies (PV, 77, 235)
Recommendation 2
The International Committee for Weights and Measures (CIPM),
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considering that

• a common list of “Recommended values of standard frequencies forapplications including the practical realization of the meter andsecondary representations of the second” has been established;• the CCL-CCTF Frequency Standards Working Group (FSWG) has
reviewed several promising candidates for inclusion in the list;
recommends
that the following transition frequencies shall be included or updated in thelist of recommended standard frequencies:• the unperturbed optical transition 5s2 1S0 – 5s 5p 3P0 of the 87Sr neutral
atom with a frequency of f = 429 228 004 229 873.7 Hz and a relative
standard uncertainty of 1 × 10−15 (this radiation is already endorsed by
the CIPM as a secondary representation of the second);• the unperturbed optical transition 5s2 1S0 – 5s 5p 3P0 of the 88Sr neutral
atom with a frequency of f = 429 228 066 418 012 Hz and a relative
standard uncertainty of 1 × 10−14;• the unperturbed optical transition 4s 2S1/2 – 3d 2D5/2 of the 40Ca+ ion witha frequency of f = 411 042 129 776 393 Hz and a relative standard
uncertainty of 4 × 10−14;• the unperturbed optical transition 2S1/2 (F = 0) – 2F7/2 (F = 3, mF = 0) of
the 171Yb+ ion with a frequency of f = 642 121 496 772 657 Hz and a
relative standard uncertainty of 6 × 10−14;•

the unperturbed optical transition 6s2 1S0 (F = 1/2) – 6s 6p 3P0 (F = 1/2)of the 171Yb neutral atom with a frequency of f = 518 295 836 590 864
Hz and a relative standard uncertainty of 1.6 × 10−13.

24th CGPM, 2011 On the possible future revision of the International System of Units,
the SI (CR, 532)

89

The 26th CGPM in 2018
(Resolution 1, See p. 101)
finally approved the revisionof the SI.

Resolution 1
The General Conference on Weights and Measures (CGPM), at its 24th meeting,considering

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the international consensus on the importance, value, and potential benefits of aredefinition of a number of units of the International System of Units (SI),•that the national metrology institutes (NMIs) as well as the International Bureau of
Weights and Measures (BIPM) have rightfully expended significant effort during thelast several decades to advance the International System of Units (SI) by extending
the frontiers of metrology so that SI base units can be defined in terms of theinvariants of nature - the fundamental physical constants or properties of atoms,•

that a prominent example of the success of such efforts is the current definition of the
SI unit of length, the meter (17th meeting of the CGPM, 1983, Resolution 1), whichlinks it to an exact value of the speed of light in vacuum c, namely, 299 792 458
meter per second,•that of the seven base units of the SI, only the kilogram is still defined in terms of amaterial artifact, namely, the international prototype of the kilogram (1st meeting of
the CGPM, 1889, 3rd meeting of the CGPM, 1901), and that the definitions of theampere, mole and candela depend on the kilogram,•that although the international prototype has served science and technology wellsince it was sanctioned by the CGPM at its 1st meeting in 1889, it has a number ofimportant limitations, one of the most significant being that its mass is not explicitly
linked to an invariant of nature and in consequence its long-term stability is notassured,•that the CGPM at its 21st meeting in 1999 adopted Resolution 7 in which it
recommended that "national laboratories continue their efforts to refine experimentsthat link the unit of mass to fundamental or atomic constants with a view to a future
redefinition of the kilogram",•that many advances have been made in recent years in relating the mass of theinternational prototype to the Planck constant h, by methods which include wattbalances and measurements of the mass of a silicon atom,•that the uncertainties of all SI electrical units realized directly or indirectly by meansof the Josephson and quantum Hall effects together with the SI values of theJosephson and von Klitzing constants KJ and RK could be significantly reduced if thekilogram were redefined so as to be linked to an exact numerical value of h, and if
the ampere were to be redefined so as to be linked to an exact numerical value of theelementary charge e,•that the kelvin is currently defined in terms of an intrinsic property of water that,while being an invariant of nature, in practice depends on the purity and isotopic
composition of the water used,

90

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that it is possible to redefine the kelvin so that it is linked to an exact
numerical value of the Boltzmann constant k,•that it is also possible to redefine the mole so that it is linked to an exact
numerical value of the Avogadro constant NA, and is thus no longer
dependent on the definition of the kilogram even when the kilogram isdefined so that it is linked to an exact numerical value of h, thereby
emphasizing the distinction between amount of substance and mass,•that the uncertainties of the values of many other important fundamental
constants and energy conversion factors would be eliminated or greatly
reduced if h, e, k and NA had exact numerical values when expressed in
SI units,•that the General Conference, at its 23rd meeting in 2007, adopted
Resolution 12 in which it outlined the work that should be carried out
by the NMIs, the BIPM and the International Committee for Weights
and Measures (CIPM) together with its Consultative Committees (CCs)so that new definitions of the kilogram, ampere, kelvin, and mole interms of fundamental constants could be adopted,•

that, although this work has progressed well, not all the requirements set
out in Resolution 12 adopted by the General Conference at its 23rd
meeting in 2007 have been satisfied and so the International Committee
for Weights and Measures is not yet ready to make a final proposal,•

that, nevertheless, a clear and detailed explanation of what is likely tobe proposed can now be presented,

takes note of the intention of the International Committee for Weights andMeasures to propose a revision of the SI as follows:• the International System of Units, the SI, will be the system of units inwhich:• the ground state hyperfine splitting frequency of the cesium 133
atom Δν(133Cs)hfs is exactly 9 192 631 770 hertz,• the speed of light in vacuum c is exactly 299 792 458 meter per
second,• the Planck constant h is exactly 6.626 06X ×10−-34 joule second*,• the elementary charge e is exactly 1.602 17X ×10−19 coulomb,• the Boltzmann constant k is exactly 1.380 6X ×10−23 joule perkelvin,• the Avogadro constant NA is exactly 6.022 14X ×1023 reciprocal
mole,

91

* The X digit appearing in
the expression of theconstants indicates that
this digit was unknown at
the time of the resolution.

• the luminous efficacy Kcd of monochromatic radiation of frequency
540 ×1012 Hz is exactly 683 lumen per watt,
whereThis publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019(i) the hertz, joule, coulomb, lumen, and watt, with unit symbols Hz, J, C, lm,
and W, respectively, are related to the units second, meter, kilogram, ampere,kelvin, mole, and candela, with unit symbols s, m, kg, A, K, mol, and cd,
respectively, according to Hz = s−1, J = m2 kg s−2, C = s A, lm = cd m2 m−2 = cd
sr, and W = m2 kg s−3,(ii) the symbol X in this Draft Resolution represents one or more additional
digits to be added to the numerical values of h, e, k, and NA, using values basedon the most recent CODATA adjustment,from which it follows that the SI will continue to have the present set of seven base units,
in particular• the kilogram will continue to be the unit of mass, but its magnitude will be set
by fixing the numerical value of the Planck constant to be equal to exactly
6.626 06X × 10−34 when it is expressed in the SI unit m2 kg s−1, which is equal
to J s,• the ampere will continue to be the unit of electric current, but its magnitude
will be set by fixing the numerical value of the elementary charge to be equal
to exactly 1.602 17X × 10−19 when it is expressed in the SI unit s A, which isequal to C,• the kelvin will continue to be the unit of thermodynamic temperature, but its
magnitude will be set by fixing the numerical value of the Boltzmann constant
to be equal to exactly 1.380 6X × 10−23 when it is expressed in the SI unit m2
kg s−2 K-1, which is equal to J K−1,

• the mole will continue to be the unit of amount of substance of a specified
elementary entity, which may be an atom, molecule, ion, electron, any otherparticle or a specified group of such particles, but its magnitude will be set by
fixing the numerical value of the Avogadro constant to be equal to exactly
6.022 14X × 1023 when it is expressed in the SI unit mol−1.
The General Conference on Weights and Measuresfurther notes that since• the new definitions of the kilogram, ampere, kelvin and mole are intended to be of the
explicit-constant type, that is, a definition in which the unit is defined indirectly by
specifying explicitly an exact value for a well-recognized fundamental constant,• the existing definition of the meter is linked to an exact value of the speed of light invacuum, which is also a well-recognized fundamental constant,92

• the existing definition of the second is linked to an exact value of a well-definedproperty of the cesium atom, which is also an invariant of nature,• although the existing definition of the candela is not linked to a fundamental constant,it may be viewed as being linked to an exact value of an invariant of nature,• it would enhance the understandability of the International System if all of its baseunits were of similar wording,
the International Committee for Weights and Measures will also propose
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the reformulation of the existing definitions of the second, meter and candela incompletely equivalent forms, which might be the following:• the second, symbol s, is the unit of time; its magnitude is set by fixing the numericalvalue of the ground state hyperfine splitting frequency of the cesium 133 atom, at rest
and at a temperature of 0 K, to be equal to exactly 9 192 631 770 when it is expressedin the SI unit s−1, which is equal to Hz,• the meter, symbol m, is the unit of length; its magnitude is set by fixing the numericalvalue of the speed of light in vacuum to be equal to exactly 299 792 458 when it isexpressed in the SI unit m s−1,

