ISO 80000-1:2009
(Main)Quantities and units — Part 1: General
Quantities and units — Part 1: General
ISO 80000-1:2009 gives general information and definitions concerning quantities, systems of quantities, units, quantity and unit symbols, and coherent unit systems, especially the International System of Quantities, ISQ, and the International System of Units, SI. The principles laid down in ISO 80000-1:2009 are intended for general use within the various fields of science and technology and as an introduction to other parts of the Quantities and units series. Ordinal quantities and nominal properties are outside the scope of ISO 80000-1:2009.
Grandeurs et unités — Partie 1: Généralités
L'ISO 80000‑1:2009 donne des informations générales et des définitions à propos des grandeurs, des systèmes de grandeurs, des unités, des symboles de grandeurs et d'unités, et des systèmes cohérents d'unités, notamment le Système international de grandeurs (ISQ) et le Système international d'unités (SI). Les principes établis dans l'ISO 80000‑1:2009 sont prévus pour un usage général dans les divers domaines scientifiques et techniques, ainsi qu'en introduction aux autres parties de la présente Norme internationale. Les grandeurs ordinales et les propriétés qualitatives sont hors du domaine d'application de l'ISO 80000‑1:2009.
Veličine in enote - 1. del: Splošno
Standard ISO 80000-1 podaja splošne informacije in definicije v zvezi z veličinami, sistemi veličin, enotami, simboli za veličine in enote ter skladne sisteme enot, zlasti mednarodni sistem veličin (ISQ) in mednarodni sistem enot (SI). Načela, opisana v standardu ISO 80000-1, so namenjena za splošno uporabo na različnih področjih znanosti in tehnike ter kot uvod v druge dele tega mednarodnega standarda. Vrstilne veličine in nominalne lastnosti ne spadajo na področje uporabe standarda ISO 80000-1.
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SLOVENSKI STANDARD
SIST ISO 80000-1:2013
01-maj-2013
1DGRPHãþD
SIST ISO 1000+A1:2008
SIST ISO 31-0+A1+A2:2007
9HOLþLQHLQHQRWHGHO 6SORãQR
Quantities and units - Part 1: General
Grandeurs et unités - Partie 1: Généralités
Ta slovenski standard je istoveten z: ISO 80000-1:2009
ICS:
01.060 9HOLþLQHLQHQRWH Quantities and units
SIST ISO 80000-1:2013 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST ISO 80000-1:2013
INTERNATIONAL ISO
STANDARD 80000-1
First edition
2009-11-15
Quantities and units
Part 1:
General
Grandeurs et unités
Partie 1: Généralités
Reference number
ISO 80000-1:2009(E)
©
ISO 2009
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SIST ISO 80000-1:2013
ISO 80000-1:2009(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
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accepts no liability in this area.
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Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
COPYRIGHT PROTECTED DOCUMENT
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All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
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Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
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SIST ISO 80000-1:2013
ISO 80000-1:2009(E)
Contents Page
Foreword .iv
Introduction.vi
1 Scope.1
2 Normative references.1
3 Terms and definitions .1
4 Quantities .11
5 Dimensions .14
6 Units.14
7 Printing rules .22
Annex A (normative) Terms in names for physical quantities.31
Annex B (normative) Rounding of numbers .35
Annex C (normative) Logarithmic quantities and their units .37
Annex D (informative) International organizations in the field of quantities and units.39
Bibliography.41
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Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of ISO 80000-1 may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 80000-1 was prepared by Technical Committee ISO/TC 12, Quantities and units in co-operation with
IEC/TC 25, Quantities and units.
This first edition of ISO 80000-1 cancels and replaces ISO 31-0:1992 and ISO 1000:1992. It also incorporates
the Amendments ISO 31-0:1992/Amd.1:1998, ISO 31-0:1992/Amd.2:2005 and ISO 1000:1992/Amd.1:1998.
The major technical changes from the previous standard are the following:
⎯ the structure has been changed to emphasize that quantities come first and units then follow;
⎯ definitions in accordance with ISO/IEC Guide 99:2007 have been added;
⎯ Annexes A and B have become normative;
⎯ a new normative Annex C has been added.
ISO 80000 consists of the following parts, under the general title Quantities and units:
⎯ Part 1: General
⎯ Part 2: Mathematical signs and symbols to be used in the natural sciences and technology
⎯ Part 3: Space and time
⎯ Part 4: Mechanics
⎯ Part 5: Thermodynamics
⎯ Part 7: Light
⎯ Part 8: Acoustics
⎯ Part 9: Physical chemistry and molecular physics
⎯ Part 10: Atomic and nuclear physics
⎯ Part 11: Characteristic numbers
⎯ Part 12: Solid state physics
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IEC 80000 consists of the following parts, under the general title Quantities and units:
⎯ Part 6: Electromagnetism
⎯ Part 13: Information science and technology
⎯ Part 14: Telebiometrics related to human physiology
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Introduction
0.1 Quantities
Systems of quantities and systems of units can be treated in many consistent, but different, ways. Which
treatment to use is only a matter of convention. The presentation given in this International Standard is the
one that is the basis for the International System of Units, the SI (from the French: Système international
d’unités), adopted by the General Conference on Weights and Measures, the CGPM (from the French:
Conférence générale des poids et mesures).
The quantities and relations among the quantities used here are those almost universally accepted for use
throughout the physical sciences. They are presented in the majority of scientific textbooks today and are
familiar to all scientists and technologists.
1)
NOTE For electric and magnetic units in the CGS-ESU, CGS-EMU and Gaussian systems, there is a difference in
the systems of quantities by which they are defined. In the CGS-ESU system, the electric constant ε (the permittivity of
0
vacuum) is defined to be equal to 1, i.e. of dimension one; in the CGS-EMU system, the magnetic constant µ
0
(permeability of vacuum) is defined to be equal to 1, i.e. of dimension one, in contrast to those quantities in the ISQ where
they are not of dimension one. The Gaussian system is related to the CGS-ESU and CGS-EMU systems and there are
similar complications. In mechanics, Newton’s law of motion in its general form is written F = c⋅ma. In the old technical
2)
system, MKS , c = 1/g , where g is the standard acceleration of free fall; in the ISQ, c = 1.
n n
The quantities and the relations among them are essentially infinite in number and are continually evolving as
new fields of science and technology are developed. Thus, it is not possible to list all these quantities and
relations in this International Standard; instead, a selection of the more commonly used quantities and the
relations among them is presented.
It is inevitable that some readers working in particular specialized fields may find that the quantities they are
interested in using may not be listed in this International Standard or in another International Standard.
However, provided that they can relate their quantities to more familiar examples that are listed, this will not
prevent them from defining units for their quantities.
Most of the units used to express values of quantities of interest were developed and used long before the
concept of a system of quantities was developed. Nonetheless, the relations among the quantities, which are
simply the equations of the physical sciences, are important, because in any system of units the relations
among the units play an important role and are developed from the relations among the corresponding
quantities.
The system of quantities, including the relations among them the quantities used as the basis of the units of
the SI, is named the International System of Quantities, denoted “ISQ”, in all languages. This name was not
used in ISO 31, from which the present harmonized series has evolved. However, ISQ does appear in
[8]
ISO/IEC Guide 99:2007 and in the SI Brochure , Edition 8:2006. In both cases, this was to ensure
consistency with the new Quantities and units series that was under preparation at the time they were
published; it had already been announced that the new term would be used. It should be realized, however,
that ISQ is simply a convenient notation to assign to the essentially infinite and continually evolving and
expanding system of quantities and equations on which all of modern science and technology rests. ISQ is a
shorthand notation for the “system of quantities on which the SI is based”, which was the phrase used for this
system in ISO 31.
1) CGS = centimetre-gram-second; ESU = electrostatic units; EMU = electromagnetic units.
2) MKS = metre-kilogram-second.
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0.2 Units
A system of units is developed by first defining a set of base units for a small set of corresponding base
quantities and then defining derived units as products of powers of the base units corresponding to the
relations defining the derived quantities in terms of the base quantities. In this International Standard and in
the SI, there are seven base quantities and seven base units. The base quantities are length, mass, time,
electric current, thermodynamic temperature, amount of substance, and luminous intensity. The
corresponding base units are the metre, kilogram, second, ampere, kelvin, mole, and candela, respectively.
The definitions of these base units, and their practical realization, are at the heart of the SI and are the
responsibility of the advisory committees of the International Committee for Weights and Measures, the CIPM
(from the French: Comité international des poids et mesures). The current definitions of the base units, and
[8]
advice for their practical realization, are presented in the SI Brochure , published by and obtainable from the
International Bureau of Weights and Measures, the BIPM (from the French: Bureau international des poids et
mesures). Note that in contrast to the base units, each of which has a specific definition, the base quantities
are simply chosen by convention and no attempt is made to define them otherwise then operationally.
0.3 Realizing the values of units
To realize the value of a unit is to use the definition of the unit to make measurements that compare the value
of some quantity of the same kind as the unit with the value of the unit. This is the essential step in making
measurements of the value of any quantity in science. Realizing the values of the base units is of particular
importance. Realizing the values of derived units follows in principle from realizing the base units.
There may be many different ways for the practical realization of the value of a unit, and new methods may be
developed as science advances. Any method consistent with the laws of physics could be used to realize any
SI unit. Nonetheless, it is often helpful to review experimental methods for realizing the units, and the CIPM
recommends such methods, which are presented as part of the SI Brochure.
0.4 Arrangement of the tables
In parts 3 to 14 of this International Standard, the quantities and relations among them, which are a subset of
the ISQ, are given on the left-hand pages, and the units of the SI (and some other units) are given on the
right-hand pages. Some additional quantities and units are also given on the left-hand and right-hand pages,
respectively. The item numbers of quantities are written pp-nn.s (pp, part number; nn, running number in the
part, respectively; s, sub-number). The item numbers of units are written pp-nn.l (pp, part number; nn, running
number in the part, respectively; l, sub-letter).
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INTERNATIONAL STANDARD ISO 80000-1:2009(E)
Quantities and units
Part 1:
General
1 Scope
ISO 80000-1 gives general information and definitions concerning quantities, systems of quantities, units,
quantity and unit symbols, and coherent unit systems, especially the International System of Quantities, ISQ,
and the International System of Units, SI.
The principles laid down in ISO 80000-1 are intended for general use within the various fields of science and
technology, and as an introduction to other parts of this International Standard.
Ordinal quantities and nominal properties are outside the scope of ISO 80000-1.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO/IEC Guide 99:2007, International vocabulary of metrology — Basic and general concepts and associated
terms (VIM)
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
NOTE The content in this clause is essentially the same as in ISO/IEC Guide 99:2007. Some notes and examples
are modified.
3.1
quantity
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed by
means of a number and a reference
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NOTE 1 The generic concept ‘quantity’ can be divided into several levels of specific concepts, as shown in the
following table. The left hand side of the table shows specific concepts under ‘quantity’. These are generic concepts for the
individual quantities in the right hand column.
length, l radius, r radius of circle A, r or r(A)
A
wavelength, λ wavelength of the sodium D radiation, λ or λ(Na; D)
D
energy, E kinetic energy, T kinetic energy of particle i in a given system, T
i
heat, Q heat of vaporization of sample i of water, Q
i
electric charge, Q electric charge of the proton, e
electric resistance, R electric resistance of resistor i in a given circuit, R
i
amount-of-substance concentration of amount-of-substance concentration of ethanol in wine sample
entity B, c i, c (C H OH)
B i 2 5
number concentration of entity B, C number concentration of erythrocytes in blood sample i,
B
C(Erys; B )
i
Rockwell C hardness of steel sample i, HRC (150 kg)
Rockwell C hardness (150 kg load),
i
HRC(150 kg)
NOTE 2 A reference can be a measurement unit, a measurement procedure, a reference material, or a combination of
such. For magnitude of a quantity, see 3.19.
NOTE 3 Symbols for quantities are given in the ISO 80000 and IEC 80000 series, Quantities and units. The symbols
for quantities are written in italics. A given symbol can indicate different quantities.
NOTE 4 A quantity as defined here is a scalar. However, a vector or a tensor, the components of which are quantities,
is also considered to be a quantity.
NOTE 5 The concept ’quantity’ may be generically divided into, e.g. ‘physical quantity’, ‘chemical quantity’, and
‘biological quantity’, or ‘base quantity’ and ‘derived quantity’.
