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Ref. No.: IS0 / R 31 / Part I - 1965 (E)
IS0
I NT ERN AT I O NA L O RG AN IZAT 1 O N FO R STA N D AR D I Z AT I O N
IS0 R ECOM MENDATI ON
R 31
PART I
BASIC QUANTITIES AND UNITS OF THE SI
2nd EDITION
December 1965
This second edition supersedes the first edition.
COPYRIGHT RESERVED
The copyright of IS0 Recommendations and IS0 Standards
belongs to IS0 Member Bodies. Reproduction of these
documents, in any country, may be authorized therefore only
by the nationa!, standards organization of that country, being
a member of ISO.
For .each individual country the only valid standard is the national standard of that country.
Printed in Denmark
Also issued in French and Russian. Copies to be obtained through the national standards organizations.
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Brief History
The Technical Committee ISO/TC 12, Quanfities, Unifs, Symbols, Conversion Factors and Con-
oersion Tables, mas formed by the IS0 for the purpose of arriving at an agreement on units and
symbols for quantities and units (and mathematical symbols) used within the different fields
of science and technology, giving, where necessary, definitions of these quantities and units.
The Committee was also instructed to establish conversion factors between the various units
and to draw up conversion tables based on these factors.
The Danish Standards Association was commissioned by the IS0 to act as Secretatiat of the
ISO/TC 12.
The Secretariat of the Technical Committee prepared four successive proposals which were
considered by the Committee, by correspondence and at three meetings, held in Copenhagen
in 1952, 1953 and 1955.
The fourth proposal (document ISO/TC 12 (Secretariat-51) 131) was circulated in Ja-
nuary 1955 and adopted by the Technical Committee, by correspondence and at the meeting
in June 1955, as Draft IS0 Recommendation.
It should be noted that the following international organizations received the various pro-
posals and participated in the discussions of the Technical Committee at its three meetings:
Comité International des Poids et Mesures,
International Electrotechnical Commission,
International Union of Pure and Applied Physics,
International Union of Pure and Applied Chemistry,
Comité International Provisoire de Métrologie Légale.
The Draft IS0 Recommendation was submitted on 25th November 1955 to all the IS0 Mem-
ber Bodies (37 at that time), and approval was obtained by a majority.
The following 27 Member Bodies approved the Draft:
Australia India Roumania
Israel
Sustria Spain
Belgium Italy Sweden
Bulgaria Japan Switzerland
Czechoslovakia Netherlands Turkey
Denmark Norway Union of South Africa
France Pakistan United Kingdom
Germany Poland U.S.A.
Portugal Yugoslavia
Hungary
The following 3 Member Bodies stated that they had no objection to the Draft being approved:
Greece
Ireland
Mexico
The U.S.S.R. failed to approve the Draft because of objections of principle to its form.
Finland failed to approve the Draft because of objections to certain items.
The Secretariat of ISO/TC 12 made some editorial amendments in the Draft in compliance
with comments made by various Member Bodies.
The revised Draft was submitted to the IS0 Council Members who, in November 1956,
decided, by correspondance, to accept it as an IS0 RECOMMENDATION.
Brief history relating to 2nd edition
When drafting some of the other parts of IS0 Recommendation ISO/R 31, the Secretariat of
Technical Committee ISO/TC 12 found it necessary to modify points 1-1.1, 1-2.1, 1-8.1 and
1-9.1 in Part I of this IS0 Recommendation and to delete point 1-7.1.
iz Draft Revision, drawn up accordingly, was adopted by the Technical Committee in 1960.
In September of the same year, this Draft was circulated to all the IS0 Member Bodies and
was approved by 27 votes to one (Belgium). These modifications were not submitted imme-
diately to the Council for publication as it was considered preferable to prepare a new, com-
plete edition of Part I incorporating the new definitions adopted by the Conférence Générale
des Poids et Mesures concerning the metre (1960) and the litre (1964), as well as the new defi-
nition of the yard adopted by the USA (1959) and the United Kingdom (1963).