• the candela, symbol cd, is the unit of luminous intensity in a given direction; its
magnitude is set by fixing the numerical value of the luminous efficacy of
monochromatic radiation of frequency 540 ×1012 Hz to be equal to exactly 683 when
it is expressed in the SI unit m−2 kg−1 s3 cd sr, or cd sr W−1, which is equal to lm W−1.
In this way, the definitions of all seven base units will be seen to follow naturally fromthe set of seven constants given above.
In consequence, on the date chosen for the implementation of the revision of the SI:• the definition of the kilogram in force since 1889 based upon the mass of theinternational prototype of the kilogram (1st meeting of the CGPM, 1889, 3rd meetingof the CGPM, 1901) will be abrogated,• the definition of the ampere in force since 1948 (9th meeting of the CGPM, 1948)
based upon the definition proposed by the International Committee (CIPM, 1946,
Resolution 2) will be abrogated,• the conventional values of the Josephson constant KJ-90 and of the von Klitzing
constant RK-90 adopted by the International Committee (CIPM, 1988,
Recommendations 1 and 2) at the request of the General Conference (18th meeting of
the CGPM, 1987, Resolution 6) for the establishment of representations of the volt andthe ohm using the Josephson and quantum Hall effects, respectively, will beabrogated,• the definition of the kelvin in force since 1967/68 (13th meeting of the CGPM,
1967/68, Resolution 4) based upon a less explicit, earlier definition (10th meeting of
the CGPM, 1954, Resolution 3) will be abrogated,93• the definition of the mole in force since 1971 (14th meeting of the CGPM, 1971,
Resolution 3) based upon a definition whereby the molar mass of carbon 12 had theexact value 0.012 kg mol-1 will be abrogated,• the existing definitions of the meter, second and candela in force since they wereadopted by the CGPM at its 17th (1983, Resolution 1), 13th (1967/68, Resolution 1)
and 16th (1979, Resolution 3) meetings, respectively, will be abrogated.

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The General Conference on Weights and Measuresfurther notes that on the same date

• the mass of the international prototype of the kilogram m(K) will be 1 kg but with arelative uncertainty equal to that of the recommended value of h just before
redefinition and that subsequently its value will be determined experimentally,• that the magnetic constant (permeability of vacuum) µ0 will be 4π × 10−7 H m−1 butwith a relative uncertainty equal to that of the recommended value of the fine-structure
constant alpha and that subsequently its value will be determined experimentally,• that the thermodynamic temperature of the triple point of water TTPW will be 273.16 K
but with a relative uncertainty equal to that of the recommended value of k just before
redefinition and that subsequently its value will be determined experimentally,• that the molar mass of carbon 12 M(12C) will be 0.012 kg mol−1 but with a relative
uncertainty equal to that of the recommended value of NAh just before redefinition andthat subsequently its value will be determined experimentally.
The General Conference on Weights and Measuresencourages• researchers in national metrology institutes, the BIPM and academic institutions tocontinue their efforts and make known to the scientific community in general and to
CODATA in particular, the outcome of their work relevant to the determination of theconstants h, e, k, and NA, and• the BIPM to continue its work on relating the traceability of the prototypes it
maintains to the international prototype of the kilogram, and in developing a pool ofreference standards to facilitate the dissemination of the unit of mass when redefined,
invites• CODATA to continue to provide adjusted values of the fundamental physicalconstants based on all relevant information available and to make the results known to
the International Committee through its Consultative Committee for Units since these
CODATA values and uncertainties will be those used for the revised SI,• the CIPM to make a proposal for the revision of the SI as soon as therecommendations of Resolution 12 of the 23rd meeting of the General Conference are94

fulfilled, in particular the preparation of mises en pratique for the new definitions of
the kilogram, ampere, kelvin and mole,• the CIPM to continue its work towards improved formulations for the definitions of
the SI base units in terms of fundamental constants, having as far as possible a moreeasily understandable description for users in general, consistent with scientific rigour
and clarity,• the CIPM, the Consultative Committees, the BIPM, the OIML and National
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Metrology Institutes significantly to increase their efforts to initiate awarenesscampaigns aimed at alerting user communities and the general public to the intention
to redefine various units of the SI and to encourage consideration of the practical,
technical, and legislative implications of such redefinitions, so that comments andcontributions can be solicited from the wider scientific and user communities.
 On the revision of the mise en pratique of the meter and the development of new
optical frequency standards (CR, 546)
Resolution 8
The General Conference on Weight and Measures (CGPM), at its 24th meeting,considering that•

there have been rapid and important improvements in the performance of opticalfrequency standards,•

national metrology institutes are working on comparison techniques for opticalfrequency standards over short distances,•remote comparison techniques need to be developed at an international level so that
optical frequency standards can be compared,

welcomes• the activities of the joint working group of the CCTF and the CCL to review thefrequencies of optically-based representations of the second,• the additions made by the CIPM in 2009 to the common list of "Recommended
values of standard frequencies for applications including the practical realization of
the meter and secondary representations of the second",• the establishment of a CCTF working group on Coordination of the Development ofAdvanced Time and Frequency Transfer Techniques,
recommends that

• NMIs commit resources to the development of optical frequency standards and theircomparison,• the BIPM supports the coordination of an international project with the participationof NMIs, oriented to the study of the techniques which could serve to compare
optical frequency standards.
95

CIPM, 2013
 Updates to the list of standard frequencies (PV, 81, 144)
Recommendation 1
The International Committee for Weights and Measures (CIPM),
considering that
This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019•

a common list of “Recommended values of standard frequencies for applications
including the practical realization of the meter and secondary representations of thesecond” has been established,•

the CCL-CCTF Frequency Standards Working Group (FSWG) has reviewed several
candidates for inclusion into the list,

recommends the following changes to the list of “Recommended values of standard
frequencies for applications including the practical realization of the meter and secondary
representations of the second”:•

that the following transition frequency be added to the list:− the unperturbed optical transition 6s2 1S0 – 6s 6p 3P0 of the 199Hg neutral atomwith a frequency of 1 128 575 290 808 162 Hz and an estimated relative standard
uncertainty of 1.7 × 10−14;•that the following transition frequencies be updated in the list:− the unperturbed optical transition 4s 2S1/2 – 3d 2D5/2 of the 40Ca+ ion with afrequency of 411 042 129 776 395 Hz and an estimated relative standard
uncertainty of 1.5 × 10−14;− the unperturbed optical transition 1S – 2S of the 1H neutral atom with afrequency of 1 233 030 706 593 518 Hz and an estimated relative standard
uncertainty of 1.2 × 10−14;

Note: This frequency corresponds to half of the energy difference between the 1S and 2S
states;•that the following transition frequencies be updated in the list and endorsed as
secondary representations of the second:− the unperturbed optical transition 6s 2S1/2 – 4f 136s2 2F7/2 of the 171Yb+ ion(octupole) with a frequency of 642 121 496 772 645.6 Hz and an estimatedrelative standard uncertainty of 1.3 × 10−15;− the unperturbed optical transition 6s2 1S0 – 6s 6p 3P0 of the 171Yb neutral atomwith a frequency of 518 295 836 590 865.0 Hz and an estimated relative standard
uncertainty of 2.7 × 10−15;96•that the following transition frequency be added to the list and as asecondary representation of the second:− the unperturbed optical transition 3s2 1S0 – 3s 3p 3P0 of the 27Al+ ion
with a frequency of 1 121 015 393 207 857.3 Hz and an estimatedrelative standard uncertainty of 1.9 × 10−15;•that the following transition frequencies be updated in the list and as
secondary representations of the second:This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019− the unperturbed optical transition 5d 106s 2S1/2 – 5d 96s2 2D5/2 of the199
Hg+ ion with a frequency of 1 064 721 609 899 145.3 Hz and an
estimated relative standard uncertainty of 1.9 × 10−15;− the unperturbed optical transition 6s 2S1/2 (F = 0, mF = 0) – 5d 2D3/2(F = 2, mF = 0) of the 171Yb+ ion (quadrupole) with a frequency of
688 358 979 309 307.1 Hz and an estimated relative standard
uncertainty of 3 × 10−15;− the unperturbed optical transition 5s 2S1/2 – 4d 2D5/2 of the 88Sr+ ion
with a frequency of 444 779 044 095 485.3 Hz and an estimatedrelative standard uncertainty of 4.0 × 10−15;− the unperturbed optical transition 5s2 1S0 – 5s5p 3P0 of the 87Sr
neutral atom with a frequency of 429 228 004 229 873.4 Hz and an
estimated relative standard uncertainty of 1 × 10−15;•that the following transition frequency be updated as a secondary
representation of the second:− the unperturbed ground - state hyperfine transition of 87Rb with afrequency of 6 834 682 610.904 312 Hz and an estimated relative
standard uncertainty of 1.3 × 10−15.