NOTE 6 Adapted from ISO/IEC Guide 99:2007, definition 1.1, in which there is an additional note.
3.2
kind of quantity
aspect common to mutually comparable quantities
NOTE 1 Kind of quantity is often shortened to “kind”, e.g. in quantities of the same kind.
NOTE 2 The division of the concept ‘quantity’ into several kinds is to some extent arbitrary.
EXAMPLE 1 The quantities diameter, circumference, and wavelength are generally considered to be quantities of
the same kind, namely, of the kind of quantity called length.
EXAMPLE 2 The quantities heat, kinetic energy, and potential energy are generally considered to be quantities of
the same kind, namely, of the kind of quantity called energy.
NOTE 3 Quantities of the same kind within a given system of quantities have the same quantity dimension. However,
quantities of the same dimension are not necessarily of the same kind.
EXAMPLE The quantities moment of force and energy are, by convention, not regarded as being of the same kind,
although they have the same dimension. Similarly for heat capacity and entropy, as well as for number of entities,
relative permeability, and mass fraction.
NOTE 4 In English, the terms for quantities in the left half of the table in 3.1, Note 1, are often used for the
corresponding ‘kinds of quantity’. In French, the term “nature” is only used in expressions such as “grandeurs de même
nature” (in English, “quantities of the same kind”).
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NOTE 5 Adapted from ISO/IEC Guide 99:2007, definition 1.2, in which “kind” appears as an admitted term. Note 1 has
been added.
3.3
system of quantities
set of quantities together with a set of non-contradictory equations relating those quantities
NOTE 1 Ordinal quantities (see 3.26), such as Rockwell C hardness, and nominal properties (see 3.30), such as colour
of light, are usually not considered to be part of a system of quantities because they are related to other quantities through
empirical relations only.
NOTE 2 Adapted from ISO/IEC Guide 99:2007, definition 1.3, in which Note 1 is different.
3.4
base quantity
quantity in a conventionally chosen subset of a given system of quantities, where no quantity in the subset can
be expressed in terms of the other quantities within that subset
NOTE 1 The subset mentioned in the definition is termed the “set of base quantities”.
EXAMPLE The set of base quantities in the International System of Quantities (ISQ) is given in 3.6.
NOTE 2 Base quantities are referred to as being mutually independent since a base quantity cannot be expressed as a
product of powers of the other base quantities.
NOTE 3 ‘Number of entities’ can be regarded as a base quantity in any system of quantities.
NOTE 4 Adapted from ISO/IEC Guide 99:2007, definition 1.4, in which the definition is slightly different.
3.5
derived quantity
quantity, in a system of quantities, defined in terms of the base quantities of that system
EXAMPLE In a system of quantities having the base quantities length and mass, mass density is a derived quantity
defined as the quotient of mass and volume (length to the power three).
NOTE Adapted from ISO/IEC Guide 99:2007, definition 1.5, in which the example is slightly different.
3.6
International System of Quantities
ISQ
system of quantities based on the seven base quantities: length, mass, time, electric current, thermodynamic
temperature, amount of substance, and luminous intensity
NOTE 1 This system of quantities is published in the ISO 80000 and IEC 80000 series Quantities and units, Parts 3 to
14.
NOTE 2 The International System of Units (SI) (see item 3.16) is based on the ISQ.
NOTE 3 Adapted from ISO/IEC Guide 99:2007, definition 1.6, in which Note 1 is different.
3.7
quantity dimension
dimension of a quantity
dimension
expression of the dependence of a quantity on the base quantities of a system of quantities as a product of
powers of factors corresponding to the base quantities, omitting any numerical factor
−2
EXAMPLE 1 In the ISQ, the quantity dimension of force is denoted by dim F = LMT .
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−3
EXAMPLE 2 In the same system of quantities, dim ρ = ML is the quantity dimension of mass concentration of
B
−3
component B, and ML is also the quantity dimension of mass density, ρ.
EXAMPLE 3 The period, T, of a particle pendulum of length l at a place with the local acceleration of free fall g is
l 2π
T=π2 or TC= ()g l where Cg() =
g
g
−1/2
Hence dim (Cg)=⋅T L .
NOTE 1 A power of a factor is the factor raised to an exponent. Each factor is the dimension of a base quantity.
NOTE 2 The conventional symbolic representation of the dimension of a base quantity is a single upper case letter in
roman (upright) type. The conventional symbolic representation of the dimension of a derived quantity is the product of
powers of the dimensions of the base quantities according to the definition of the derived quantity. The dimension of a
quantity Q is denoted by dim Q.
NOTE 3 In deriving the dimension of a quantity, no account is taken of its scalar, vector, or tensor character.
NOTE 4 In a given system of quantities,
⎯ quantities of the same kind have the same quantity dimension,
⎯ quantities of different quantity dimensions are always of different kinds, and
⎯ quantities having the same quantity dimension are not necessarily of the same kind.
NOTE 5 Symbols representing the dimensions of the base quantities in the ISQ are:
Base quantity Symbol for dimension
length L
mass M
time T
electric current I
thermodynamic temperature Θ
amount of substance N
luminous intensity J
α β γ δ ε ζ η
Thus, the dimension of a quantity Q is denoted by dim Q = L M T I Θ N J where the exponents, named dimensional
exponents, are positive, negative, or zero. Factors with exponent zero and the exponent 1 are usually omitted. When all
exponents are zero, see 3.8.
NOTE 6 Adapted from ISO/IEC Guide 99:2007, definition 1.7, in which Note 5 and Examples 2 and 3 are different and
in which “dimension of a quantity” and “dimension” are given as admitted terms.
3.8
quantity of dimension one
dimensionless quantity
quantity for which all the exponents of the factors corresponding to the base quantities in its quantity
dimension are zero
NOTE 1 The term “dimensionless quantity” is commonly used and is kept here for historical reasons. It stems from the
fact that all exponents are zero in the symbolic representation of the dimension for such quantities. The term “quantity of
dimension one” reflects the convention in which the symbolic representation of the dimension for such quantities is the
symbol 1, see Clause 5. This dimension is not a number, but the neutral element for multiplication of dimensions.
NOTE 2 The measurement units and values of quantities of dimension one are numbers, but such quantities convey
more information than a number.
NOTE 3 Some quantities of dimension one are defined as the ratios of two quantities of the same kind. The coherent
derived unit is the number one, symbol 1.
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EXAMPLE Plane angle, solid angle, refractive index, relative permeability, mass fraction, friction factor, Mach
number.
NOTE 4 Numbers of entities are quantities of dimension one.
EXAMPLE Number of turns in a coil, number of molecules in a given sample, degeneracy of the energy levels of a
quantum system.
NOTE 5 Adapted from ISO/IEC Guide 99:2007, definition 1.8, in which Notes 1 and 3 are different and in which
“dimensionless quantity” is given as an admitted term.
3.9
unit of measurement
measurement unit
unit
real scalar quantity, defined and adopted by convention, with which any other quantity of the same kind can
be compared to express the ratio of the second quantity to the first one as a number
NOTE 1 Measurement units are designated by conventionally assigned names and symbols.
NOTE 2 Measurement units of quantities of the same quantity dimension may be designated by the same name and
symbol even when the quantities are not of the same kind. For example, joule per kelvin and J/K are respectively the
name and symbol of both a measurement unit of heat capacity and a measurement unit of entropy, which are generally
not considered to be quantities of the same kind. However, in some cases special measurement unit names are restricted
to be used with quantities of specific kind only. For example, the measurement unit ‘second to the power minus one’ (1/s)
is called hertz (Hz) when used for frequencies and becquerel (Bq) when used for activities of radionuclides. As another
example, the joule (J) is used as a unit of energy, but never as a unit of moment of force, i.e. the newton metre (N · m).
NOTE 3 Measurement units of quantities of dimension one are numbers. In some cases, these measurement units are
given special names, e.g. radian, steradian, and decibel, or are expressed by quotients such as millimole per mole equal
−3 −9
to 10 and microgram per kilogram equal to 10 .
NOTE 4 For a given quantity, the short term “unit” is often combined with the quantity name, such as “mass unit” or
“unit of mass”.
NOTE 5 Adapted from ISO/IEC Guide 99:2007, definition 1.9, in which the definition and Note 2 are slightly different
and in which “measurement unit” and “unit” are given as admitted terms.
3.10
base unit
measurement unit that is adopted by convention for a base quantity
NOTE 1 In each coherent system of units, there is only one base unit for each base quantity.
EXAMPLE In the SI, the metre is the base unit of length. In the CGS systems, the centimetre is the base unit of
length.
NOTE 2 A base unit may also serve for a derived quantity of the same quantity dimension.
EXAMPLE The derived quantity rainfall, when defined as areic volume (volume per area), has the metre as a
coherent derived unit in the SI.
NOTE 3 For number of entities, the number one, symbol 1, can be regarded as a base unit in any system of units.
Compare Note 3 in 3.4.
NOTE 4 Adapted from ISO/IEC Guide 99:2007, definition 1.10, in which the example in Note 2 is slightly different. The
last sentence in Note 3 has been added.
3.11
derived unit
measurement unit for a derived quantity
EXAMPLE The metre per second, symbol m/s, and the centimetre per second, symbol cm/s, are derived units of
speed in the SI. The kilometre per hour, symbol km/h, is a measurement unit of speed outside the SI but accepted for use
with the SI. The knot, equal to one nautical mile per hour, is a measurement unit of speed outside the SI.
[ISO/IEC Guide 99:2007, 1.11]
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3.12
coherent derived unit
derived unit that, for a given system of quantities and for a chosen set of base units, is a product of powers of
base units with no other proportionality factor than one
NOTE 1 A power of a base unit is the base unit raised to an exponent.
NOTE 2 Coherence can be determined only with respect to a particular system of quantities and a given set of base
units.
EXAMPLE If the metre, the second, and the mole are base units, the metre per second is the coherent derived unit
of velocity when velocity is defined by the quantity equation v = dr/dt and the mole per cubic metre is the coherent
derived unit of am
...
INTERNATIONAL ISO
STANDARD 80000-1
First edition
2009-11-15
Quantities and units
Part 1:
General
Grandeurs et unités
Partie 1: Généralités
Reference number
ISO 80000-1:2009(E)
©
ISO 2009
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ISO 80000-1:2009(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
COPYRIGHT PROTECTED DOCUMENT
© ISO 2009
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2009 – All rights reserved
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ISO 80000-1:2009(E)
Contents Page
Foreword .iv
Introduction.vi
1 Scope.1
2 Normative references.1
3 Terms and definitions .1
4 Quantities .11
5 Dimensions .14
6 Units.14
7 Printing rules .22
Annex A (normative) Terms in names for physical quantities.31
Annex B (normative) Rounding of numbers .35
Annex C (normative) Logarithmic quantities and their units .37
Annex D (informative) International organizations in the field of quantities and units.39
Bibliography.41
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ISO 80000-1:2009(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of ISO 80000-1 may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 80000-1 was prepared by Technical Committee ISO/TC 12, Quantities and units in co-operation with
IEC/TC 25, Quantities and units.
This first edition of ISO 80000-1 cancels and replaces ISO 31-0:1992 and ISO 1000:1992. It also incorporates
the Amendments ISO 31-0:1992/Amd.1:1998, ISO 31-0:1992/Amd.2:2005 and ISO 1000:1992/Amd.1:1998.
The major technical changes from the previous standard are the following:
⎯ the structure has been changed to emphasize that quantities come first and units then follow;
⎯ definitions in accordance with ISO/IEC Guide 99:2007 have been added;
⎯ Annexes A and B have become normative;
⎯ a new normative Annex C has been added.
