The BIPM and the Metre Convention 95
Preface to the 8th edition
1 Introduction
1.1 Quantities and units 103
1.2 The International System of Units (SI) and the corresponding
system of quantities
1.3 Dimensions of quantities
1.4 Coherent units, derived units with special names, and the SI prefixes
1.5 SI units in the framework of general relativity
1.6 Units for quantities that describe biological effects
1.7 Legislation on units
1.8 Historical note
2 SI units
2.1 SI base units
2.1.1 Definitions
2.1.1.1 Unit of length (metre
2.1.1.2 Unit of mass (kilogram)
2.1.1.3 Unit of time (second) 2.1.1.4 Unit of electric current (ampere) 2.1.1.5 Unit of thermodynamic temperature (kelvin)
2.1.1.6 Unit of amount of substance (mole)
2.1.1.7 Unit of luminous intensity (candela) 2.1.2 Symbols for the seven base units
2.2 SI derived units 2.2.1 Derived units expressed in terms of base units
2.2.2 Units with special names and symbols; units that incorporate
special names and symbols 2.2.3 Units for dimensionless quantities, also called
quantities of dimension one
3 Decimal multiples and submultiples of SI units
3.1 SI prefixes
3.2 The kilogram
Preface
to the 8th edition
We have pleasure in introducing the 8th edition of this publication, commonly called
the SI Brochure, which defines and presents the Système International d’Unités, the
SI (known in English as the International System of Units). This Brochure is
published as a hard copy, and is also available in electronic form at
Since 1970, the Bureau International des Poids et Mesures, the BIPM (known in
English as the International Bureau of Weights and Measures), has published seven
previous editions of this document. Its main purpose is to define and promote the SI,
which has been used around the world as the preferred language of science and
technology since its adoption in 1948 through a Resolution of the 9th Conférence
Générale des Poids et Mesures, the CGPM (known in English as the General
Conference on Weights and Measures).
The SI is, of course, a living system which evolves, and which reflects current best
measurement practice. This 8th edition therefore contains a number of changes since
the previous edition. As before, it lists the definitions of all the base units, and all the
Resolutions and Recommendations of the Conférence Générale des Poids et Mesures
and the Comité International des Poids et Mesures, the CIPM (known in English as
the International Committee for Weights and Measures), relating to the International
System of Units. Formal reference to CGPM and CIPM decisions are to be found in
the successive volumes of the Comptes Rendus of the CGPM (CR) and the Procès-
Verbaux of the CIPM (PV); many of these are also listed in Metrologia. To simplify
practical use of the system, the text provides explanations of these decisions, and the
first chapter provides a general introduction to establishing a system of units and to
the SI in particular. The definitions and the practical realizations of all the units are
also considered in the context of general relativity. A brief discussion of units
associated with biological quantities has been introduced for the first time.
Appendix 1 reproduces, in chronological order, all 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 exists only in the electronic version, which is available at. It outlines the practical realization of
some important units, consistent with the definitions given in the principal text,
which metrological laboratories can make to realize physical units and to calibrate
material standards and measuring instruments of the highest quality. This appendix
will be updated regularly to reflect improvements in the experimental techniques for
realizing the units.
Appendix 3 presents units used to measure actinic effects in biological materials.
Coherent units, derived units with special names,
and the SI prefixes
Derived units are defined as products of powers of the base units. When the product
of powers includes no numerical factor other than one, the derived units are called
coherent derived units. The base and coherent derived units of the SI form a coherent
set, designated the set of coherent SI units. The word coherent is used here in the
following sense: when coherent units are used, equations between the numerical
values of quantities take exactly the same form as the equations between the
quantities themselves. Thus if only units from a coherent set are used, conversion
factors between units are never required.
The expression for the coherent unit of a derived quantity may be obtained from the
dimensional product of that quantity by replacing the symbol for each dimension by
the symbol of the corresponding base unit.
Some of the coherent derived units in the SI are given special names, to simplify their
expression (see 2.2.2, p. 118). It is important to emphasize that each physical quantity
has only one coherent SI unit, even if this unit can be expressed in different forms by
using some of the special names and symbols. The inverse, however, is not true: in
some cases the same SI unit can be used to express the values of several different
quantities (see p. 119).
The CGPM has, in addition, adopted a series of prefixes for use in forming the
decimal multiples and submultiples of the coherent SI units (see 3.1, p. 121, where
the prefix names and symbols are listed). These are convenient for expressing the
values of quantities that are much larger than or much smaller than the coherent unit.
Following the CIPM Recommendation 1 (1969) (see p. 155) these are given the name
SI Prefixes. (These prefixes are also sometimes used with other non-SI units, as
described in Chapter 4 below.) However when prefixes are used with SI units, the
resulting units are no longer coherent, because a prefix on a derived unit effectively
introduces a numerical factor in the expression for the derived unit in terms of the
base units.
As an exception, the name of the kilogram, which is the base unit of mass, includes
the prefix kilo, for historical reasons. It is nonetheless taken to be a base unit of the SI.
The multiples and submultiples of the kilogram are formed by attaching prefix names
to the unit name “gram”, and prefix symbols to the unit symbol “g” (see 3.2, p. 122).
Thus 10−6 kg is written as a milligram, mg, not as a microkilogram, μkg.
The complete set of SI units, including both the coherent set and the multiples and
submultiples of these units formed by combining them with the SI prefixes, are
designated as the complete set of SI units, or simply the SI units, or the units of the SI.