Note: The value of the estimated standard uncertainty is assumed tocorrespond to a confidence level of 68 %. However, given the very limited
number of available data there is a possibility that in hindsight this might
not prove to be exact.
25th CGPM, 2014
 On the future revision of the International System of Units, the SI(CR, 416 and Metrologia, 2015, 52, 155)
Resolution 1
The General Conference on Weights and Measures (CGPM), at its 25th
meeting,97

The 26th CGPM in 2018
(Resolution 1, See p. 101)
finally approved the revisionof the SI.

recalling• Resolution 1 adopted by the CGPM at its 24th meeting (2011), which takes note of theThis publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019

intention of the International Committee for Weights and Measures (CIPM) to propose
a revision of the SI that links the definitions of the kilogram, ampere, kelvin, and mole
to exact numerical values of the Planck constant h, elementary charge e, Boltzmann
constant k, and Avogadro constant NA, respectively, and which revises the way the SI
is defined including the wording of the definitions of the SI units for time, length,
mass, electric current, thermodynamic temperature, amount of substance, andluminous intensity so that the reference constants on which the SI is based are clearly
apparent,• the many benefits summarized in Resolution 1 that will accrue to science, technology,
industry, and commerce from such a revision, especially from linking the kilogram to
an invariant of nature rather than to the mass of a material artifact, thereby ensuring its
long-term stability,• Resolution 7 adopted by the CGPM at its 21st meeting (1999), which encourages workat the National Metrology Institutes (NMIs) that can lead to such a redefinition of thekilogram,• Resolution 12 adopted by the CGPM at its 23rd meeting (2007), which outlines thework that should be carried out by the NMIs, the International Bureau of Weights andMeasures (BIPM), and the CIPM together with its Consultative Committees (CCs)that could enable the planned revision of the SI to be adopted by the CGPM,
considering that there has been significant progress in completing the necessary work,
including• the acquisition of relevant data and their analysis by the Committee on Data for
Science and Technology (CODATA) to obtain the required values of h, e, k, and NA,• establishment by the BIPM of an ensemble of reference standards of mass to facilitate
the dissemination of the unit of mass in the revised SI,• the preparation of mises-en-pratique for the new definitions of the kilogram, ampere,kelvin, and mole,noting that further work by the Consultative Committee for Units (CCU), the CIPM, theBIPM, the NMIs and the CCs should focus on• awareness campaigns to alert user communities as well as the general public to the
proposed revision of the SI,• the preparation of the 9th edition of the SI Brochure that presents the revised SI in a
way that can be understood by a diverse readership without compromising scientificrigour,that despite this progress the data do not yet appear to be sufficiently robust for the
CGPM to adopt the revised SI at its 25th meeting,98encourages• continued effort in the NMIs, the BIPM, and academic institutions to
obtain data relevant to the determination of h, e, k, and NA with therequisite uncertainties,• the NMIs to continue acting through the CCs to discuss and review thisdata,

• the CIPM to continue developing a plan to provide the path via theThis publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019

Consultative Committees and the CCU for implementing Resolution 1
adopted by the CGPM at its 24th meeting (2011), and• continued effort by the CIPM, together with its Consultative Committees,
the NMIs, the BIPM, and other organizations such as the International
Organization of Legal Metrology (OIML), to complete all work
necessary for the CGPM at its 26th meeting to adopt a resolution thatwould replace the current SI with the revised SI, provided the amount of
data, their uncertainties, and level of consistency are deemed satisfactory.
CIPM, 2015
 Updates to the list of standard frequencies (PV, 83, 207)
Recommendation 2
The International Committee for Weights and Measures (CIPM),
considering•

a common list of “Recommended values of standard frequencies forapplications including the practical realization of the meter andsecondary representations of the second” has been established,•

the CCL-CCTF Frequency Standards Working Group (WGFS) has
reviewed several candidates for updating the list,

recommends
that the following transition frequencies shall be updated in the list ofrecommended values of standard frequencies:•

the unperturbed optical transition 6s2 1S0 – 6s6p 3P0 of the 199Hg neutral
atom with a frequency of f199Hg = 1 128 575 290 808 154.8 Hz and an
estimated relative standard uncertainty of 6 × 10−16;•

the unperturbed optical transition 6s 2S1/2 – 4f13 6s2 2F7/2 of the 171Yb+
ion with a frequency of f171Yb+ (octupole) = 642 121 496 772 645.0 Hz
and an estimated relative standard uncertainty of 6 × 10−16 (thisradiation is already endorsed by the CIPM as a secondary representationof the second);•

the unperturbed optical transition 6s 2S1/2 (F = 0, mF = 0) – 5d 2D3/2 (F =2, mF = 0) of the 171Yb+ ion with a frequency of f171Yb+ (quadrupole) =688 358 979 309 308.3 Hz and an estimated relative standard
99

Further updates areavailable on the BIPM
website.

uncertainty of 6 × 10−16 (this radiation is already endorsed by the CIPM as asecondary representation of the second);

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

the unperturbed optical transition 5s 2S1/2 – 4d 2D5/2 of the 88Sr+ ion with a frequency
of f88Sr+ = 444 779 044 095 486.6 Hz and an estimated relative standard uncertainty
of 1.6 × 10−15 (this radiation is already endorsed by the CIPM as a secondary
representation of the second);•

the unperturbed optical transition 4s 2S1/2 – 3d 2D5/2 of the 40Ca+ ion with a frequencyof f40Ca+ = 411 042 129 776 398.4 Hz and an estimated relative standard uncertainty
of 1.2 × 10−14;•

the unperturbed optical transition 1S – 2S of the 1H neutral atom with a frequency of
f1H = 1 233 030 706 593 514 Hz and an estimated relative standard uncertainty of
9 × 10−15.

Note: This frequency corresponds to half of the energy difference between the 1S and 2S
states;•the unperturbed optical transition 5s2 1S0 – 5s5p 3P0 of the 87Sr neutral atom with afrequency of f87Sr = 429 228 004 229 873.2 Hz and an estimated relative standard
uncertainty of 5 × 10−16 (this radiation is already endorsed by the CIPM as asecondary representation of the second);•

the unperturbed optical transition 6s2 1S0 – 6s6p 3P0 of the 171Yb neutral atom with afrequency of f171Yb = 518 295 836 590 864.0 Hz and an estimated relative standard
uncertainty of 2 × 10−15 (this radiation is already endorsed by the CIPM as asecondary representation of the second);•

the unperturbed ground-state hyperfine transition of 87Rb with a frequency of
f87Rb = 6 834 682 610.904 310 Hz and an estimated relative standard uncertainty of
7 × 10−16 (this radiation is already endorsed by the CIPM as a secondary
representation of the second).

and also recommends
that the following transition frequencies shall be included in the list of recommended
values of standard frequencies:•

Absorbing molecule 127I2, saturated absorption a1 component, R(36) 32-0 transition.
The values

fa1 = 564 074 632.42 MHz

λa1 = 531 476 582.65 fm
with an estimated relative standard uncertainty of 1 × 10−10 apply to the radiation of afrequency-doubled diode DFB laser, stabilized with an iodine cell external to the laser.
• Absorbing atom 87Rb 5S1/2 - 5P3/2 crossover between the d and f hyperfine
components of the saturated absorption at 780 nm (D2 transition)
The values

fd/f crossover = 384 227 981.9 MHz
λd/f crossover = 780 246 291.6 fm

100

with an estimated relative standard uncertainty of 5 × 10−10 apply to the radiation of atunable External Cavity Diode Laser, stabilized to the d/f crossover in a rubidium cell
external to the laser.
Note: The value of the standard uncertainty is assumed to correspond to a confidence
level of 68 %. However, given the limited availability of data there is a possibility that in
hindsight this might not prove to be exact