ISO 80000 consists of the following parts, under the general title Quantities and units:
⎯ Part 1: General
⎯ Part 2: Mathematical signs and symbols to be used in the natural sciences and technology
⎯ Part 3: Space and time
⎯ Part 4: Mechanics
⎯ Part 5: Thermodynamics
⎯ Part 7: Light
⎯ Part 8: Acoustics
⎯ Part 9: Physical chemistry and molecular physics
⎯ Part 10: Atomic and nuclear physics
⎯ Part 11: Characteristic numbers
⎯ Part 12: Solid state physics
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ISO 80000-1:2009(E)
IEC 80000 consists of the following parts, under the general title Quantities and units:
⎯ Part 6: Electromagnetism
⎯ Part 13: Information science and technology
⎯ Part 14: Telebiometrics related to human physiology
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ISO 80000-1:2009(E)
Introduction
0.1 Quantities
Systems of quantities and systems of units can be treated in many consistent, but different, ways. Which
treatment to use is only a matter of convention. The presentation given in this International Standard is the
one that is the basis for the International System of Units, the SI (from the French: Système international
d’unités), adopted by the General Conference on Weights and Measures, the CGPM (from the French:
Conférence générale des poids et mesures).
The quantities and relations among the quantities used here are those almost universally accepted for use
throughout the physical sciences. They are presented in the majority of scientific textbooks today and are
familiar to all scientists and technologists.
1)
NOTE For electric and magnetic units in the CGS-ESU, CGS-EMU and Gaussian systems, there is a difference in
the systems of quantities by which they are defined. In the CGS-ESU system, the electric constant ε (the permittivity of
0
vacuum) is defined to be equal to 1, i.e. of dimension one; in the CGS-EMU system, the magnetic constant µ
0
(permeability of vacuum) is defined to be equal to 1, i.e. of dimension one, in contrast to those quantities in the ISQ where
they are not of dimension one. The Gaussian system is related to the CGS-ESU and CGS-EMU systems and there are
similar complications. In mechanics, Newton’s law of motion in its general form is written F = c⋅ma. In the old technical
2)
system, MKS , c = 1/g , where g is the standard acceleration of free fall; in the ISQ, c = 1.
n n
The quantities and the relations among them are essentially infinite in number and are continually evolving as
new fields of science and technology are developed. Thus, it is not possible to list all these quantities and
relations in this International Standard; instead, a selection of the more commonly used quantities and the
relations among them is presented.
It is inevitable that some readers working in particular specialized fields may find that the quantities they are
interested in using may not be listed in this International Standard or in another International Standard.
However, provided that they can relate their quantities to more familiar examples that are listed, this will not
prevent them from defining units for their quantities.
Most of the units used to express values of quantities of interest were developed and used long before the
concept of a system of quantities was developed. Nonetheless, the relations among the quantities, which are
simply the equations of the physical sciences, are important, because in any system of units the relations
among the units play an important role and are developed from the relations among the corresponding
quantities.
The system of quantities, including the relations among them the quantities used as the basis of the units of
the SI, is named the International System of Quantities, denoted “ISQ”, in all languages. This name was not
used in ISO 31, from which the present harmonized series has evolved. However, ISQ does appear in
[8]
ISO/IEC Guide 99:2007 and in the SI Brochure , Edition 8:2006. In both cases, this was to ensure
consistency with the new Quantities and units series that was under preparation at the time they were
published; it had already been announced that the new term would be used. It should be realized, however,
that ISQ is simply a convenient notation to assign to the essentially infinite and continually evolving and
expanding system of quantities and equations on which all of modern science and technology rests. ISQ is a
shorthand notation for the “system of quantities on which the SI is based”, which was the phrase used for this
system in ISO 31.
1) CGS = centimetre-gram-second; ESU = electrostatic units; EMU = electromagnetic units.
2) MKS = metre-kilogram-second.
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ISO 80000-1:2009(E)
0.2 Units
A system of units is developed by first defining a set of base units for a small set of corresponding base
quantities and then defining derived units as products of powers of the base units corresponding to the
relations defining the derived quantities in terms of the base quantities. In this International Standard and in
the SI, there are seven base quantities and seven base units. The base quantities are length, mass, time,
electric current, thermodynamic temperature, amount of substance, and luminous intensity. The
corresponding base units are the metre, kilogram, second, ampere, kelvin, mole, and candela, respectively.
The definitions of these base units, and their practical realization, are at the heart of the SI and are the
responsibility of the advisory committees of the International Committee for Weights and Measures, the CIPM
(from the French: Comité international des poids et mesures). The current definitions of the base units, and
[8]
advice for their practical realization, are presented in the SI Brochure , published by and obtainable from the
International Bureau of Weights and Measures, the BIPM (from the French: Bureau international des poids et
mesures). Note that in contrast to the base units, each of which has a specific definition, the base quantities
are simply chosen by convention and no attempt is made to define them otherwise then operationally.
0.3 Realizing the values of units
To realize the value of a unit is to use the definition of the unit to make measurements that compare the value
of some quantity of the same kind as the unit with the value of the unit. This is the essential step in making
measurements of the value of any quantity in science. Realizing the values of the base units is of particular
importance. Realizing the values of derived units follows in principle from realizing the base units.
There may be many different ways for the practical realization of the value of a unit, and new methods may be
developed as science advances. Any method consistent with the laws of physics could be used to realize any
SI unit. Nonetheless, it is often helpful to review experimental methods for realizing the units, and the CIPM
recommends such methods, which are presented as part of the SI Brochure.
0.4 Arrangement of the tables
In parts 3 to 14 of this International Standard, the quantities and relations among them, which are a subset of
the ISQ, are given on the left-hand pages, and the units of the SI (and some other units) are given on the
right-hand pages. Some additional quantities and units are also given on the left-hand and right-hand pages,
respectively. The item numbers of quantities are written pp-nn.s (pp, part number; nn, running number in the
part, respectively; s, sub-number). The item numbers of units are written pp-nn.l (pp, part number; nn, running
number in the part, respectively; l, sub-letter).
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INTERNATIONAL STANDARD ISO 80000-1:2009(E)
Quantities and units
Part 1:
General
1 Scope
ISO 80000-1 gives general information and definitions concerning quantities, systems of quantities, units,
quantity and unit symbols, and coherent unit systems, especially the International System of Quantities, ISQ,
and the International System of Units, SI.
The principles laid down in ISO 80000-1 are intended for general use within the various fields of science and
technology, and as an introduction to other parts of this International Standard.
Ordinal quantities and nominal properties are outside the scope of ISO 80000-1.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO/IEC Guide 99:2007, International vocabulary of metrology — Basic and general concepts and associated
terms (VIM)
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
NOTE The content in this clause is essentially the same as in ISO/IEC Guide 99:2007. Some notes and examples
are modified.
3.1
quantity
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed by
means of a number and a reference
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ISO 80000-1:2009(E)
NOTE 1 The generic concept ‘quantity’ can be divided into several levels of specific concepts, as shown in the
following table. The left hand side of the table shows specific concepts under ‘quantity’. These are generic concepts for the
individual quantities in the right hand column.
length, l radius, r radius of circle A, r or r(A)
A
wavelength, λ wavelength of the sodium D radiation, λ or λ(Na; D)
D
energy, E kinetic energy, T kinetic energy of particle i in a given system, T
i
heat, Q heat of vaporization of sample i of water, Q
i
electric charge, Q electric charge of the proton, e
electric resistance, R electric resistance of resistor i in a given circuit, R
i
amount-of-substance concentration of amount-of-substance concentration of ethanol in wine sample
entity B, c i, c (C H OH)
B i 2 5
number concentration of entity B, C number concentration of erythrocytes in blood sample i,
B
C(Erys; B )
i
Rockwell C hardness of steel sample i, HRC (150 kg)
Rockwell C hardness (150 kg load),
i
HRC(150 kg)
NOTE 2 A reference can be a measurement unit, a measurement procedure, a reference material, or a combination of
such. For magnitude of a quantity, see 3.19.
NOTE 3 Symbols for quantities are given in the ISO 80000 and IEC 80000 series, Quantities and units. The symbols
for quantities are written in italics. A given symbol can indicate different quantities.
NOTE 4 A quantity as defined here is a scalar. However, a vector or a tensor, the components of which are quantities,
is also considered to be a quantity.
NOTE 5 The concept ’quantity’ may be generically divided into, e.g. ‘physical quantity’, ‘chemical quantity’, and
‘biological quantity’, or ‘base quantity’ and ‘derived quantity’.
NOTE 6 Adapted from ISO/IEC Guide 99:2007, definition 1.1, in which there is an additional note.
3.2
kind of quantity
aspect common to mutually comparable quantities
NOTE 1 Kind of quantity is often shortened to “kind”, e.g. in quantities of the same kind.
NOTE 2 The division of the concept ‘quantity’ into several kinds is to some extent arbitrary.
EXAMPLE 1 The quantities diameter, circumference, and wavelength are generally considered to be quantities of
the same kind, namely, of the kind of quantity called length.
EXAMPLE 2 The quantities heat, kinetic energy, and potential energy are generally considered to be quantities of
the same kind, namely, of the kind of quantity called energy.
NOTE 3 Quantities of the same kind within a given system of quantities have the same quantity dimension. However,
quantities of the same dimension are not necessarily of the same kind.
EXAMPLE The quantities moment of force and energy are, by convention, not regarded as being of the same kind,
although they have the same dimension. Similarly for heat capacity and entropy, as well as for number of entities,
relative permeability, and mass fraction.
NOTE 4 In English, the terms for quantities in the left half of the table in 3.1, Note 1, are often used for the
corresponding ‘kinds of quantity’. In French, the term “nature” is only used in expressions such as “grandeurs de même
nature” (in English, “quantities of the same kind”).
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ISO 80000-1:2009(E)
NOTE 5 Adapted from ISO/IEC Guide 99:2007, definition 1.2, in which “kind” appears as an admitted term. Note 1 has
been added.
3.3
system of quantities
set of quantities together with a set of non-contradictory equations relating those quantities
NOTE 1 Ordinal quantities (see 3.26), such as Rockwell C hardness, and nominal properties (see 3.30), such as colour
of light, are usually not considered to be part of a system of quantities because they are related to other quantities through
empirical relations only.
NOTE 2 Adapted from ISO/IEC Guide 99:2007, definition 1.3, in which Note 1 is different.
3.4
base quantity
quantity in a conventionally chosen subset of a given system of quantities, where no quantity in the subset can
be expressed in terms of the other quantities within that subset
NOTE 1 The subset mentioned in the definition is termed the “set of base quantities”.
EXAMPLE The set of base quantities in the International System of Quantities (ISQ) is given in 3.6.
NOTE 2 Base quantities are referred to as being mutually independent since a base quantity cannot be expressed as a
product of powers of the other base quantities.
NOTE 3 ‘Number of entities’ can be regarded as a base quantity in any system of quantities.
NOTE 4 Adapted from ISO/IEC Guide 99:2007, definition 1.4, in which the definition is slightly different.
3.5
derived quantity
quantity, in a system of quantities, defined in terms of the base quantities of that system
EXAMPLE In a system of quantities having the base quantities length and mass, mass density is a derived quantity
defined as the quotient of mass and volume (length to the power three).
NOTE Adapted from ISO/IEC Guide 99:2007, definition 1.5, in which the example is slightly different.
3.6
International System of Quantities
ISQ
system of quantities based on the seven base quantities: length, mass, time, electric current, thermodynamic
temperature, amount of substance, and luminous intensity
NOTE 1 This system of quantities is published in the ISO 80000 and IEC 80000 series Quantities and units, Parts 3 to
14.
NOTE 2 The International System of Units (SI) (see item 3.16) is based on the ISQ.
NOTE 3 Adapted from ISO/IEC Guide 99:2007, definition 1.6, in which Note 1 is different.
3.7
quantity dimension
dimension of a quantity
dimension
expression of the dependence of a quantity on the base quantities of a system of quantities as a product of
powers of factors corresponding to the base quantities, omitting any numerical factor
−2
EXAMPLE 1 In the ISQ, the quantity dimension of force is denoted by dim F = LMT .
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ISO 80000-1:2009(E)
−3
EXAMPLE 2 In the same system of quantities, dim ρ = ML is the quantity dimension of mass concentration of
B
−3
component B, and ML is also the quantity dimension of mass density, ρ.
EXAMPLE 3 The period, T, of a particle pendulum of length l at a place with the local acceleration of free fall g is
l 2π
T=π2 or TC= ()g l where Cg() =
g
g
−1/2
Hence dim (Cg)=⋅T L .
NOTE 1 A power of a factor is the factor raised to an exponent. Each factor is the dimension of a base quantity.