The Draft Revision of IS0 Recommendation R/31, Part I, thus completed, was then sub-
mitted by correspondence to the IS0 Council which decided, in December 1965, to accept it.
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Introduction
General remarks
This document, containing the tables:
O. Basic units of the International System of Units
1. Quantities and units of space and time,
is the first part of a more comprehensive publication dealing also with quantities and units within the
fields of
Periodic and related Phenomena
Mechanics
Heat
Electricity and Magnetism
Light and related Electromagnetic Radiations
Acoustics
Physical Chemistry and Molecular Physics
Atomic and Nuclear Physics
Nuclear Reactions and Ionizing Radiations
and also
Mathematical Signs and Symbols to be
-
used in Physical Sciences and Technology.
v
The purpose of this series of documents is to give recommendations for standardization and also to give
information, e.g. on the conversion from units in common use (but not always recommended) to
recommended units.
Arrangement of the tables
Table O contains the basic quantities and units of the International System of Units together with the
corresponding international symbols and definitions of the units.
Table 1 is divided into a left-hand side and a right-hand side.
The left-hand side contains the most important quantities of space and time, together with their
symbols and in some cases their definitions. The definitions are given merely for identification; they
are not intended to be complete definitions. For length, time and various other quantities that are
identical with elementary concepts of daily life, no definition is given. The vectorial or tensorial cha-
racter of certain quantities is not dealt with.
The right-hand side contains the units for the quantities together with their international symbols
(or, in certain cases, abbreviations for their names), and their definitions. Where several units are
given for one and the same quantity they are arranged in the following order:
L-
SI units (units of the International System of Units)
CGS units
Technical units (metre, kilogramme-force, second units)')
Other metric units
FPS units (foot, pound, second units)
British technical units (foot, pound-force, second units)
Other units.
The SI units are placed first.
The SI units and their decimal multiples and submultiples are particularly recommended.
Decimal multiples and submultiples of units are usually not included except when they have a special
name (e.g. in the case of are, tonne, Angstrom etc.).
') This name refers to the system derived from the metre, the second and the force which gives to a mass of 1 kg an acceleration
of 9.80665 m/se. The name is not intended to indicate that this system is specially recommended for technical (or other) pur-
poses.
-1-
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Symbols for Quantities
These symbols are to be printed in italic (sloping) type. Where several symbols are given for one
quantity, and no special distinction is made, they are on an equal footing, for instance a, B, y. . . etc.
for plane angle. If one symbol is used in certain fields and another symbol is used in others, a remark
is inserted in the column “Kcmarks”, for instance the symbols Y and f for frequency. When a pre-
ferred symbol and a reserve symbol are given, the reserve symbol is in parentheses.
Capital letters may be used as variants for small letters, and vice versa, if no ambiguity is to be feared.
For example, instead of di and cl, for internal and external diameter, it is permissible to write d and U.
Symbols for Units
Where international symbols for units exist these are given in the appropriate column of the table.
These symbols should be strictly observed. They should be printed in roman (upright) type, should
remain unaltered in the plural, and should be written without a final full stop (period).
Where symbols for units are combined in a product this process of combination may be indicated by
a dot in the following manner: N-m
Other ways of indicating this are: N m, N.m
Where symbols for units are combined in a quotient this process of combination may be indicated
by a solidus in the following manner: kg/m3
./
kg
Other ways of indicating this are: - kg m-3, kg.m-3, kg.m-3
m3 ’
In no case should more than one solidus be included in such a combination unless parentheses be
inserted to avoid all ambiguity. In complicated cases, it is recommended that negative powers or
parentheses should be used.
Abbreviations for Names of Units
In cases where no internationally adopted symbols exist for a unit, an abbreviation for the name
of the unit is in general given in the column where the name of the unit is found. This abbreviation
is given to facilitate the presentation of the table. It relates to the name of the unit in the language
used. Its presence does not imply that the abbreviation is accepted internationally. These abbrevi-
ations are printed in roman (upright) type. They are in most cases followed by a full stop, but this
is not an invariable rule.