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CIPM, 2017
 On progress towards the possible redefinition of the SI (PV, 85, 101)
Decision 10
The International Committee for Weights and Measures (CIPM) welcomedrecommendations regarding the redefinition of the SI from its Consultative Committees.
The CIPM noted that the agreed conditions for the redefinition are now met and decided
to submit draft Resolution A to the 26th meeting of the General Conference on Weights
and Measures (CGPM) and to undertake all other necessary steps to proceed with theplanned redefinition of the kilogram, ampere, kelvin and mole.
26th CGPM, 2018
 On the revision of the International System of Units, the SI (CR, in press andMetrologia, 2018, X, XXX)
Resolution 1
The General Conference on Weights and Measures (CGPM), at its 26th meeting,considering•

the essential requirement for an International System of Units (SI) that is uniform
and accessible world-wide for international trade, high-technology manufacturing,human health and safety, protection of the environment, global climate studies
and the basic science that underpins all these,•that the SI units must be stable in the long term, internally self-consistent andpractically realizable being based on the present theoretical description of nature
at the highest level,•that a revision of the SI to meet these requirements was described in Resolution 1of the 24th General Conference in 2011, adopted unanimously, that laid out indetail a new way of defining the SI based on a set of seven defining constants,
drawn from the fundamental constants of physics and other constants of nature,from which the definitions of the seven base units are deduced,•that the conditions set by the 24th General Conference, confirmed by the 25th
General Conference, before such a revised SI could be adopted have now been
met,

101

decidesthat, effective from 20 May 2019, the International System of Units, the SI, is the systemof units in which

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

the unperturbed ground state hyperfine transition frequency of the cesium
133 atom ∆ν Cs is 9 192 631 770 Hz,•

the speed of light in vacuum c is 299 792 458 m/s,•

the Planck constant h is 6.626 070 15 × 10−34 J s,•

the elementary charge e is 1.602 176 634 × 10−19 C,•

the Boltzmann constant k is 1.380 649 × 10−23 J/K,•

the Avogadro constant NA is 6.022 140 76 × 1023 mol−1,•

the luminous efficacy of monochromatic radiation of frequency 540 × 1012
Hz, Kcd, is 683 lm/W,

where the hertz, joule, coulomb, lumen, and watt, with unit symbols Hz, J, C, lm, and W,
respectively, are related to the units second, meter, kilogram, ampere, kelvin, mole, andcandela, with unit symbols s, m, kg, A, K, mol, and cd, respectively, according to
Hz = s–1, J = kg m2 s–2, C = A s, lm = cd m2 m –2 = cd sr, and W = kg m2 s–3.
In making this decision, the General Conference notes the consequences as set out in
Resolution 1 of the 24th General Conference in respect to the base units of the SI andconfirms these in the following Appendices to this Resolution, which have the same force
as the Resolution itself.
The General Conference invites the International Committee to produce a new edition ofits Brochure The International System of Units, SI in which a full description of the SI isgiven.
Appendix 1. Abrogation of former definitions of the base units:
It follows from the new definition of the SI adopted above that•the definition of the second in force since 1967/68 (13th meeting of the CGPM,
Resolution 1) is abrogated,•the definition of the meter in force since 1983 (17th meeting of the CGPM,
Resolution 1), is abrogated,•the definition of the kilogram in force since 1889 (1st meeting of the CGPM, 1889,
3rd meeting of the CGPM, 1901) based upon the mass of the international
prototype of the kilogram is abrogated,•the definition of the ampere in force since 1948 (9th meeting of the CGPM) based
upon the definition proposed by the International Committee (CIPM, 1946,
Resolution 2) is abrogated,•the definition of the kelvin in force since 1967/68 (13th meeting of the CGPM,
Resolution 4) is abrogated,
102

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

the definition of the mole in force since 1971 (14th meeting of the CGPM,
Resolution 3) is abrogated,•the definition of the candela in force since 1979 (16th meeting of the CGPM,
Resolution 3) is abrogated,•the decision to adopt the conventional values of the Josephson constant KJ–90 and of
the von Klitzing constant RK–90 taken by the International Committee (CIPM, 1988,
Recommendations 1 and 2) at the request of the General Conference (18th meetingof the CGPM, 1987, Resolution 6) for the establishment of representations of thevolt and the ohm using the Josephson and quantum Hall effects, respectively, isabrogated.

Appendix 2. Status of constants previously used in the former definitions:
It follows from the new definition of the SI adopted above, and from the recommended
values of the 2017 special CODATA adjustment on which the values of the defining
constants are based, that at the time this Resolution was adopted•

the mass of the international prototype of the kilogram m(K) is equal to 1 kg
within a relative standard uncertainty equal to that of the recommended value of hat the time this Resolution was adopted, namely 1.0 × 10-8 and that in the future
its value will be determined experimentally,•

the vacuum magnetic permeability µ0 is equal to 4π ×10–7 H m–1 within a relative
standard uncertainty equal to that of the recommended value of the fine-structure
constant α at the time this Resolution was adopted, namely 2.3 × 10-10 and that in
the future its value will be determined experimentally,•

the thermodynamic temperature of the triple point of water TTPW is equal to273.16 K within a relative standard uncertainty closely equal to that of therecommended value of k at the time this Resolution was adopted, namely 3.7 ×
10-7, and that in the future its value will be determined experimentally,•

the molar mass of carbon 12, M(12C), is equal to 0.012 kg mol–1 within a relative
standard uncertainty equal to that of the recommended value of NAh at the time
this Resolution was adopted, namely 4.5 × 10-10, and that in the future its value
will be determined experimentally.

Appendix 3. The base units of the SI
Starting from the definition of the SI adopted above in terms of fixed numerical values ofthe defining constants, definitions of each of the seven base units are deduced by taking,as appropriate, one or more of these defining constants to give the following set ofdefinitions:• The second, symbol s, is the SI unit of time. It is defined by taking the fixed

numerical value of the cesium frequency ∆ν Cs, the unperturbed ground-state
hyperfine transition frequency of the cesium 133 atom, to be 9 192 631 770 when
expressed in the unit Hz, which is equal to s–1.
103• The meter, symbol m, is the SI unit of length. It is defined by taking the fixed

numerical value of the speed of light in vacuum c to be 299 792 458 when
expressed in the unit m/s, where the second is defined in terms of the cesium
frequency ∆ν Cs.
• The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed

numerical value of the Planck constant h to be 6.626 070 15 × 10–34 when
expressed in the unit J s, which is equal to kg m2 s–1, where the meter and thesecond are defined in terms of c and ∆ν Cs.
This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019• The ampere, symbol A, is the SI unit of electric current. It is defined by taking the

fixed numerical value of the elementary charge e to be 1.602 176 634 × 10–19 when
expressed in the unit C, which is equal to A s, where the second is defined in termsof ∆ν Cs.
• The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined bytaking the fixed numerical value of the Boltzmann constant k to be
1.380 649 × 10– 23 when expressed in the unit J K–1, which is equal to kg m2 s–2 K–1,
where the kilogram, meter and second are defined in terms of h, c and ∆ν Cs.
• The mole, symbol mol, is the SI unit of amount of substance. One mole contains

exactly 6.022 140 76 × 1023 elementary entities. This number is the fixed numericalvalue of the Avogadro constant, NA, when expressed in the unit mol-1 and is called
the Avogadro number.
The amount of substance, symbol n, of a system is a measure of the number of
specified elementary entities. An elementary entity may be an atom, a molecule, anion, an electron, any other particle or specified group of particles.
• The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It isdefined by taking the fixed numerical value of the luminous efficacy of
monochromatic radiation of frequency 540 × 1012 Hz, Kcd, to be 683 when expressedin the unit lm W–1, which is equal to cd sr W–1, or cd sr kg–1 m–2 s3, where thekilogram, meter and second are defined in terms of h, c and ∆ν Cs.

104

Appendix 2. Practical realization of the definitions of some
important units
Appendix 2 is published in electronic form only, and is available on the BIPM website(www.bipm.org).

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Appendix 3. Units for photochemical and photobiologicalquantities
Appendix 3 is published in electronic form only, and is available on the BIPM website(www.bipm.org).