NOTE 2 The conventional symbolic representation of the dimension of a base quantity is a single upper case letter in
roman (upright) type. The conventional symbolic representation of the dimension of a derived quantity is the product of
powers of the dimensions of the base quantities according to the definition of the derived quantity. The dimension of a
quantity Q is denoted by dim Q.
NOTE 3 In deriving the dimension of a quantity, no account is taken of its scalar, vector, or tensor character.
NOTE 4 In a given system of quantities,
⎯ quantities of the same kind have the same quantity dimension,
⎯ quantities of different quantity dimensions are always of different kinds, and
⎯ quantities having the same quantity dimension are not necessarily of the same kind.
NOTE 5 Symbols representing the dimensions of the base quantities in the ISQ are:
Base quantity Symbol for dimension
length L
mass M
time T
electric current I
thermodynamic temperature Θ
amount of substance N
luminous intensity J
α β γ δ ε ζ η
Thus, the dimension of a quantity Q is denoted by dim Q = L M T I Θ N J where the exponents, named dimensional
exponents, are positive, negative, or zero. Factors with exponent zero and the exponent 1 are usually omitted. When all
exponents are zero, see 3.8.
NOTE 6 Adapted from ISO/IEC Guide 99:2007, definition 1.7, in which Note 5 and Examples 2 and 3 are different and
in which “dimension of a quantity” and “dimension” are given as admitted terms.
3.8
quantity of dimension one
dimensionless quantity
quantity for which all the exponents of the factors corresponding to the base quantities in its quantity
dimension are zero
NOTE 1 The term “dimensionless quantity” is commonly used and is kept here for historical reasons. It stems from the
fact that all exponents are zero in the symbolic representation of the dimension for such quantities. The term “quantity of
dimension one” reflects the convention in which the symbolic representation of the dimension for such quantities is the
symbol 1, see Clause 5. This dimension is not a number, but the neutral element for multiplication of dimensions.
NOTE 2 The measurement units and values of quantities of dimension one are numbers, but such quantities convey
more information than a number.
NOTE 3 Some quantities of dimension one are defined as the ratios of two quantities of the same kind. The coherent
derived unit is the number one, symbol 1.
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ISO 80000-1:2009(E)
EXAMPLE Plane angle, solid angle, refractive index, relative permeability, mass fraction, friction factor, Mach
number.
NOTE 4 Numbers of entities are quantities of dimension one.
EXAMPLE Number of turns in a coil, number of molecules in a given sample, degeneracy of the energy levels of a
quantum system.
NOTE 5 Adapted from ISO/IEC Guide 99:2007, definition 1.8, in which Notes 1 and 3 are different and in which
“dimensionless quantity” is given as an admitted term.
3.9
unit of measurement
measurement unit
unit
real scalar quantity, defined and adopted by convention, with which any other quantity of the same kind can
be compared to express the ratio of the second quantity to the first one as a number
NOTE 1 Measurement units are designated by conventionally assigned names and symbols.
NOTE 2 Measurement units of quantities of the same quantity dimension may be designated by the same name and
symbol even when the quantities are not of the same kind. For example, joule per kelvin and J/K are respectively the
name and symbol of both a measurement unit of heat capacity and a measurement unit of entropy, which are generally
not considered to be quantities of the same kind. However, in some cases special measurement unit names are restricted
to be used with quantities of specific kind only. For example, the measurement unit ‘second to the power minus one’ (1/s)
is called hertz (Hz) when used for frequencies and becquerel (Bq) when used for activities of radionuclides. As another
example, the joule (J) is used as a unit of energy, but never as a unit of moment of force, i.e. the newton metre (N · m).
NOTE 3 Measurement units of quantities of dimension one are numbers. In some cases, these measurement units are
given special names, e.g. radian, steradian, and decibel, or are expressed by quotients such as millimole per mole equal
−3 −9
to 10 and microgram per kilogram equal to 10 .
NOTE 4 For a given quantity, the short term “unit” is often combined with the quantity name, such as “mass unit” or
“unit of mass”.
NOTE 5 Adapted from ISO/IEC Guide 99:2007, definition 1.9, in which the definition and Note 2 are slightly different
and in which “measurement unit” and “unit” are given as admitted terms.
3.10
base unit
measurement unit that is adopted by convention for a base quantity
NOTE 1 In each coherent system of units, there is only one base unit for each base quantity.
EXAMPLE In the SI, the metre is the base unit of length. In the CGS systems, the centimetre is the base unit of
length.
NOTE 2 A base unit may also serve for a derived quantity of the same quantity dimension.
EXAMPLE The derived quantity rainfall, when defined as areic volume (volume per area), has the metre as a
coherent derived unit in the SI.
NOTE 3 For number of entities, the number one, symbol 1, can be regarded as a base unit in any system of units.
Compare Note 3 in 3.4.
NOTE 4 Adapted from ISO/IEC Guide 99:2007, definition 1.10, in which the example in Note 2 is slightly different. The
last sentence in Note 3 has been added.
3.11
derived unit
measurement unit for a derived quantity
EXAMPLE The metre per second, symbol m/s, and the centimetre per second, symbol cm/s, are derived units of
speed in the SI. The kilometre per hour, symbol km/h, is a measurement unit of speed outside the SI but accepted for use
with the SI. The knot, equal to one nautical mile per hour, is a measurement unit of speed outside the SI.
[ISO/IEC Guide 99:2007, 1.11]
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ISO 80000-1:2009(E)
3.12
coherent derived unit
derived unit that, for a given system of quantities and for a chosen set of base units, is a product of powers of
base units with no other proportionality factor than one
NOTE 1 A power of a base unit is the base unit raised to an exponent.
NOTE 2 Coherence can be determined only with respect to a particular system of quantities and a given set of base
units.
EXAMPLE If the metre, the second, and the mole are base units, the metre per second is the coherent derived unit
of velocity when velocity is defined by the quantity equation v = dr/dt and the mole per cubic metre is the coherent
derived unit of amount-of-substance concentration when amount-of-substance concentration is defined by the
quantity equation c = n/V. The kilometre per hour and the knot, given as examples of derived units in 3.11, are not
coherent derived units in such a system of quantities.
NOTE 3 A derived unit can be coherent with respect to one system of quantities but not to another.
EXAMPLE The centimetre per second is the coherent derived unit of speed in a CGS system of units but is not a
coherent derived unit in the SI.
NOTE 4 The coherent derived unit for every derived quantity of dimension one in a given system of units is the number
one, symbol 1. The name and symbol of the measurement unit one are generally not indicated.
[ISO/IEC Guide 99:2007, 1.12]
3.13
system of units
set of base units and derived units, together with their multiples and submultiples, defined in accordance with
given rules, for a given system of quantities
[ISO/IEC Guide 99:2007, 1.13]
3.14
coherent system of units
system of u
...
NORME ISO
INTERNATIONALE 80000-1
Première édition
2009-11-15
Grandeurs et unités —
Partie 1:
Généralités
Quantities and units —
Part 1: General
Numéro de référence
ISO 80000-1:2009(F)
©
ISO 2009
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ISO 80000-1:2009(F)
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ISO 80000-1:2009(F)
Sommaire Page
Avant-propos .iv
Introduction.vi
1 Domaine d'application .1
2 Références normatives.1
3 Termes et définitions .1
4 Grandeurs.12
5 Dimensions .14
6 Unités.15
7 Règles d'impression.24
Annexe A (normative) Termes dans les noms des grandeurs physiques .33
Annexe B (normative) Arrondissage des nombres.38
Annexe C (normative) Grandeurs logarithmiques et leurs unités.40
Annexe D (informative) Organisations internationales dans le domaine des grandeurs et unités.42
Bibliographie.44
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ISO 80000-1:2009(F)
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes nationaux de
normalisation (comités membres de l'ISO). L'élaboration des Normes internationales est en général confiée
aux comités techniques de l'ISO. Chaque comité membre intéressé par une étude a le droit de faire partie du
comité technique créé à cet effet. Les organisations internationales, gouvernementales et non
gouvernementales, en liaison avec l'ISO participent également aux travaux. L'ISO collabore étroitement avec
la Commission électrotechnique internationale (CEI) en ce qui concerne la normalisation électrotechnique.
Les Normes internationales sont rédigées conformément aux règles données dans les Directives ISO/CEI,
Partie 2.
La tâche principale des comités techniques est d'élaborer les Normes internationales. Les projets de Normes
internationales adoptés par les comités techniques sont soumis aux comités membres pour vote. Leur
publication comme Normes internationales requiert l'approbation de 75 % au moins des comités membres
votants.
L'attention est appelée sur le fait que certains des éléments du présent document peuvent faire l'objet de
droits de propriété intellectuelle ou de droits analogues. L'ISO ne saurait être tenue pour responsable de ne
pas avoir identifié de tels droits de propriété et averti de leur existence.
L'ISO 80000-1 a été élaborée par le comité technique ISO/TC 12, Grandeurs et unités, en coopération avec la
CEI/CE 25, Grandeurs et unités.
Cette première édition de l'ISO 80000-1 annule et remplace l'ISO 31-0:1992 et l'ISO 1000:1992. Elle
incorpore également les Amendements ISO 31-0:1992/Amd.1:1998, ISO 31-0:1992/Amd.2:2005 et
ISO 1000:1992/Amd.1:1998. Les principales modifications techniques par rapport à la précédente norme sont
les suivantes:
⎯ la structure a été modifiée pour bien montrer que les grandeurs viennent en premier, suivies des unités;
⎯ des définitions conformes au Guide ISO/CEI 99:2007, ont été ajoutées;
⎯ les Annexes A et B sont devenues normatives;
⎯ une nouvelle Annexe C normative a été ajoutée.
L'ISO 80000 comprend les parties suivantes, présentées sous le titre général Grandeurs et unités:
⎯ Partie 1: Généralités
⎯ Partie 2: Signes et symboles mathématiques à employer dans les sciences de la nature et dans la
technique
⎯ Partie 3: Espace et temps
⎯ Partie 4: Mécanique
⎯ Partie 5: Thermodynamique
⎯ Partie 7: Lumière
⎯ Partie 8: Acoustique
iv © ISO 2009 – Tous droits réservés
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ISO 80000-1:2009(F)
⎯ Partie 9: Chimie physique et physique moléculaire
⎯ Partie 10: Physique atomique et nucléaire
⎯ Partie 11: Nombres caractéristiques
⎯ Partie 12: Physique de l'état solide
La CEI 80000 comprend les parties suivantes, présentées sous le titre général Grandeurs et unités:
⎯ Partie 6: Électromagnétisme
⎯ Partie 13: Science et technologies de l'information
⎯ Partie 14: Télébiométrique relative à la physiologie humaine
© ISO 2009 – Tous droits réservés v
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ISO 80000-1:2009(F)
Introduction
0.1 Grandeurs
Les systèmes de grandeurs et les systèmes d'unités peuvent être traités de nombreuses manières
cohérentes mais différentes. Le traitement à appliquer n'est qu'une question de convention. La présentation
donnée dans la présente Norme internationale, Grandeurs et unités, est celle qui est à la base du Système
international d'unités (SI) adopté par la Conférence générale des poids et mesures (CGPM).
Les grandeurs et les relations entre grandeurs utilisées ici sont celles dont l'usage est accepté de manière
quasi universelle dans les sciences physiques. Elles sont aujourd'hui présentées dans la majorité des
manuels scientifiques et tous les scientifiques et ingénieurs les connaissent.
1)
NOTE Pour les unités électriques et magnétiques dans les systèmes CGS-ESU, CGS-EMU et gaussien, il existe
une différence dans les systèmes de grandeurs les définissant. Dans le système CGS-ESU, la constante électrique ε (la
0
permittivité du vide) est définie égale à 1, c'est-à-dire sans dimension, dans le système CGS-EMU, la constante
magnétique µ (perméabilité du vide) est définie égale à 1, c'est-à-dire sans dimension, alors que ces grandeurs ne sont
0
pas sans dimension dans l'ISQ. Le système gaussien est associé aux systèmes CGS-ESU et CGS-EMU et des
complications similaires existent. En mécanique, la forme générale de la loi du mouvement de Newton est F = c⋅ma. Dans
2)
l'ancien système technique, le MKS , c = 1/g , où g est l'accélération normale due à la pesanteur; dans l'ISQ, c = 1.
n n
Il existe, par essence, un nombre infini de grandeurs et de relations entre elles, et elles évoluent
continuellement, suivant le développement de nouveaux domaines dans les sciences et les techniques. Il est
donc impossible de dresser la liste de toutes ces grandeurs et relations dans la présente Norme
internationale; une sélection des grandeurs les plus fréquemment utilisées et des relations entre elles est
présentée à la place.