Note, however, that the decimal multiples and submultiples of the SI units do no
Appendix 1. Decisions of the CGPM and the CIPM
This appendix lists those decisions of the CGPM and the CIPM that bear directly
upon definitions of the units of the SI, prefixes defined for use as part of the SI, and
conventions for the writing of unit symbols and numbers. It is not a complete list of
CGPM and CIPM decisions. For a complete list, reference must be made to
successive volumes of the Comptes Rendus des Séances de la Conférence Générale
des Poids et Mesures (CR) and Procès-Verbaux des Séances du Comité International
des Poids et Mesures (PV) or, for recent decisions, to Metrologia.
Since the SI is not a static convention, but evolves following developments in the
science of measurement, some decisions have been abrogated or modified; others
have been clarified by additions. Decisions that have been subject to such changes are
identified by an asterisk (*) and are linked by a note to the modifying decision.
The original text of each decision (or its translation) is shown in a different font (sans
serif) of normal weight to distinguish it from the main text. The asterisks and notes
were added by the BIPM to make the text more understandable. They do not form
part of the original text.
The decisions of the CGPM and CIPM are listed in this appendix in strict
chronological order, from 1889 to 2005, 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 of contents is included below, ordered by subject, with
page references to the particular meetings at which decisions relating to each subject
were taken.
Measurement of photochemical or photobiological quantities
and their corresponding units
The photometric quantities and photometric units which are used at present for vision
are well established and have been widely used for a long time. They are not affected
by the following rules. For all other photochemical and photobiological quantities the
following rules shall be applied for defining the units to be used.
A photochemical or photobiological quantity is defined in purely physical terms as
the quantity derived from the corresponding radiant quantity by evaluating the
radiation according to its action upon a selective receptor, the spectral sensitivity of
which is defined by the actinic action spectrum of the photochemical or
photobiological effect considered. The quantity is given by the integral over
wavelength of the spectral distribution of the radiant quantity weighted by the
appropriate actinic action spectrum. The use of integrals implicitly assumes a law of
arithmetic additivity for actinic quantities, although such a law is not perfectly
obeyed by actual actinic effects. The action spectrum is a relative quantity; it is
dimensionless, with the SI unit one. The radiant quantity has the radiometric unit
corresponding to that quantity. Thus, following the rule for obtaining the SI unit for a
derived quantity, the unit of the photochemical or photobiological quantity is the
radiometric unit of the corresponding radiant quantity. When giving a quantitative
value, it is essential to specify whether a radiometric or actinic quantity is intended as
the unit is the same. If an actinic effect exists in several action spectra, the action
spectrum used for measurement has to be clearly specified.
This method of defining the units to be used for photochemical or photobiological
quantities has been recommended by the Consultative Committee for Photometry and
Radiometry at its 9th meeting in 1977.
As an example, the erythemal effective irradiance Eer from a source of ultraviolet
radiation is obtained by weighting the spectral irradiance of the radiation at
wavelength λ by the effectiveness of radiation at this wavelength to cause an
erythema, and summing over all wavelengths present in the source spectrum. This
can be expressed mathematically as:
Eer E ser( )d λ = ∫ λ λ
where Eλ is the spectral irradiance at wavelength λ (usually reported in the SI unit
W m−2 nm−1), and ser(λ) is the actinic spectrum normalized to 1 at its maximum
spectral value. The erythemal irradiance Eer determined in this way is usually quoted
in the SI unit W m−2.
List of acronyms
used in the present volume
Acronyms for laboratories, committees and conferences*
BAAS British Association for the Advancement of Science
BIH Bureau International de l’Heure
BIPM International Bureau of Weights and Measures/Bureau International des
Poids et Mesures
CARICOM Carribean Community
CCAUV Consultative Committee for Acoustics, Ultrasound and Vibration/
Comité Consultatif de l’Acoustique, des Ultrasons et des Vibrations
CCDS* Consultative Committee for the Definition of the Second/
Comité Consultatif pour la Définition de la Seconde, see CCTF
CCE* Consultative Committee for Electricity/Comité Consultatif d'Électricité,
see CCEM
CCEM (formerly the CCE) Consultative Committee for Electricity and
Magnetism/Comité Consultatif d'Électricité et Magnétisme
CCL Consultative Committee for Length/Comité Consultatif des Longueurs
CCM Consultative Committee for Mass and Related Quantities/
Comité Consultatif pour la Masse et les Grandeurs Apparentées
CCPR Consultative Committee for Photometry and Radiometry/
Comité Consultatif de Photométrie et Radiométrie
CCQM Consultative Committee for Amount of Substance: Metrology in
Chemistry/Comité Consultatif pour la Quantité de Matière : Métrologie
en Chimie
CCRI Consultative Committee for Ionizing Radiation/Comité Consultatif des
Rayonnements Ionisants
CCT Consultative Committee for Thermometry/Comité Consultatif de
Thermométrie
CCTF (formerly the CCDS) Consultative Committee for Time and Frequency/
Comité Consultatif du Temps et des Fréquences
CCU Consultative Committee for Units/Comité Consultatif des Unités
CGPM General Conference on Weights and Measures/Conférence Générale des
Poids et Mesures
CIE International Commission on Illumination/Commission Internationale
de l’Éclairage
CIPM International Committee for Weights and Measures/
Comité International des Poids et Mesures
CODATA Committee on Data for Science and Technology
CR Comptes Rendus of the Conférence Générale des Poids et Mesures,
CGPM
IAU International Astronomical Union
ICRP International Commission on Radiological Protection
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