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Appendix 4. Historical notes on the development of theInternational System of Units and its base units
Part 1. The historical development of the realization of SI units

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Experimental methods used for the realization of units and which use equations ofphysics are known as primary methods. The essential characteristic of a primary method
is that it allows a quantity to be measured in a particular unit directly from its definition
by using only quantities and constants that themselves do not contain that unit.
Traditionally, a unit for a given quantity was taken to be a particular example of thatquantity, which was chosen to provide numerical values of common measurements of aconvenient size. Before the rise of modern science, units were necessarily defined interms of material artifacts, notably the meter and kilogram for length and mass, or theproperty of a particular object, namely the rotation of the earth for the second. Even at theorigin of the metric system at the end of the 18th century it was recognized that a moredesirable definition of a unit of length for example would be one based on a universal
property of nature such as the length of a pendulum beating seconds. Such a definition
would be independent of time and place and would in principle be accessible all over theworld. At the time, practical considerations resulted in the simpler, artifact definitions forthe meter and the kilogram and the second remained linked to the rotation of the Earth. It
was only in 1960 that the first non-material definition was adopted, namely the
wavelength of a specified optical radiation for the meter.
Since then, definitions of the ampere, kelvin, mole and candela have been adopted that do
not refer to material artifacts. In the case of the ampere it refers to a specified electric
current required to produce a given electromagnetic force and, in the case of the kelvin,to a particular thermodynamic state, namely the triple point of water. Even the atomic
definition of the second was in terms of a specified transition of the cesium atom. The
kilogram has always stood out as the one unit that had resisted the transformation from an
artifact. The definition that opened the way to real universality was that of the meter in
1983. This definition implied, although it did not state, a fixed numerical value for the
speed of light. The definition was worded, however, in the traditional form and statedessentially that the meter was the distance travelled by light in a specified time. In thisway it reflected the other definitions of the base units of the SI each of which has thesame form, for example “the ampere is the current which…” and “the kelvin is a fractionof a specified temperature.” Such definitions can be called explicit unit definitions.
Although these definitions meet many of the requirements for universality andaccessibility, and a variety of realizations are often possible, they nevertheless constrain
practical realizations to experiments that are directly or indirectly linked to the particularconditions or states specified in each definition. In consequence, the accuracy ofrealization of such definitions can never be better than the accuracy of realization of theparticular conditions or states specified in the definitions.
This is a particular problem with the present definition of the second, which is based on a
microwave transition of an atom of cesium. Frequencies of optical transitions of different

107atoms or ions are now demonstrably more reproducible, by some orders of magnitude,
than the defined frequency of cesium.

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In the present definition of the SI based on the set of defining constants, instead of eachdefinition specifying a particular condition or state, which sets a fundamental limit to theaccuracy of realization, any convenient equation of physics that links the particularconstant or constants to the quantity we want to measure may be used. This is a much
more general way of defining the basic units of measurement. It is one that is not limited
by today’s science or technology as future developments may lead to as yet unknown
equations that could result in different ways of realizing units with a much higher
accuracy. When defined in this way, there is, in principle, no limit to the accuracy withwhich a unit can be realized. The exception remains the definition of the second in which
the original microwave transition of cesium remains, for the time being, the basis of thedefinition.
The difference between an explicit unit and an explicit constant definition can be clearly
illustrated using the two previous definitions of the meter that depended upon a fixed
numerical value of the speed of light and secondly the two definitions of the kelvin.
The original 1983 definition of the meter states, in effect, that “the meter is the length ofthe path travelled by light in vacuum during a time interval of 1/299 792 458 of asecond”. The new definition simply states that the meter is defined by taking the constantthat defines the second, the specified cesium frequency and the fixed numerical value ofthe speed of light expressed in units m·s−1. We can thus use any equation of physics
including, of course, that indicated by the former definition, the time taken to travel the
given distance which is used for astronomical distances, but also the simple equation
relating frequency and wavelength to the speed of light. The former definition of thekelvin based on a fixed numerical value for the temperature of the triple point of waterrequires ultimately a measurement at the triple point of water. The new definition, basedon the fixed numerical value for the Boltzmann constant, is much more general in thatany thermodynamic equation in which k appears can in principle be used to determine athermodynamic temperature at any point on the temperature scale. For example, bydetermining the total radiant exitance of a black body at temperature T, equal to(2π5k4/15c2h3) T4, in Wm−2 we can determine T directly.
For the kilogram, the unit whose definition has undergone the most fundamental change,
realization can be through any equation of physics that links mass, the Planck constant,the velocity of light and the cesium frequency. One such equation is that which describes
the operation of an electro-mechanical balance, previously known as a watt balance, more
recently known as a Kibble 11 balance. With this apparatus, a mechanical power,
measured in terms of a mass, m, the local acceleration due to gravity, g, and a velocity, v,
can be measured in terms of an electrical power measured in terms of an electric current
and voltage measured in terms of the quantum Hall and Josephson effects respectively.
The resulting equation is mgv = Ch where C is a calibration constant that includes
measured frequencies and h is Planck’s constant.
Another method that can be used for a primary realization of the kilogram is through thedetermination of the number of atoms in a silicon sphere and using the equation:
11 To recognize Bryan Kibble’s invention of the watt balance.

108

𝑚𝑚 =

8𝑉𝑉 2𝑅𝑅∞ ℎ 𝑚𝑚𝑆𝑆𝑆𝑆
𝑎𝑎03 𝑐𝑐𝛼𝛼 2𝑚𝑚𝑒𝑒with the mass m and volume V of the sphere, lattice parameter a0, Rydberg constant R∞,
fine structure constant α, and the masses of a silicon atom (averaged over the threeisotopes used for the sphere) mSi, and the electron me, respectively. The first fraction
corresponds to the number of atoms in the sphere, the second to the electron mass and thethird fraction is the ratio of the mass of the (isotopically averaged) silicon atom to theelectron mass.
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Another possibility for measuring mass through the new definition, but this time at the
microscopic level, is through measurements of atomic recoil using the relation that
includes h/m.
All these provide a striking illustration of the generality of the new way of defining units.
Detailed information on the current realization of the base and other units is given on the
BIPM website.

Part 2. The historical development of the International System
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 enquiry, the opinion prevailing inscientific, technical and educational circles in all countries;•

to make recommendations on the establishment of a practical system of units ofmeasurement suitable for adoption by all signatories to the Meter Convention.

The same CGPM also laid down, in Resolution 7 (CR 70), ‘general principles for thewriting of unit symbols’ and listed some coherent derived units that were assigned specialnames.
The 10th CGPM (1954, Resolution 6; CR 80) adopted as base quantities and units for thispractical system the following six quantities: length, mass, time, electric current,
thermodynamic temperature and luminous intensity, as well as the six corresponding baseunits: meter, kilogram, second, ampere, kelvin and candela. After a lengthy discussion
between physicists and chemists, the 14th CGPM (1971, Resolution 3, CR 78 andMetrologia 1972, 8, 36) added amount of substance, unit mole, as the seventh basequantity and unit.
The 11th CGPM (1960, Resolution 12; CR 87) adopted the name Système internationald’unités, with the international abbreviation SI, for this practical system of units and laid
down rules for prefixes, derived units and the former supplementary units, as well asother matters; it thus established a comprehensive specification for units of measurement.
Subsequent meetings of the CGPM and the CIPM have added to and modified theoriginal structure of the SI to take account of advances in science and of the changing
needs of users.
The historical sequence that led to these important decisions may be summarized asfollows.
109• The creation of the decimal metric system at the time of the French Revolution andthe subsequent deposition of two platinum standards representing the meter and thekilogram, on 22 June 1799, in the Archives de la République in Paris, which can beseen as the first step that led to the present International System of Units.

This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019• 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 physicalsciences. 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 otherelectrical phenomena.
• These applications in the field of electricity and magnetism were further extended
in the 1860s under the active leadership of Maxwell and Thomson through the
British Association for the Advancement of Science (BAAS). They formulated therequirement 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 sub-multiples andmultiples. The subsequent development of physics as an experimental science waslargely 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 theohm for electrical resistance, the volt for electromotive force, and the ampere forelectric current.
• After the signing of the Meter Convention on 20 May 1875, which created the
BIPM and established the CGPM and the CIPM, work began on establishing newinternational prototypes for the meter and the kilogram. In 1889 the 1st CGPM
sanctioned the international prototypes for the meter and the kilogram. Together
with the astronomical second as the unit of time, these units constituted athree-dimensional mechanical unit system similar to the CGS system, but with thebase units meter, kilogram and second, known as the MKS system.
• In 1901 Giorgi showed that it is possible to combine the mechanical units of thisMKS system with the practical electrical units to form a 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 also rewriting the equations occurring inelectromagnetism in the so-called rationalized form. Giorgi’s proposal opened thepath to a number of new developments.
• After the revision of the Meter Convention by the 6th CGPM (1921), which
extended the scope and responsibilities of the BIPM to other fields in physics andthe subsequent creation of the Consultative Committee for Electricity (CCE) by the
7th CGPM (1927), the Giorgi proposal was thoroughly discussed by the IEC, the110International Union of Pure and Applied Physics (IUPAP) and other internationalorganizations. This led the CCE to propose in 1939 the adoption of afour-dimensional system based on the meter, kilogram, second and ampere, the
MKSA system, a proposal approved by the CIPM in 1946.