Il est inévitable que certains lecteurs travaillant dans des domaines spécialisés ne trouvent pas les grandeurs
qui les intéressent dans la présente Norme internationale ou dans une autre Norme internationale. Cependant,
s'ils peuvent relier leurs grandeurs à des exemples plus courants figurant dans la liste, cela ne les empêchera
pas de définir des unités pour celles-ci.
La plupart des unités utilisées pour exprimer les valeurs des grandeurs d'intérêt ont été développées et
utilisées longtemps avant le développement du concept de système de grandeurs. Néanmoins, les relations
entre les grandeurs, qui sont simplement les équations des sciences physiques, sont importantes, car les
relations entre les unités jouent un rôle majeur dans tout système d'unités, et elles sont développées à partir
des relations entre les grandeurs correspondantes.
Le système de grandeurs, y compris les relations entre elles, qui est utilisé comme base des unités SI, est
appelé Système international de grandeurs, abrégé en «ISQ» dans toutes les langues. Ce nom n'a pas été
utilisé dans l'ISO 31, qui est à l'origine de la présente série harmonisée. L'ISQ apparaît toutefois dans le
[8] e
Guide ISO/CEI 99:2007, ainsi que dans la Brochure sur le SI , 8 édition, 2006. Dans les deux cas, le but
était de s'assurer de la cohérence avec la présente nouvelle série sur les Grandeurs et unités, qui était en
cours d'élaboration au moment de leur publication. Il convient cependant de bien comprendre que «ISQ» n'est
qu'une notation pratique pour désigner le système de grandeurs et d'équations intrinsèquement infini et en
continuelle évolution et expansion sur lequel reposent les sciences et techniques modernes. «ISQ» est une
notation abrégée du «système de grandeurs sur lequel repose le SI», expression utilisée pour ce système
dans l'ISO 31.
1) CGS = centimètre-gramme-seconde; ESU = unités électrostatiques; EMU = unités électromagnétiques.
2) MKS = mètre-kilogramme-seconde.
vi © ISO 2009 – Tous droits réservés
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ISO 80000-1:2009(F)
0.2 Unités
Un système d'unités se développe en commençant par définir un ensemble d'unités de base pour un petit
ensemble de grandeurs de base correspondantes, puis en définissant les unités dérivées comme les produits
de puissances des unités de base, qui correspondent aux relations définissant les grandeurs dérivées en
fonction des grandeurs de base. Dans la présente Norme internationale et le SI, il y a sept grandeurs de base
et sept unités de base. Les grandeurs de base sont la longueur, la masse, le temps, le courant électrique, la
température thermodynamique, la quantité de matière et l'intensité lumineuse, dont les unités de bases
respectives sont le mètre, le kilogramme, la seconde, l'ampère, le kelvin, la mole et la candela. Les définitions
de ces unités de base et leur mise en pratique sont au cœur du SI et sont sous la responsabilité des comités
consultatifs du Comité international des poids et mesures (CIPM). Les définitions actuelles des unités de base
[8]
et les conseils pour leur mise en pratique sont présentés dans la Brochure sur le SI , publiée par le Bureau
international des poids et mesures (BIPM) et disponible auprès de celui-ci. À noter qu'à la différence des
unités de base, possédant chacune une définition spécifique, les grandeurs de base sont simplement choisies
par convention et aucune tentative de les définir autrement que fonctionnellement n'a été effectuée.
0.3 Réalisation des valeurs d'unités
Réaliser la valeur d'une unité signifie utiliser la définition de l'unité pour effectuer des mesurages qui
comparent la valeur d'une grandeur de même nature que l'unité avec la valeur de l'unité. Il s'agit de l'étape
essentielle pour le mesurage de la valeur de toute grandeur dans les sciences. La réalisation des valeurs des
unités de base est d'une importance particulière. La réalisation des valeurs des unités dérivées découle en
principe de la réalisation des unités de base.
Il peut exister de nombreuses manières différentes de réaliser la valeur d'une unité en pratique et de
nouvelles méthodes peuvent être développées avec les avancées de la science. Toute méthode cohérente
avec les lois de la physique peut être utilisée pour réaliser toute unité SI. Néanmoins, il est souvent utile de
passer en revue les méthodes expérimentales de réalisation des unités, et le CIPM recommande de telles
méthodes, dont la présentation fait partie de la Brochure sur le SI.
0.4 Disposition des tableaux
Dans les parties 3 à 14 de la présente Norme internationale, les grandeurs et les relations entre elles, formant
un sous-ensemble de l'ISQ, sont présentées sur les pages de gauche, et les unités SI (et quelques autres)
sont présentées sur les pages de droite. Certaines grandeurs et unités supplémentaires sont également
respectivement présentées sur les pages de gauche et de droite. Les numéros des grandeurs sont notés
pp-nn.s (pp, numéro de partie; nn, numéro courant dans la partie; s, numéro complémentaire). Les numéros
des unités sont notés pp-nn.l (pp, numéro de partie; nn, numéro dans la partie; l, lettre complémentaire).
© ISO 2009 – Tous droits réservés vii
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NORME INTERNATIONALE ISO 80000-1:2009(F)
Grandeurs et unités —
Partie 1:
Généralités
1 Domaine d'application
L'ISO 80000-1 donne des informations générales et des définitions à propos des grandeurs, des systèmes de
grandeurs, des unités, des symboles de grandeurs et d'unités, et des systèmes cohérents d'unités,
notamment le Système international de grandeurs (ISQ) et le Système international d'unités (SI).
Les principes établis dans l'ISO 80000-1 sont prévus pour un usage général dans les divers domaines
scientifiques et techniques, ainsi qu'en introduction aux autres parties de la présente Norme internationale.
Les grandeurs ordinales et les propriétés qualitatives sont hors du domaine d'application de l'ISO 80000-1.
2 Références normatives
Les documents de référence suivants sont indispensables pour l'application du présent document. Pour les
références datées, seule l'édition citée s'applique. Pour les références non datées, la dernière édition du
document de référence (y compris les éventuels amendements) s'applique.
Guide ISO/CEI 99:200 7, Vocabulaire international de métrologie — Concepts fondamentaux et généraux et
termes associés (VIM)
3 Termes et définitions
Pour les besoins du présent document, les termes et définitions suivants s'appliquent.
NOTE Le contenu de cet article est essentiellement le même que celui du Guide ISO/CEI 99:2007. Certaines notes
et exemples ont été modifiés.
3.1
grandeur
propriété d'un phénomène, d'un corps ou d'une substance, que l'on peut exprimer quantitativement au moyen
d'un nombre et d'une référence
NOTE 1 Le concept générique de grandeur peut être subdivisé en plusieurs niveaux de concepts spécifiques, comme
indiqué dans le tableau suivant. La moitié gauche du tableau présente des concepts spécifiques du concept de grandeur.
Ce sont des concepts génériques pour les grandeurs individuelles de la moitié droite.
© ISO 2009 – Tous droits réservés 1
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ISO 80000-1:2009(F)
longueur, l rayon, r rayon du cercle A, r ou r(A)
A
longueur d'onde, λ longueur d'onde de la radiation D du sodium, λ ou λ(Na; D)
D
énergie, E énergie cinétique, T énergie cinétique de la particule i dans un système donné, T
i
chaleur, Q chaleur de vaporisation du spécimen i d'eau, Q
i
charge électrique, Q charge électrique du proton, e
résistance électrique, R résistance électrique de la résistance i dans un circuit donné, R
i
concentration en quantité de matière du concentration en quantité de matière d'éthanol dans le spécimen i
constituant B, c de vin, c (C H OH)
i 2 5
B
nombre volumique du constituant B, C nombre volumique d'érythrocytes dans le spécimen i de sang,
B
C(Erys; B )
i
dureté C de Rockwell (charge de dureté C de Rockwell du spécimen i d'acier, HRC (150 kg)
i
150 kg), HRC(150 kg)
NOTE 2 La référence peut être une unité de mesure, une procédure de mesure, un matériau de référence ou une de
leurs combinaisons. Pour l'expression quantitative d'une grandeur (voir 3.19).
NOTE 3 La série ISO 80000 et CEI 80000, Grandeurs et unités, donne des symboles de grandeurs. Les symboles de
grandeurs sont écrits en italique. Un symbole donné peut noter des grandeurs différentes.
NOTE 4 Une grandeur telle que définie ici est une grandeur scalaire. Cependant, un vecteur ou un tenseur dont les
composantes sont des grandeurs est aussi considéré comme une grandeur.
NOTE 5 Le concept de «grandeur» peut être subdivisé génériquement, par exemple «grandeur physique», «grandeur
chimique» et «grandeur biologique», ou «grandeur de base» et «grandeur dérivée».
NOTE 6 Adapté du Guide ISO/CEI 99:2007, définition 1.1, dans laquelle il y a une note supplémentaire.
3.2
nature de grandeur
aspect commun à des grandeurs mutuellement comparables
NOTE 1 Nature de grandeur est souvent abrégé en «nature», par exemple dans grandeurs de même nature.
NOTE 2 La répartition des grandeurs selon leur nature est dans une certaine mesure arbitraire.
EXEMPLE 1 Les grandeurs diamètre, circonférence et longueur d'onde sont généralement considérées comme
des grandeurs de même nature, à savoir la nature de la longueur.
EXEMPLE 2 Les grandeurs chaleur, énergie cinétique et énergie potentielle sont généralement considérées
comme des grandeurs de même nature, à savoir la nature de l'énergie.
NOTE 3 Les grandeurs de même nature dans un système de grandeurs donné ont la même dimension. Cependant
des grandeurs de même dimension ne sont pas nécessairement de même nature.
EXEMPLE On ne considère pas, par convention, les grandeurs moment d'une force et énergie comme étant de
même nature, bien que ces grandeurs aient la même dimension. Il en est de même pour la capacité thermique et
l'entropie, ainsi que pour un nombre d'entités, la perméabilité relative et la fraction massique.
NOTE 4 En anglais, les termes désignant les grandeurs de la moitié gauche du tableau en 3.1, Note 1, sont souvent
employés pour désigner les «natures» correspondantes. En français, le terme «nature» n'est employé que dans des
expressions telles que «grandeurs de même nature» (en anglais «quantities of the same kind»).
NOTE 5 Adapté du Guide ISO/CEI 99:2007, définition 1.2, dans laquelle «nature» est donné comme un terme admis.
2 © ISO 2009 – Tous droits réservés
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ISO 80000-1:2009(F)
3.3
système de grandeurs
ensemble de grandeurs associé à un ensemble de relations non contradictoires entre ces grandeurs
NOTE 1 Les grandeurs ordinales (voir 3.26), telles que la dureté C de Rockwell, et les propriétés qualitatives
(voir 3.30), telles que la couleur de la lumière, ne sont généralement pas considérées comme faisant partie d'un système
de grandeurs, parce qu'elles ne sont reliées à d'autres grandeurs que par des relations empiriques.
NOTE 2 Adapté du Guide ISO/CEI 99:2007, définition 1.3, dans laquelle la Note 1 est différente.
3.4
grandeur de base
grandeur d'un sous-ensemble choisi par convention dans un système de grandeurs donné de façon
qu'aucune grandeur du sous-ensemble ne puisse être exprimée en fonction des autres
NOTE 1 Le sous-ensemble mentionné dans la définition est appelé «ensemble des grandeurs de base».
EXEMPLE L'ensemble des grandeurs de base du Système international de grandeurs (ISQ) est donné en 3.6.
NOTE 2 Les grandeurs de base sont considérées comme mutuellement indépendantes puisqu'une grandeur de base
ne peut être exprimée par un produit de puissances des autres grandeurs de base.
NOTE 3 On peut considérer la grandeur «nombre d'entités» comme une grandeur de base dans tout système de
grandeurs.
NOTE 4 Adapté du Guide ISO/CEI 99:2007, définition 1.4, dans laquelle la définition est légèrement différente.