Sometimes, even when an international symbol for the unit exists, an abbreviation for the name
of the unit is also given for information. In most cases, the information is given in the “Remarks”
column.
Number of figures in numerical statements
All numbers in the column “Definition” are exact.
In the column “Conversion factors” some of the conversion factors on which the calculation of others is
based are printed in heavy type. These are normally given in 7 significant figures. When they are
exact and contain 7 or fewer figures the word “exactly” is added, but when they can be terminated
after more than 7 figures they may be given in full. If the conversion factors are derived from esperi-
ment they are given to the precision justified by the accuracy of the experiments. Generally, this
means that in such cases the last digit only is in doubt. When, however, experiment justifies more
than 7 figures, the factor is usually rounded off to 7 significant figures.
The other conversion factors are printed in ordinary type. They are given to not more than 6 signifi-
cant figures; if they are exactly knoLvn and contain 6 or fewer figures the word “exactly” is added.
Numbers in the column “Remarlts” are given to a precision appropriate to the particular case.
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O. Basic Units of the International System of Units1)
I
~
Name of unit i International
Quantity Definition of unit Remarks
i 1 symbols
No.
i
i
1 I
'm The metre is the unit of length For details, see page 12
i metre
defined under that name by the
~ length
Conférence Générale des Poids
et Mesures.
_____~_______ -
The kilogramme is the unit of For details, see page 12
mass defined under that name
by the Conférence GBnérale des
Poids et Mesures.
I
0-3 1 time IS The second is the unit of time
second
defined under that name by For details, see page 12
the Conférence Générale des
Poids et Mesures.
I
The ampere is the unit of electric For details, see page 12
0-4 1 electric current l ampere h
current defined under that name
by the Conférence Générale des
Poids et Mesures.
The degree Kelvin is the unit For details, see page 13
0-5 thermodynamic degree Kelvin! OK
of thermodynamic temperature
defined under that name by the For further information about
I
I temperature
Conférence Générale des Poids temperature units and scales, see
also Part IV: Heat.
et Mesures.
For details, see page 13
The candela is the unit of lumi-
nous intensitydefined underthat
name by the Conférence Géné-
rale des Poids et Mesures.
I
I) The 11th Conférence Générale des Poids et Mesures (1960) adopted Resolution 12 as follows:
"La Onzième Conférence Générale des Poids et Mesures,
considérant
la résolution 6 de la Dixième Conférence Générale des Poids et Mesures par laquelle elle a adopté les six unités devant servir
de base à l'établissement d'un système pratique de mesure pour les relations internationales:
longueur mètre m
masse kilogramme kg
temps seconde S
intensité de courant Blectrique ampere A
température thermodynamique degré Kelvin "K
intensite lumineuse candela cd
..........................................................................
décide:
1" le système fondé sur les six unités de base ci-dessus est désigné sous le nom de Système International d'Unités;
2" l'abréviation internationale du nom de ce système est: SI
..........................................................................
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1. Space and Time
Quant it ies
1-1.1 . . .1-3.7
I l
l
Quantity Definition') Remarks
I
The angle between two half-lines ter- i In this definition, which is generally
1-1.1 1 angle (plane angle)
minating at the same point is defined as 1 used in the physical sciences and tech-
the ratio of the arc cut out on a circle ~ nology, angle is defined as a dirnension-
(with its centre at that point) to the ~ less quantity.
radius of the circle.
~ ~~~ __ -~ ~~
___~
The solid angle of a cone is defined as In this definition, which is generally
1-2.1 1 solid angle 1 R, 0
used in the physical sciences and tech-
the ratio of the area cut out on a sphe-
its centre at the apex nology, solid angle is defined as a di-
rical surface (with
mensionless quantity.
of that cone) to the square of the
of the sphere.
radius
i
-
__ ~
1-3.1 length I
b
1-3.2 breadth
1-3.3 height h
1-3.4 thickness
d, d
1-3.5 radius r
1-3.6 diameter d
P
1-3.7 length of path
1) The statements in this column are given merely for identification and they are not intended to be complete definitions.
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