This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.330-2019• Following an international enquiry by the BIPM, which began in 1948, the 10th
CGPM (1954), approved the further introduction of the kelvin and the candela, asbase units for thermodynamic temperature and luminous intensity, respectively.
The name International System of Units, with the abbreviation SI, was given to thesystem by the 11th CGPM (1960). Rules for prefixes, derived units, the former
supplementary units as well as other matters, were established, thus providing acomprehensive specification for all units of measurement.
• At the 14th CGPM (1971) a new base unit, the mole, symbol mol, was adopted forthe quantity amount of substance. This followed a proposal from the International
Organization for Standardization originating in a proposal from the Commission on
Symbols, Units and Nomenclature (SUN Commission) of IUPAP, which was
supported by the International Union for Pure and Applied Chemistry (IUPAC).
This brought the number of base units of the SI to seven.
• Since then, extraordinary advances have been made in relating SI units to truly
invariant quantities such as the fundamental constants of physics and the propertiesof atoms. Recognizing the importance of linking SI units to such invariant
quantities, the 24th CGPM (2011), adopted the principles of a new definition of the
SI based on using a set of seven such constants as references for the definitions. At
the time of the 24th CGPM, experiments to determine their values in terms of thethen base units were not completely consistent but by the time of the 26th CGPM
(2018) this had been achieved and the new definition of the SI was adopted in
Resolution 1. This is the basis of the definition presented in this brochure and it is
the simplest and most fundamental way of defining the SI.
• The SI was previously defined in terms of seven base units and derived units

defined as products of powers of the base units. The seven base units were chosen
for historical reasons, as the metric system, later the SI, evolved and developed
over the last 130 years. Their choice was not unique, but it has become establishedand familiar over the years, not only by providing a framework for describing theSI, but also for defining the derived units. This role for the base units continues in
the present SI even though the SI itself is now defined in terms of the sevendefining constants. In this brochure therefore, definitions of the seven base units
can still be found but are henceforth based on the seven defining constants: thecesium hyperfine frequency ∆ν Cs; the speed of light in vacuum c; the Planck
constant h; elementary charge e; Boltzmann constant k; Avogadro constant NA; andthe luminous efficacy of a defined visible radiation Kcd.
The definitions of the seven base units can be related unambiguously to the numericalvalues of the seven defining constants. However, there is not a one-to-one relationshipbetween the seven defining constants and the seven base units as many of the base units
call upon more than one of the defining constants.

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Part 3. Historical perspective on the base units
Unit of time, second

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Before 1960, the unit of time the second, was defined as the fraction 1/86 400 of the meansolar day. The exact definition of “mean solar day” was left to astronomers. However
measurements showed that irregularities in the rotation of the Earth made this anunsatisfactory definition. In order to define the unit of time more precisely, the 11th CGPM
(1960, Resolution 9, CR, 86) adopted a definition given by the International Astronomical
Union based on the tropical year 1900. Experimental work, however, had already shownthat an atomic standard of time, based on a transition between two energy levels of an atom
or a molecule, could be realized and reproduced much more accurately. Considering that avery precise definition of the unit of time is indispensable for science and technology, the13th CGPM (1967-1968, Resolution 1, CR, 103 and Metrologia, 1968, 4, 43) chose a new
definition of the second referenced to the frequency of the ground state hyperfine transitionin the cesium-133 atom. A revised more precise wording of this same definition now interms of a fixed numerical value of the unperturbed ground-state hyperfine transition
frequency of the cesium-133 atom, ∆ν Cs, was adopted in Resolution 1 of the 26th CGPM
(2018).
Unit of length, meter
The 1889 definition of the meter, namely, the length of the international prototype of
platinum-iridium, was replaced by the 11th CGPM (1960) using a definition based on the
wavelength of the radiation corresponding to a particular transition in krypton 86. Thischange was adopted in order to improve the accuracy with which the definition of themeter could be realized, this being achieved using an interferometer with a travelling
microscope to measure the optical path difference as the fringes were counted. In turn,this was replaced in 1983 by the 17th CGPM (Resolution 1, CR, 97, and Metrologia,
1984, 20, 25) with a definition referenced to the distance that light travels in vacuum in a
specified interval of time, as presented in 2.3.1. The original international prototype ofthe meter, which was sanctioned by the 1st CGPM in 1889 (CR, 34-38), is still kept at the
BIPM under conditions specified in 1889. In order to make clear its dependence on the
fixed numerical value of the speed of light, c, the wording of the definition was changed
in Resolution 1 of the 26th CGPM (2018).
Unit of mass, kilogram
The 1889 definition of the kilogram was simply the mass of the international prototype of
the kilogram, an artifact made of platinum-iridium. This was, and still is, kept at the
BIPM under the conditions specified by the 1st CGPM (1889, CR, 34-38) when it
sanctioned the prototype and declared that “this prototype shall henceforth be considered
to be the unit of mass”. Forty similar prototypes were made at about the same time andthese were all machined and polished to have closely the same mass as the international
prototype. At the 1st CGPM (1889), after calibration against the international prototype,most of these “national prototypes” were individually assigned to Member States, and112

some also to the BIPM. The 3rd CGPM (1901, CR, 70), in a declaration intended to end
the ambiguity in common usage concerning the use of 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 version of these declarations appears on p. 70 of the abovementioned CGPM proceedings.

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By the time of the second verification of national prototypes in 1946 it was found that on
average the masses of these prototypes were diverging from that of the international
prototype. This was confirmed by the third verification carried out from 1989 to 1991, themedian difference being about 25 micrograms for the set of original prototypes
sanctioned by the 1st CGPM (1889). In order to assure the long-term stability of the unitof mass, to take full advantage of quantum electrical standards and to be of more utility tomodern science, a new definition for the kilogram based on the value of a fundamental
constant, for which purpose the Planck constant h was chosen, was adopted by
Resolution 1 of the 26th CGPM (2018).
Unit of electric current, ampere
Electric units, called “international units,” for current and resistance were introduced by
the International Electrical Congress held in Chicago in 1893 and definitions of the“international ampere” and “international ohm” were confirmed by the International
Conference in London in 1908.
By the time of the 8th CGPM (1933) there was a unanimous desire to replace the“international units” by so-called “absolute units”. However because some laboratories
had not yet completed experiments needed to determine the ratios between theinternational and absolute units, the CGPM gave authority to the CIPM to decide at an
appropriate time both these ratios and the date at which the new absolute units would
come into effect. The CIPM did so in 1946 (1946, Resolution 2, PV, 20, 129-137), when
it decided that the new units would come into force on 1 January 1948. In October 1948
the 9th CGPM approved the decisions taken by the CIPM. The definition of the ampere,chosen by the CIPM, was referenced to the force between parallel wires carrying anelectric current and it had the effect of fixing the numerical value of the vacuum magnetic
permeability μ0 (also called the magnetic constant). The numerical value of the vacuum
electric permittivity ε0 (also called the electric constant) then became fixed as aconsequence of the new definition of the meter adopted in 1983.
However the 1948 definition of the ampere proved difficult to realize and practicalquantum standards (based on Josephson and quantum-Hall effects), which link both thevolt and the ohm to particular combinations of the Planck constant h and elementarycharge e, became almost universally used as a practical realization of the ampere throughOhm’s law (18th CGPM (1987), Resolution 6, CR 100). As a consequence, it became
natural not only to fix the numerical value of h to redefine the kilogram, but also to fix
the numerical value of e to redefine the ampere in order to bring the practical quantum
electrical standards into exact agreement with the SI. The present definition based on a
fixed numerical value for the elementary charge, e, was adopted in Resolution 1 of the
26th CGPM (2018).

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The definition of the unit of thermodynamic temperature was given by the 10th CGPM
(1954, Resolution 3; CR 79) which selected the triple point of water, TTPW, as afundamental fixed point and assigned to it the temperature 273.16 K, thereby defining thekelvin. 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 ºK, for the unit
defined in this way. However, the practical difficulties in realizing this definition,requiring a sample of pure water of well-defined isotopic composition and thedevelopment of new primary methods of thermometry, led to the adoption of a new
definition of the kelvin based on a fixed numerical value of the Boltzmann constant k.
The present definition, which removed both of these constraints, was adopted in
Resolution 1 of the 26th CGPM (2018).
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 “molecularweights”, which are in fact relative atomic and molecular masses. The first compilationsof “Atomic weights” were originally linked to the atomic weight of oxygen, which was,by general agreement, taken as being 16. Whereas physicists separated the isotopes in a
mass spectrometer and attributed the value 16 to one of the isotopes of oxygen, chemists
attributed the same value to the (slightly variable) mixture of isotopes 16, 17 and 18,
which for them constituted the naturally occurring element oxygen. An agreement
between the International Union of Pure and Applied Physics (IUPAP) and theInternational Union of Pure and Applied Chemistry (IUPAC) brought this duality to an
end in 1959-1960. Physicists and chemists had agreed to assign the value 12, exactly, tothe so-called atomic weight, correctly referred to as the relative atomic mass Ar, of theisotope of carbon with mass number 12 (carbon-12, 12C). The unified scale thus obtained
gives the relative atomic and molecular masses, also known as the atomic and molecularweights, respectively. This agreement is unaffected by the redefinition of the mole.
The quantity used by chemists to specify the amount of chemical elements or compounds
is called “amount of substance”. Amount of substance, symbol n, is defined to be
proportional to the number of specified elementary entities N in a sample, theproportionality constant being a universal constant which is the same for all entities. The
proportionality constant is the reciprocal of the Avogadro constant NA, so that n = N/NA.
The unit of amount of substance is called the mole, symbol mol. Following proposals by
the IUPAP, IUPAC and ISO, the CIPM developed a definition of the mole in 1967 andconfirmed it in 1969, by specifying that the molar mass of carbon 12 should be exactly
0.012 kg/mol. This allowed the amount of substance nS(X) of any pure sample S of entity
X to be determined directly from the mass of the sample mS and the molar mass M(X) of
entity X, the molar mass being determined from its relative atomic mass Ar (atomic ormolecular weight) without the need for a precise knowledge of the Avogadro constant, byusing the relations
114

nS(X) = mS/M(X), and M(X) = Ar(X) g/mol
Thus, this definition of the mole was dependent on the artifact definition of the kilogram.