3.5
grandeur dérivée
grandeur définie, dans un système de grandeurs, en fonction des grandeurs de base de ce système
EXEMPLE Dans un système de grandeurs ayant pour grandeurs de base la longueur et la masse, la masse
volumique est une grandeur dérivée définie comme le quotient d'une masse par un volume (longueur au cube).
[Guide ISO/CEI 99:2007, définition 1.5]
3.6
Système international de grandeurs
ISQ
système de grandeurs fondé sur les sept grandeurs de base: longueur, masse, temps, courant électrique,
température thermodynamique, quantité de matière, intensité lumineuse
NOTE 1 Ce système de grandeurs est publié dans la série ISO 80000 et CEI 80000, Grandeurs et unités, Parties 3
à 14.
NOTE 2 Le Système international d'unités (SI) (voir 3.16) est fondé sur l'ISQ.
NOTE 3 Adapté du Guide ISO/CEI 99:2007, définition 1.6, dans laquelle Note 1 est différente.
3.7
dimension
dimension d'une grandeur
expression de la dépendance d'une grandeur par rapport aux grandeurs de base d'un système de grandeurs
sous la forme d'un produit de puissances de facteurs correspondant aux grandeurs de base, en omettant tout
facteur numérique
−2
EXEMPLE 1 Dans l'ISQ, la dimension de la force est notée dim F = LMT .
−3
EXEMPLE 2 Dans le même système de grandeurs, dim ρ = ML est la dimension de la concentration en masse du
B
−3
constituant B, et ML est aussi la dimension de la masse volumique, ρ.
© ISO 2009 – Tous droits réservés 3
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ISO 80000-1:2009(F)
EXEMPLE 3 La période, T, d'un pendule de longueur l en un endroit où l'accélération locale de la pesanteur vaut g
est:
l 2π
T=π2 ou TC= ()g l où Cg =
()
g
g
−1/2
Par conséquent, dim (Cg)=⋅T L .
NOTE 1 Une puissance d'un facteur est le facteur muni d'un exposant. Chaque facteur exprime la dimension d'une
grandeur de base.
NOTE 2 Par convention, la représentation symbolique de la dimension d'une grandeur de base est une lettre
majuscule unique en caractère romain (droit) sans empattement. Par convention, la représentation symbolique de la
dimension d'une grandeur dérivée est le produit de puissances des dimensions des grandeurs de base conformément à la
définition de la grandeur dérivée. La dimension de la grandeur Q est notée dim Q.
NOTE 3 Pour établir la dimension d'une grandeur, on ne tient pas compte du caractère scalaire, vectoriel ou tensoriel.
NOTE 4 Dans un système de grandeurs donné,
⎯ les grandeurs de même nature ont la même dimension,
⎯ des grandeurs de dimensions différentes sont toujours de nature différente,
⎯ des grandeurs ayant la même dimension ne sont pas nécessairement de même nature.
NOTE 5 Dans l'ISQ, les symboles correspondant aux dimensions des grandeurs sont:
Grandeur de base Symbole de la dimension
longueur L
masse M
temps T
courant électrique I
température thermodynamique Θ
quantité de matière N
intensité lumineuse J
α β γ δ ε ζ η
La dimension d'une grandeur Q est donc notée dim Q = L M T IΘ N J où les exposants, appelés exposants
dimensionnels, sont positifs, négatifs ou nuls. Les facteurs dont l'exposant est nul et les exposants 1 sont généralement
omis. Lorsque tous les exposants sont nuls (voir 3.8).
NOTE 6 Adapté du Guide ISO/CEI 99:2007, définition 1.7, dans laquelle la Note 5 et les Exemples 2 et 3 sont
différents et dans laquelle «dimension d'une grandeur» est donné comme un terme admis.
3.8
grandeur sans dimension
grandeur de dimension un
grandeur pour laquelle tous les exposants des facteurs correspondant aux grandeurs de base dans sa
dimension sont nuls
NOTE 1 Le terme «grandeur sans dimension» est d'usage courant en français. Il provient du fait que tous les
exposants sont nuls dans la représentation symbolique de la dimension de telles grandeurs. Le terme «grandeur de
dimension un» reflète la convention selon laquelle la représentation symbolique de la dimension de telles grandeurs est le
symbole 1 (voir l'Article 5). Cette dimension n'est pas un nombre, mais l'élément neutre pour la multiplication des
dimensions.
NOTE 2 Les unités de mesure et les valeurs des grandeurs sans dimension sont des nombres, mais ces grandeurs
portent plus d'information qu'un nombre.
4 © ISO 2009 – Tous droits réservés
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ISO 80000-1:2009(F)
NOTE 3 Certaines grandeurs sans dimension sont définies comme des rapports de deux grandeurs de même nature.
L'unité dérivée cohérente est le nombre un, de symbole 1.
EXEMPLE Angle plan, angle solide, indice de réfraction, perméabilité relative, fraction massique, facteur de
frottement, nombre de Mach.
NOTE 4 Les nombres d'entités sont des grandeurs sans dimension.
EXEMPLE Nombre de tours dans une bobine, nombre de molécules dans un spécimen donné, dégénérescence
des niveaux d'énergie d'un système quantique.
NOTE 5 Adapté du Guide ISO/CEI 99:2007, définition 1.8, dans laquelle les Notes 1 et 3 sont différentes et dans
laquelle «grandeur de dimension un» est donné comme un terme admis.
3.9
unité de mesure
unité
grandeur scalaire réelle, définie et adoptée par convention, à laquelle on peut comparer toute autre grandeur
de même nature pour exprimer le rapport de la deuxième grandeur à la première sous la forme d'un nombre
NOTE 1 On désigne les unités de mesure par des noms et des symboles attribués par convention.
NOTE 2 Les unités des grandeurs de même dimension peuvent être désignées par le même nom et le même symbole
même si ces grandeurs ne sont pas de même nature. On emploie, par exemple, le nom «joule par kelvin» et le symbole
J/K pour désigner à la fois une unité de capacité thermique et une unité d'entropie, bien que ces grandeurs ne soient
généralement pas considérées comme étant de même nature. Toutefois, dans certains cas, des noms spéciaux sont
utilisés exclusivement pour des grandeurs d'une nature spécifiée. C'est ainsi que l'unité seconde à la puissance moins un
(1/s) est appelée hertz (Hz) pour les fréquences et becquerel (Bq) pour les activités de radionucléides. Un autre exemple
est le joule (J), utilisé comme unité d'énergie, mais jamais comme unité de moment de force, à savoir le newton mètre
(N · m).
NOTE 3 Les unités des grandeurs sans dimension sont des nombres. Dans certains cas, on leur donne des noms
spéciaux, par exemple radian, stéradian et décibel, ou on les exprime par des quotients comme la millimole par mole
−3 −9
égale à 10 , et le microgramme par kilogramme égal à 10 .
NOTE 4 Pour une grandeur donnée, le nom abrégé «unité» est souvent combiné avec le nom de la grandeur, par
exemple «unité de masse».
NOTE 5 Adapté du Guide ISO/CEI 99:2007, définition 1.9, dans laquelle la définition et la Note 2 sont différents et
dans laquelle «unité» est donné comme un terme admis.
3.10
unité de base
unité de mesure adoptée par convention pour une grandeur de base
NOTE 1 Dans chaque système cohérent d'unités, il y a une seule unité de base pour chaque grandeur de base.
EXEMPLE Dans le SI, le mètre est l'unité de base de longueur. Dans les systèmes CGS, le centimètre est
l'unité de base de longueur.
NOTE 2 Une unité de base peut aussi servir pour une grandeur dérivée de même dimension.
EXEMPLE La grandeur dérivée hauteur de pluie, définie comme un volume surfacique (volume par aire) a le
mètre comme unité dérivée cohérente dans le SI.
NOTE 3 Pour un nombre d'entités, on peut considérer le nombre un, de symbole 1, comme une unité de base dans
tout système d'unité. Comparer à la Note 3 en 3.4.
NOTE 4 Adapté du Guide ISO/CEI 99:2007, définition 1.10, dans laquelle l'exemple dans la Note 2 est différent. La
dernière phrase dans la Note 3 est nouvelle.
© ISO 2009 – Tous droits réservés 5
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ISO 80000-1:2009(F)
3.11
unité dérivée
unité de mesure d'une grandeur dérivée
EXEMPLE Le mètre par seconde, symbole m/s, et le centimètre par seconde, symbole cm/s, sont des unités
dérivées de vitesse dans le SI. Le kilomètre par heure, symbole km/h, est une unité de vitesse en dehors du SI mais dont
l'usage est accepté avec le SI. Le nœud, égal à un mille marin par heure, est une unité de vitesse en dehors du SI.
[Guide ISO/CEI 99:2007, définition 1.11]
3.12
unité dérivée cohérente
unité dérivée qui, pour un système de grandeurs donné et pour un ensemble choisi d'unités de ba
...
SLOVENSKI SIST ISO 80000-1
STANDARD
maj 2013
Veličine in enote – 1. del: Splošno
Quantities and units – Part 1: General
Grandeurs et unités – Partie 1: Généralités
Referenčna oznaka
ICS 01.060 SIST ISO 80000-1:2013 (sl)
Nadaljevanje na straneh 2 do 44
© 2013-05. Standard je založil in izdal Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST ISO 80000-1 : 2013
NACIONALNI UVOD
Standard SIST ISO 80000-1 (sl), Veličine in enote – 1. del: Splošno, maj 2013, ima status
slovenskega standarda in je enakovreden mednarodnemu standardu ISO 80000-1 (en), Quantities
and units – Part 1: General, 2009-11.
NACIONALNI PREDGOVOR
Mednarodni standard ISO 80000-1:2009 je pripravil tehnični odbor ISO/TC 12 Veličine, enote, simboli
v sodelovanju z IEC/TC 25 Veličine in enote in njihovi črkovni simboli.
Slovenski standard SIST ISO 80000-1:2013 je prevod mednarodnega standarda ISO 80000-1:2009. V
primeru spora glede besedila slovenskega prevoda v tem standardu je odločilen izvirni mednarodni
standard v angleškem jeziku. Slovensko izdajo standarda je pripravil tehnični odbor SIST/TC TRS
Tehnično risanje, veličine, enote, simboli in grafični simboli.
ZVEZA Z NACIONALNIMI STANDARDI
S privzemom tega mednarodnega standarda veljajo za omejeni namen referenčnih standardov vsi
standardi, navedeni v izvirniku, razen standardov, ki so že sprejeti v nacionalno standardizacijo:
SIST ISO 80000-2:2013 (sl) Veličine in enote – 2. del: Matematični znaki in simboli za
uporabo v naravoslovnih vedah in tehniki
SIST EN 60027-1:2007 (en) Črkovni simboli za uporabo v elektrotehniki – 1. del: Splošno
(IEC 60027-1:1995 (reprint) + A1:1997)
SIST EN 60027-2:2008 (en,fr,de) Črkovni simboli za uporabo v elektrotehniki – 2. del:
Telekomunikacije in elektronika (IEC 60027-2:2005)
SIST EN 80000-13:2008 (en,fr) Veličine in enote – 13. del: Informacijska znanost in tehnologija
(IEC 80000-13:2008)
PREDHODNA IZDAJA
SIST ISO 31-0+A1+A2:2007(sl) Veličine in enote – 0. del: Splošna načela
SIST ISO 1000+A1:2008 (sl) Enote SI s priporočili za uporabo njihovih večkratnikov in
nekaterih drugih enot
OPOMBE
– Povsod, kjer se v besedilu standarda uporablja izraz “mednarodni standard”, v
SIST ISO 80000-1:2013 to pomeni “slovenski standard”.
– Nacionalni uvod in nacionalni predgovor nista sestavni del standarda.