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The numerical value of the Avogadro constant defined in this way was equal to thenumber of atoms in 12 grams of carbon-12. However, because of recent technologicaladvances, this number is now known with such precision that a simpler and more
universal definition of the mole has become possible, namely, by specifying exactly the
number of entities in one mole of any substance, thus fixing the numerical value of the
Avogadro constant. This has the effect that the new definition of the mole and the valueof the Avogadro constant are no longer dependent on the definition of the kilogram. The
distinction between the fundamentally different quantities ‘amount of substance’ and‘mass’ is thereby emphasized. The present definition of the mole based on a fixed
numerical value for the Avogadro constant, NA, was adopted in Resolution 1 of the 26th
CGPM (2018).
Unit of luminous intensity, candela
The units of luminous intensity, which were based on flame or incandescent filament
standards in use in various countries before 1948, were replaced initially by the “newcandle” based on the luminance of a Planckian radiator (a black body) at the temperatureof freezing platinum. This modification had been prepared by the International
Commission on Illumination (CIE) and by the CIPM before 1937 and the decision waspromulgated by the CIPM in 1946. It was then ratified in 1948 by the 9th CGPM, which
adopted a new international name for this unit, the candela, symbol cd; in 1954 the 10th
CGPM established the candela as a base unit; In 1967 the 13th CGPM (Resolution 5, CR,
104 and Metrologia, 1968, 4, 43-44) amended this definition.
In 1979, because of the 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 present definition of the candela uses a fixed numerical value for the luminous
efficacy of monochromatic radiation of frequency 540 ×1012 Hz, Kcd, adopted in
Resolution 1 of the 26th CGPM (2018).

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List of acronyms used in the present volume
1. Acronyms for laboratories, committees and conferences*

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BAAS
BIPM
CARICOM
CC
CCAUV
CCDS*
CCE*
CCEM

British Association for the Advancement of Science
International Bureau of Weights and Measures
Caribbean Community
Consultative Committees
Consultative Committee for Acoustics, Ultrasound and Vibration
Consultative Committee for the Definition of the Second, see CCTF
Consultative Committee for Electricity, see CCEM
(formerly the CCE) Consultative Committee for Electricity andMagnetism
CCL
Committee for Length
CCM
Consultative Committee for Mass and Related Quantities
CCPR
Consultative Committee for Photometry and Radiometry
CCQM
Consultative Committee for Amount of Substance: Metrology in
Chemistry and Biology
CCRI
Consultative Committee for Ionizing Radiation
CCT
Consultative Committee for Thermometry
CCTF(formerly the CCDS) Consultative Committee for Time and Frequency
CCU
Consultative Committee for Units
CGPM
General Conference on Weights and Measures
CIPM
International Committee for Weights and Measures
CODATA
Committee on Data for Science and Technology
CR
Report of the General Conference on Weights and Measures, CGPM
IAUInternational Astronomical Union
ICRP
International Commission on Radiological Protection
ICRU
International Commission on Radiation Units and Measurements
IEC
International Electrotechnical Commission
IERS
International Earth Rotation and Reference Systems Service
ISO
International Organization for Standardization
IUPAC
International Union of Pure and Applied Chemistry
IUPAPInternational Union of Pure and Applied Physics
NIST
National Institute of Standards and Technology
NMI
National Measurement Institute
OIML
International Organization of Legal Metrology
PV
Report of the International Committee for Weights and Measures, CIPM
SUNAMCO Commission for Symbols, Units, Nomenclature, Atomic Masses, andFundamental Constants, IUPAPWHOWorld Health Organization* Organizations marked with an asterisk either no longer exist or operate under a different acronym.

117

2. Acronyms for scientific terms
CGS

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EPT-76GUM
IPTS-68
ISQ
ITS-90
IU
MKS
MKSA
SI
TAI
TCG
TT
UTC
VSMOW

Three-dimensional coherent system of units based on the three mechanicalunits centimeter, gram and second
Provisional Low Temperature Scale of 1976
Guide to the Expression of Uncertainty in Measurement
International Practical Temperature Scale of 1968
International System of Quantities
International Temperature Scale of 1990
International Units
System of units based on the three mechanical units meter, kilogram, andsecondFour-dimensional system of units based on the meter, kilogram, second,
and the ampere
International System of Units
International Atomic Time
Geocentric Coordinated Time
Terrestrial Time
Coordinated Universal Time
Vienna Standard Mean Ocean Water

118

Indexcarbon, 11, 26, 65, 94, 103, 114, 115
Celsius temperature, 10, 15, 32, 40, 41
cesium frequency, 5, 6, 7, 103, 104, 108
CGS, 50, 110clinical chemistry, 11, 77
CODATA, 26, 92, 94, 98, 103, 117
coherent derived units, 9, 14, 16, 17, 18,78, 109
continuity, xii, 4Coordinated Universal Time (UTC), 39,
65, 66
coulomb (C), 4, 15, 18, 48, 51, 56, 91,
92, 102
counting quantities, 14
curie (Ci), 42, 59

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absolute units, 113
absorbed dose, 15, 18, 19, 20, 42, 66, 68,
71, 80, 81
acceleration due to gravity, standard
value of (gn), 46, 108
activity referred to a radionuclide, 15, 16
amount of substance, 5, 6, 10, 11, 13, 17,34, 65, 83, 91, 92, 98, 104, 109, 111,
114, 115
ampere (A), 2, 4, 6, 8, 9, 19, 40, 48, 51,
52, 55, 56, 77, 87, 88, 89, 90, 91, 92,
93, 95, 98, 101, 102, 104, 107, 109,
110, 111, 113
angle, 14, 15, 16, 25, 26, 32, 34, 35, 47,
56, 69arcsecond, 26
astronomical unit, 25
atomic weight, 83
Avogadro constant, 4, 5, 10, 11, 88, 91,
92, 98, 102, 104, 111, 114, 115
Avogadro number, 10, 104Ddalton (Da), 25, 26
day (d), 25
decibel (dB), 25, 27
decimal marker, 32, 42, 81, 82
decimal metric system, 110
defining constants, 1, 2, 3, 4, 5, 6, 7, 8,
9, 12, 14, 101, 103, 108, 111
definitions, 6
definitions of base units, 5, 6, 8, 12
degree Celsius ○C, 10, 15, 16, 20, 30,
32, 41, 49, 51
derived quantity, 15, 17, 18
derived unit(s), 1, 2, 5, 9, 14, 16, 17, 18,30, 38, 42, 56, 62, 63, 69, 76, 77, 109,
110, 111
digits in groups of three, grouping digits,32
dimension (of a quantity), 13
dimensionless quantities, 69
dose equivalent, see sievert dynamic
viscosity (poise), 15, 80
dyne (dyn), 51

Bbar, 51
Base quantity, 6, 13
base units, 1, 2, 5, 6, 14, 15, 16, 17, 18,
52, 53, 55, 63, 69, 76, 77, 78, 87, 88,
90, 92, 93, 95, 101, 102, 103, 107,
109, 110, 111, 112
becquerel (Bq), 15, 16, 19, 42, 66
bel (B), 25, 27
Boltzmann constant, 3, 4, 5, 9, 88, 91,
92, 98, 102, 104, 108, 111, 114
British Association for the Advancementof Science (BAAS), 110Ccalorie, 49, 51
candela (cd), 2, 4, 6, 11, 12, 20, 41, 51,
52, 55, 56, 61, 62, 67, 77, 87, 90, 92,
93, 94, 102, 103, 104, 107, 109, 111,
115

E
electric current, 6, 8, 13, 19, 48, 52, 55,
92, 98, 104, 107, 108, 109, 110, 113
electrical units, 40, 72, 90, 110
119International Temperature Scale of 1990
(ITS-90), 10, 75
International Units (IU) WHO, 20
ionizing radiation, 19, 20, 66, 68, 71, 80
ISO/IEC 80000 series, 2, 5, 30
ISO/TC 12, 69
IUPAC, 83, 111, 114
Green Book, 30
IUPAP SUNAMCO
Red Book, 30

electron mass, 109
electronvolt (eV), 25, 26
elementary charge, 3, 4, 5, 8, 90, 91, 92,
98, 102, 104, 111, 113
erg., 51
establishment of the SI, xi, 38
explicit constant definition, 108
explicit unit definition, 107
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F
farad (F), 15, 18, 48, 51, 56
fine structure constant, 109foot, 27
Formatting the value of a quantity, 32
fundamental constants (of physics), 4,
79, 88, 91, 95, 101, 111

J
Josephson constant (KJ, KJ-90), 40, 73,
93, 103
Josephson effect, 72, 73
joule (J), 4, 5, 15, 16, 18, 19, 48, 49, 56,
62, 66, 68, 91, 92, 102GK

gal (Gal), 26
Gauss, 110
general relativity, 78
Giorgi, 110gram, 24, 39, 51, 59, 110
gram-atom, gram-molecule, 114
gray (Gy), 15, 18, 19, 42, 66, 71, 81

katal (kat), 15, 18, 41, 77
kelvin (K), 1, 4, 5, 6, 9, 10, 16, 18, 19,
41, 60, 61, 62, 83, 86, 87, 88, 89, 90,
91, 92, 93, 95, 98, 101, 102, 104, 107,108, 109, 111, 114
Kibble balance, 108
kibibyte (kilobyte), 23
kilogram, 1, 4, 6, 7, 8, 9, 11, 14, 18, 19,
24, 39, 45, 46, 47, 52, 55, 56, 59, 62,
65, 66, 68, 71, 76, 77, 80, 81, 87, 88,
89, 90, 91, 92, 93, 95, 98, 101, 102,
104, 107, 108, 109, 110, 111, 112,
113, 115
kinematic viscosity (stokes), 56

H
Hall effect (incl. quantum Hall effect),72, 74heat capacity, 18, 19, 30, 62
hectare (ha), 25, 26
henry (H), 9, 15, 18, 48, 51, 56
hertz (Hz), 4, 15, 16, 19, 51, 56, 92, 102
Historical notes, 107hour (h), 25, 51
hyperfine splitting of the cesium atom,
91, 93L
legislation on units, 2
length, 6, 7, 13, 25, 38, 47, 52, 55, 90,
93, 98, 104, 107, 108, 109, 110, 112
logarithmic ratio quantities, 27
lumen (lm), 4, 15, 20, 51, 56, 92, 102
new lumen, 41, 47
luminous efficacy, 4, 5, 11, 67, 92, 93,
102, 104, 111, 115
luminous intensity, 6, 11, 12, 13, 47, 52,
55, 61, 62, 67, 93, 98, 104, 109, 111,
115
lux (lx), 15, 20, 51, 56

Iinch, 27
International Atomic Time (TAI), 63,
64, 66
international prototype of the kilogram,
8, 46, 87, 90, 93, 94, 102, 103, 112international prototype of the meter, 54International System of Units (SI), v, 39,
40, 41, 76, 77, 79, 81, 87, 90, 101
120

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MO

magnetic constant, permeability of
vacuum, 9, 94, 113
mandatory symbols for units, 30
mass, 6, 7, 8, 13, 25, 39, 45, 46, 52, 55,
59, 76, 77, 88, 90, 91, 92, 93, 94, 98,
102, 103, 104, 107, 108, 109, 110,
112, 113, 115
mass and weight, 39
Maxwell, 110
mesopic, 67
meter, 2, 4, 6
meter (m), 2, 7, 8, 9, 11, 38, 39, 40, 45,
47, 51, 52, 54, 55, 65, 70, 71, 78, 79,
84, 85, 86, 89, 90, 92, 93, 94, 95, 96,
99, 102, 104, 107, 108, 109, 110, 111,
112, 113
Meter Convention, iv, v, vii, xi, 1, 45,
50, 53, 109, 110
metric system, iii, v, xi, 26, 46, 107, 111
metric ton, 25, 26, 51
microarcsecond (μas), 26
milliarcsecond (mas), 26
minute (min), 25, 32
MKS system, 50, 110
MKSA system, 111
molar mass, 11, 94, 103, 114
mole (mol), 4, 5, 6, 10, 11, 41, 65, 77,
87, 88, 89, 90, 91, 92, 94, 95, 98, 101,
102, 103, 104, 107, 109, 111, 114, 115
molecular weight, 114
multiples (and submultiples) of thekilogram, 24, 59
multiples, prefixes for, 14, 16, 23, 55,
59, 63, 66, 75, 110

ohm (fi), 15, 40, 48, 51, 56, 63, 72, 73,
74, 93, 103, 110, 113
OIML, 2, 95, 99
Ppascal (Pa), 15, 18, 63
percent, 34
photobiological quantities, 20, 106
photometric quantities, 67
photometric units, 41, 47, 61
photopic vision, 67
Planck constant, xi, 3, 4, 5, 7, 8, 26, 88,
90, 91, 92, 98, 102, 104, 108, 111, 113
poise (P), 51
ppb, 34
ppm, 34
ppt, 34
practical units, 110
prefixes, 14, 16, 23, 25, 26, 29, 34, 37,
38, 39, 42, 55, 59, 63, 66, 75, 109,
110, 111
Q
quantity, 3
quantity calculus, 30, 31
quantity symbols, 29, 31, 33
quantity, base, 13, 14, 69, 109
quantity, derived, 11, 13, 16, 19
quantum Hall effect, 72, 74, 90, 93, 103
quantum standard, 113
R
radian (rad), 14, 15, 16, 18, 19, 34, 56,
69, 76
realization of a unit, 4, 12, 20, 65, 67,
70, 71, 78, 79, 83, 84, 85, 87, 89, 95,
96, 99, 105, 107, 108, 109, 113
recommended symbols for quantities, 30
relativity, 7, 20, 21, 79
Rydberg constant, 109

Nneper (Np), 25, 27
new candle, 41, 42, 47, 51, 62, 67, 115
newton (N), 9, 15, 18, 19, 46, 48, 51, 56,
63
non-SI units, 25, 27, 32
numerical value of a quantity, 30

Sscotopic, 67
second (s), 4, 6, 7, 8, 9, 11, 12, 25, 29,
32, 39, 40, 51, 52, 53, 54, 55, 58, 59,
60, 63, 64, 84, 85, 86, 89, 92, 93, 94,121thermodynamic temperature scale, 52Thomson, 110
time (duration), 6, 13, 25, 39, 52, 53, 54,
55, 59, 60, 64, 93, 98, 103, 109, 110,112
tonne, 26, 51
triple point of water, 1, 9, 40, 41, 49, 52,
61, 83, 86, 94, 103, 107, 108, 114

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95, 96, 97, 99, 100, 102, 103, 104,
107, 108, 109, 110, 111, 112
SI prefixes, 16, 23, 25, 26, 34, 42, 59,
63, 66, 75
SI, see Système international d’Unités,
1, 38, 50, 53, 55, 58, 59, 60, 62, 63,
64, 65, 66, 68, 76, 109
siemens (S), 15, 40, 63
sievert (Sv), 15, 16, 19, 20, 42, 68, 71,
72, 80, 81
silicon sphere, 108
sound, units for, 20
special names and symbols for units, 15,
16, 18, 19
speed of light in vacuum, 3, 4, 5, 7, 78,
90, 91, 92, 93, 102, 104, 111
standard atmosphere, 41, 52
steradian (sr), 12, 14, 15, 16, 34, 35, 47,
56, 69, 76
stilb (sb), 51
submultiples, prefixes for, 23, 55, 59, 63,
75
supplementary units, 38, 42, 63, 69, 76,
109, 111

U
uncertainty, 4, 33
unit names, 30, 42
unit symbols, 29
Vvalue of a quantity, 3, 30, 31, 32, 33, 82
volt (V), 15, 40, 48, 51, 56, 72, 73, 74,
93, 103, 110, 113
von Klitzing constant (RK, RK-90), 40, 74,
93, 103W
water, isotopic composition, 41, 83, 87,
90, 114
watt (W), 4, 15, 48, 51, 56, 92, 102
Weber, 110
weber (Wb), 15, 48, 56
WHO, 20T
tesla (T), 15, 56
thermodynamic temperature, 6, 9, 10,
13, 41, 52, 55, 60, 61, 75, 83, 86, 92,
94, 98, 103, 104, 108, 109, 111, 114
Thermodynamic temperature, 40

Yyard, 27122