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SIST ISO 80000-1 : 2013
VSEBINA Stran
Predgovor .4
Uvod .5
1 Področje uporabe .7
2 Zveza z drugimi standardi .7
3 Izrazi in definicije .7
4 Veličine .16
5 Dimenzije.18
6 Enote .18
7 Pravila tiskanja .26
Dodatek A (normativni): Izrazi v imenih fizikalnih veličin.34
Dodatek B (normativni): Zaokroževanje števil.38
Dodatek C (normativni): Logaritemske veličine in njihove enote .40
Dodatek D (informativni): Mednarodne organizacije na področju veličin in enot .42
Literatura.44
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SIST ISO 80000-1 : 2013
Predgovor
ISO (Mednarodna organizacija za standardizacijo) je svetovna zveza nacionalnih organov za
standarde (članov ISO). Mednarodne standarde navadno pripravljajo tehnični odbori ISO. Vsak član,
ki želi delovati na določenem področju, za katero je bil ustanovljen tehnični odbor, ima pravico biti
zastopan v tem odboru. Pri delu sodelujejo tudi vladne in nevladne mednarodne organizacije,
povezane z ISO. V vseh zadevah, ki so povezane s standardizacijo na področju elektrotehnike, ISO
tesno sodeluje z Mednarodno elektrotehniško komisijo (IEC).
Mednarodni standardi so pripravljeni v skladu s pravili, podanimi v Direktivah ISO/IEC, 2. del.
Glavna naloga tehničnih odborov je priprava mednarodnih standardov. Osnutki mednarodnih
standardov, ki jih sprejmejo tehnični odbori, se pošljejo vsem članom v glasovanje. Za objavo
mednarodnega standarda je treba pridobiti soglasje najmanj 75 % članov, ki se udeležijo glasovanja.
Opozoriti je treba na možnost, da je lahko nekaj elementov standarda ISO 80000-1 predmet patentnih
pravic. ISO ne prevzema odgovornosti za identifikacijo katerih koli ali vseh takih patentnih pravic.
ISO 80000-1 je pripravil tehnični odbor ISO/TC 12 Veličine in enote v sodelovanju z IEC/TC 25
Veličine in enote.
Prva izdaja standarda ISO 80000-1 razveljavlja in nadomešča ISO 31-0:1992 in ISO 1000:1992. Vključuje
tudi dopolnila ISO 31-0:1992/Amd.1:1998, ISO 31-0:1992/Amd.2:2005 in ISO 1000:1992/Amd.1:1998.
V primerjavi s prejšnjim standardom so glavne tehnične spremembe naslednje:
– spremenjena je zgradba standarda, da se poudari, da so na prvem mestu navedene veličine, tem
pa sledijo enote;
– dodane so definicije v skladu z Vodilom ISO/IEC 99:2007;
– dodatka A in B sta postala normativna;
– dodan je nov normativni dodatek C.
ISO 80000 s skupnim naslovom Veličine in enote sestavljajo naslednji deli:
– 1. del: Splošno
– 2. del: Matematični znaki in simboli za uporabo v naravoslovnih vedah in tehniki
– 3. del: Prostor in čas
– 4. del: Mehanika
– 5. del: Termodinamika
– 7. del: Svetloba
– 8. del: Akustika
– 9. del: Fizikalna kemija in molekulska fizika
– 10. del: Atomska in jedrska fizika
– 11. del: Značilna števila
– 12. del: Fizika trdne snovi
IEC 80000 s skupnim naslovom Veličine in enote sestavljajo naslednji deli:
– 6. del: Elektromagnetizem
– 13. del: Informacijska znanost in tehnologija
– 14. del: Telebiometrija, povezana s fiziologijo človeka
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SIST ISO 80000-1 : 2013
Uvod
0.1 Veličine
Sisteme veličin in sisteme enot je mogoče obravnavati na več usklajenih, vendar različnih načinov.
Kateri način obravnavanja se uporabi, je samo stvar dogovora. V tem mednarodnem standardu je
podana tista predstavitev, ki je podlaga za mednarodni sistem enot, SI (Système international
d'unités), sprejet na Generalni konferenci za uteži in mere, CGPM (Conférence générale des poids et
mesures).
Veličine in povezave med veličinami, ki so uporabljene v tem dokumentu, se skoraj enotno uporabljajo
v vseh fizikalnih vedah. Predstavljene so v večini današnjih znanstvenih učbenikov in jih poznajo vsi
znanstveniki in tehniki.
1
OPOMBA: Pri enotah s področja elektrike in magnetizma v sistemih CGS-ESU, CGS-EMU in Gaussovem sistemu obstaja
razlika v sistemih veličin, s katerimi so definirane. V sistemu CGS-ESU je električna konstanta ε (permitivnost
0
vakuuma) definirana kot enaka 1, tj. z dimenzijo ena; v sistemu CGS-EMU je magnetna konstanta µ
0
(permeabilnost vakuuma) definirana kot enaka 1, tj. z dimenzijo ena, za razliko od mednarodnega sistema
veličin ISQ, kjer ti dve veličini nimata dimenzije ena. V Gaussovem sistemu, ki je povezan s sistemoma
CGS-ESU in CGS-EMU, prihaja do podobnih zapletov. V mehaniki se Newtonov zakon gibanja v svoji splošni
2
obliki zapiše F = c⋅ma. V starem tehničnem sistemu MKS je c = 1/g , kjer je g standardni pospešek prostega
n n
pada; v ISQ je c = 1.
Veličin in povezav med njimi je v bistvu neskončno število in z razvojem novih znanstveno-tehničnih
področij nenehno nastajajo nove. Zato v tem mednarodnem standardu ni mogoče našteti vseh teh
veličin in povezav in je namesto tega predstavljen izbor pogosteje uporabljenih veličin ter povezav
med njimi.
Neizogibno lahko pride do tega, da bodo nekateri bralci, ki delajo na določenih posebnih področjih,
ugotovili, da veličine, katerih uporaba jih zanima, niso navedene v tem ali katerem drugem
mednarodnem standardu. Vendar če bodo svoje veličine povezali z bolj znanimi primeri, ki so
navedeni, jim to ne bo preprečilo definirati enot za svoje veličine.
Večina enot, ki se uporabljajo za izražanje vrednosti aktualnih veličin, je bilo razvitih in v rabi dosti
prej, kot je bil razvit koncept sistema veličin. Kljub temu pa so povezave med veličinami, ki so
preproste enačbe iz fizikalnih ved, pomembne, saj povezave med enotami igrajo pomembno vlogo v
vsakem sistemu enot in so razvite iz povezav med ustreznimi veličinami.
Sistem veličin, vključno s povezavami med njimi, ki se uporablja kot podlaga za enote SI, se v vseh
jezikih imenuje mednarodni sistem veličin z oznako "ISQ". To ime ni bilo uporabljeno v standardu
ISO 31, iz katerega je nastala sedanja skupina harmoniziranih standardov, se pa ISQ pojavi v Vodilu
[8]
ISO/IEC 99:2007 in v Brošuri SI , 8. izdaja, 2006. V obeh primerih je bil izraz uporabljen zaradi
zagotavljanja skladnosti z novo skupino standardov Veličine in enote, ki je bila v času, ko sta bila
Vodilo in Brošura izdana, v pripravi; že takrat je bilo napovedano, da bo uporabljen nov izraz. Vedeti
pa je treba, da ISQ ni nič drugega kot ustrezna oznaka za sistem veličin in enačb, ki je v bistvu
neskončen in se nenehno spreminja ter širi in na katerem slonita moderna znanost in tehnika. ISQ je
skrajšan zapis za "sistem veličin, na katerih temelji SI", tj. besedne zveze, ki je bila za ta sistem
uporabljena v standardu ISO 31.
0.2 Enote
Sistem enot nastane tako, da se najprej določi skupina osnovnih enot za manjšo skupino ustreznih
osnovnih veličin, nato pa se določijo izpeljane enote kot zmnožki potenc osnovnih enot, ki ustrezajo
povezavam, ki določajo izpeljane enote z osnovnimi veličinami. V tem mednarodnem standardu ter v
SI je sedem osnovnih veličin in sedem osnovnih enot. Osnovne veličine so dolžina, masa, čas,
električni tok, termodinamična temperatura, množina snovi in svetilnost. Ustrezajoče osnovne enote
so meter, kilogram, sekunda, amper, kelvin, mol in kandela. Definicije teh osnovnih enot in njihove
1
CGS = centimeter-gram sekunda; ESU = elektrostatične enote; EMU = elektromagnetne enote.
2
MKS = meter-kilogram-sekunda.
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SIST ISO 80000-1 : 2013
dejanske izvedbe so v osrčju sistema enot SI in so zanje odgovorni svetovalni odbori Mednarodnega
odbora za uteži in mere CIPM (Comité international des poids et mesures). Veljavne definicije
[8]
osnovnih enot in nasveti za njihovo dejansko izvedbo so navedeni v Brošuri SI , ki jo je mogoče
dobiti pri izdajatelju, Mednarodnem uradu za uteži in mere BIPM (Bureau international des poids et
mesures). Upoštevati je treba, da so osnovne veličine, v nasprotju z osnovnimi enotami, ki imajo
vsaka svojo posebno definicijo, preprosto izbrane z dogovorom in jih ne poskušajo definirati drugače
kot operativno.
0.3 Določanje vrednosti enot
Določiti vrednost enote pomeni uporabiti definicijo enote za izvedbo meritev, s katerimi se primerja
vrednost veličine, ki je iste vrste kot enota, z vrednostjo te enote. To je bistveni korak pri merjenju
vrednosti katere koli veličine v znanosti. Posebno pomembno je določanje vrednosti osnovnih enot.
Določanje vrednosti izpeljanih enot načeloma sledi določanju osnovnih enot.
Dejanska izvedba vrednosti enote je mogoča na več različnih načinov, z razvojem znanosti pa se
lahko razvijejo še nove metode. Za določanje katere koli enote SI se lahko uporabi vsaka metoda, ki je
skladna z zakoni fizike. Kljub temu pa pogosto pomaga, če se pregledajo eksperimentalne metode za
določanje enot, in CIPM priporoča take metode, ki so predstavljene v dodatku Brošure SI.
0.4 Ureditev preglednic
Od 3. do 14. dela tega mednarodnega standarda so veličine in povezave med njimi, ki so podskupina
ISQ, podane na levih straneh, in enote SI (ter nekatere druge enote) na desnih straneh. Prav tako so
na levih oziroma desnih straneh podane nekatere dodatne veličine in enote. Zaporedne številke veličin
se zapišejo kot šd-tš.p (šd: številka dela; tš: tekoča številka v delu; p: podštevilka). Zaporedne številke
enot se zapišejo kot šd-tš.č (šd: številka dela; tš: tekoča številka v delu; č: podčrka).
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SIST ISO 80000-1 : 2013
Veličine in enote
1. del: Splošno
1 Področje uporabe
ISO 80000-1 podaja splošne informacije in definicije, ki se nanašajo na veličine, sisteme veličin,
enote, simbole veličin in enot ter na koherentne (soodvisne) sisteme enot, zlasti mednarodni sistem
veličin ISQ in mednarodni sistem enot SI.
Načela, opisana v ISO 80000-1, so namenjena za splošno uporabo na različnih področjih znanosti in
tehnike ter kot uvod v druge dele tega mednarodnega standarda.
Stopenjske veličine in nazivne lastnosti so zunaj področja uporabe ISO 80000-1.
2 Zveza z drugimi standardi
Za uporabo tega dokumenta so nujno potrebni spodaj navedeni standardi. Pri datiranem sklicevanju
se upošteva samo navedena izdaja. Pri nedatiranem sklicevanju se upošteva zadnja izdaja
navedenega dokumenta (vključno z morebitnimi dopolnili).
Vodilo ISO/IEC 99:2007, Mednarodni slovar meroslovja – Osnovni in splošni koncepti ter z njimi
povezani izrazi (VIM)
3 Izrazi in definicije
V tem dokumentu se uporabljajo naslednji izrazi in definicije.
OPOMBA: Vsebina te točke je v glavnem enaka kot pri Vodilu ISO/IEC 99:2007. Spremenjeni so nekateri primeri in opombe.
3.1
veličina
lastnost pojava, telesa ali snovi, pri čemer ima ta lastnost velikost, ki jo je mogoče izraziti kot število in
referenco
OPOMBA 1: Kot kaže spodnja preglednica, je splošni pojem "veličina" mogoče razdeliti v nekaj ravni posebnih pojmov. Leva
stran preglednice kaže posebne pojme pod "veličino". To so splošni pojmi za posamezne veličine v desnem
stolpcu.
dolžina, l polmer, r polmer kroga A, r ali r(A)
A
valovna dolžina sevanja natrija D, λ ali
D
valovna dolžina, λ
λ(Na; D)
energija, E kinetična energija, T kinetična energija delca i v danem sistemu, T
i
toplota, Q izparilna toplota vzorca i vode, Q
i
električni naboj, Q električni naboj protona, e
električna upornost, R električna upornost upora i v danem vezju, R
i
množinska koncentracija
množinska koncentracija etanola v vzorcu vina i, c (C H OH)
i 2 5
osnovnih delcev B, c
B
številčna koncentracija
številčna koncentracija eritrocitov v vzorcu krvi i, C(Erys; B )
i
osnovnih delcev B, C
B
trdota po Rockwellu C
(pri bremenu 150 kg), trdota po Rockwellu C vzorca jekla i, HRC (150 kg)
i
HRC(150 kg)
OPOMBA 2: Referenca je lahko merska enota, merilni postopek, referenčni material ali kombinacija le-teh. Za velikost
veličine glej 3.19.
OPOMBA 3: Simboli veličin so podani v skupinah standardov ISO 80000 in IEC 80000 Veličine in enote. Simboli veličin so
zapisani v poševnem tisku. Dani simbol lahko označuje različne veličine.
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SIST ISO 80000-1 : 2013
OPOMBA 4: Tukaj je veličina definirana kot skalar. Vendar pa se kot veličina šteje tudi vektor ali tenzor, katerega
komponente so veličine.
OPOMBA 5: Pojem "veličina" se lahko na splošno deli npr. na "fizikalne veličine", "kemijske veličine" in "biološke veličine" ali
na osnovne veličine in izpeljane veličine.
OPOMBA 6: Prirejeno po Vodilu ISO/IEC 99:2007, definicija 1.1, v kateri je še ena dodatna opomba.
3.2
vrsta veličine
vidik, skupen medsebojno primerljivim veličinam
OPOMBA 1: Vrsta veličine je npr. pri istovrstnih veličinah pogosto skrajšana na "vrsta".
OPOMBA 2: Delitev pojma "veličine" glede na "vrsto veličine" je do neke mere po prosti presoji.
1. PRIMER: Veličine premer, obseg in valovna dolžina se na splošno štejejo za istovrstne veličine, tj. veličine
vrste, imenovane dolžina.
2. PRIMER: Veličine toplota, kinetična energija in potencialna energija, se na splošno štejejo za istovrstne
veličine, tj. veličine vrste, imenovane energija.
OPOMBA 3: Istovrstne veličine znotraj danega sistema veličin imajo isto dimenzijo veličine. Vendar pa veličine z isto
dimenzijo niso nujno istovrstne.
PRIMER: Veličini navor in energija se dogovorno ne štejeta za istovrstni, čeprav imata isto dimenzijo. Podobno
velja za toplotno kapaciteto in entropijo ter tudi za število osnovnih delcev, relativno permeabilnost in masni delež.
OPOMBA 4: V angleščini se izrazi za veličine v levi polovici preglednice pod opombo 1 v točki 3.1 pogosto uporabljajo za
ustrezajoče "narave veličin". V francoščini se izraz "narava" uporablja samo v izrazih, kot je "grandeurs de
même nature", tako kot je uporabljen angleški "quantities of the same kind".
OPOMBA 5: Prirejeno po Vodilu ISO/IEC 99:2007, definicija 1.2, v kateri se "vrsta" pojavlja kot dopusten izraz. Dodana je
opomba 1.
3.3
sistem veličin
niz veličin skupaj z nizom neprotislovnih enačb, ki te veličine povezujejo
OPOMBA 1: Stopenjske veličine (glej 3.26), kot je npr. trdota po Rockwellu C, in nazivne lastnosti (glej 3.30), kot je npr. barva
svetlobe, se ponavadi ne štejejo za del sistema veličin, ker so z drugimi veličinami povezane samo z izkustvenimi
odnosi.
OPOMBA 2: Prirejeno po Vodilu ISO/IEC 99:2007, definicija 1.3, v kateri je opomba 1 drugačna.
3.4
osnovna veličina
veličina v dogovorjenem izbranem podnizu danega sistema veličin, podana tako, da nobena veličina
podniza ne more biti izražena z drugimi veličinami iz tega podniza
OPOMBA 1: V definiciji omenjeni podniz se imenuje "niz osnovnih veličin".
PRIMER: V mednarodnem sistemu veličin (ISQ) je niz osnovnih veličin podan v točki 3.6.
OPOMBA 2: Za osnovne veličine velja, da so medsebojno neodvisne, saj osnovne veličine ni mogoče izraziti kot zmnožka
potenc drugih osnovnih veličin.
OPOMBA 3: Veličina "število osnovnih delcev" se lahko šteje za osnovno veličino v vsakem sistemu veličin.
OPOMBA 4: Prirejeno po Vodilu ISO/IEC 99:2007, definicija 1.4, s tem da je definicija malce drugačna.
3.5
izpeljana veličina
veličina v sistemu veličin, določena z osnovnimi veličinami tega sistema
PRIMER: V sistemu veličin, ki ima za osnovni veličini dolžino in maso, je masna gostota izpeljana veličina, definirana kot
količnik mase in prostornine (dolžina na potenco tri).
OPOMBA: Prirejeno po Vodilu ISO/IEC 99:2007, definicija 1.5, v kateri je primer nekoliko drugačen.
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SIST ISO 80000-1 : 2013
3.6
mednarodni sistem veličin
ISQ
sistem veličin, temelječ na sedmih osnovnih veličinah: dolžini, masi, času, električnem toku,
termodinamični temperaturi, množini snovi in svetilnosti
OPOMBA 1: Ta sistem veličin je objavljen v skupinah standardov ISO 80000 in IEC 80000 Veličine in enote, od 3. do 14. dela.
OPOMBA 2: Mednarodni sistem enot (SI) (glej 3.16) temelji na ISQ.
OPOMBA 3: Prirejeno po Vodilu ISO/IEC 99:2007, definicija 1.6, v kateri je opomba 1 drugačna.
3.7
dimenzija veličine
dimenzija
izraz odvisnosti neke veličine od osnovnih veličin iz sistema veličin kot zmnožek potenc faktorjev, ki
ustrezajo osnovnim veličinam, s tem da se zanemari vsak številski faktor
–2
1. PRIMER: V mednarodnem sistemu veličin ISQ je dimenzija veličine sile označena z dim F = LMT .
–3
2. PRIMER: V istem sistemu veličin je dim ρ = ML dimenzija veličine masne koncentracije komponente B, hkrati pa je
B
–3
ML tudi dimenzija veličine prostorninske mase ρ.
3. PRIMER: Nihajni čas T nihala delcev z dolžino l na kraju s krajevnim pospeškom prostega pada g je:
l
ali
T = C()g l
T = 2π
g
2π
kjer je ()
C g =
g
–1/2
Iz tega sledi, da je dim C(g) = T ⋅ L .
OPOMBA 1: Potenca faktorja je ta faktor na eksponent. Vsak faktor je dimenzija ene osnovne veličine.
OPOMBA 2: Dogovorjeni simbolni zapis dimenzije osnovne veličine je enojna velika tiskana črka v pisavi latinici (pokončni).
Dogovorjeni simbolni zapis dimenzije izpeljane veličine je zmnožek potenc dimenzij osnovnih veličin skladno z
definicijo izpeljane veličine. Dimenzija veličine Q je označena z dim Q.
OPOMBA 3: Pri izpeljavi dimenzije veličine ni upoštevan njen skalarni, vektorski ali tenzorski značaj.
OPOMBA 4: V danem sistemu veličin:
– imajo istovrstne veličine enako dimenzijo veličine,
– so veličine različnih dimenzij vedno različne vrste in
– ni nujno, da so veličine z enako dimenzijo istovrstne.
OPOMBA 5: Simboli, ki v sistemu ISQ označujejo dimenzije osnovnih veličin, so:
Osnovna veličina Simbol za dimenzijo
dolžina L
masa M
čas T
električni tok I
termodinamična temperatura Θ
množina snovi N
svetilnost J
α β γ δ ε ζ η
Tako se dimenzija veličine Q označuje z dim Q = L M T IΘ N J , pri čemer so t.i. dimenzijski eksponenti
pozitivni, negativni ali nič. Faktorji z eksponentom nič in 1 se ponavadi izpustijo. Kadar so vsi eksponenti nič,
glej 3.8.
OPOMBA 6: Prirejeno po Vodilu ISO/IEC 99:2007, definicija 1.7, v kateri so opomba 5 in primera 2 in 3 drugačni in je izraz
"dimenzija" naveden kot dopusten izraz.
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SIST ISO 80000-1 : 2013
3.8
veličina z dimenzijo ena
brezdimenzijska veličina
veličina, pri kateri so vsi eksponenti faktorjev, ki ustrezajo osnovnim veličinam v njeni dimenziji veličine, nič.
OPOMBA 1: Izraz "brezdimenzijska veličina" se uporablja v vsakdanjem govoru in je v tem dokumentu ohranjen iz
zgodovinskih razlogov. Izhaja iz dejstva, da so v simbolnem zapisu dimenzije takih veličin vsi eksponenti nič.
Izraz "veličina z dimenzijo ena" odraža dogovor, po katerem je simbolni zapis dimenzije za take veličine simbol
1, glej točko 5. Ta dimenzija ni število, temveč je nevtralni element za množenje dimenzij.
OPOMBA 2: Merske enote in vrednosti veličin z dimenzijo ena so števila, vendar take veličine posredujejo več informacij kot število.
OPOMBA 3: Nekatere veličine z dimenzijo ena so definirane kot razmerja med dvema istovrstnima veličinama. Koherentna
izpeljana enota je število ena, simbol 1.
PRIMERI: Ravninski kot, prostorski kot, lomni količnik, relativna prepustnost, masni delež, faktor trenja,
Machovo število.
OPOMBA 4: Števila osnovnih delcev so veličine z dimenzijo ena.
PRIMERI: Število navojev tuljave, število molekul v danem vzorcu, degeneracija energijskih nivojev v kvantnem
sistemu.
OPOMBA 5: Prirejeno po Vodilu ISO/IEC 99:2007, definicija 1.8, v kateri sta opombi 1 in 3 drugačni in je izraz
"brezdimenzijska veličina" naveden kot dopusten izraz.
3.9
merska enota
enota
dogovorno določena in sprejeta realna skalarna veličina, s katero se lahko primerja vsaka druga
istovrstna veličina, da se izrazi številčno razmerje med obema veličinama
OPOMBA 1: Merske enote so označene z dogovorno dodeljenimi imeni in simboli.
OPOMBA 2: Merske enote veličin z enako dimenzijo veličine so lahko označene z enakim imenom in simbolom, tudi če
veličine niso istovrstne. Tako se na primer ime joule na kelvin in simbol J/K uporabljata tako za mersko enoto
entalpije kot za mersko enoto entropije, ki se na splošno ne štejeta za istovrstni veličini. Nasprotno pa je v
nekaterih primerih uporaba posebnih imen merskih enot omejena izključno na veličine posebne vrste. Tako se
na primer merska enota "sekunda na minus ena" (1/s) imenuje hertz (Hz), kadar se uporablja za frekvenco, in
becquerel (Bq), kadar se uporablja za aktivnosti radionuklidov. Kot drugi primer se na primer joule (J) uporablja
kot enota za energijo, nikoli pa kot enota za moment sile, tj. newton meter (N ⋅ m).
OPOMBA 3: Merske enote za veličine z dimenzijo ena so števila. V nekaterih primerih se tem merskim enotam dodelijo
posebna imena, npr. radian, steradian in decibel, ali pa so izražene s količniki, kot npr. milimol na mol enako
–3 –9
10 in mikrogram na kilogram enako 10 .
OPOMBA 4: Za dano veličino se krajši izraz "enota" pogosto kombinira z imenom veličine kot na primer "enota mase" ali
"enota za maso".
OPOMBA 5: Prirejeno po Vodilu ISO/IEC 99:2007, definicija 1.9, v kateri sta definicija in opomba 2 nekoliko drugačni in je
izraz "enota" naveden kot dopusten izraz.
3.10
osnovna enota
merska enota, ki je dogovorno sprejeta za osnovno veličino
OPOMBA 1: V vsakem koherentnem sistemu enot je za vsako osnovno veličino samo ena osnovna enota.
PRIMER: V sistemu SI je osnovna enota za dolžino meter. V sistemih CGS pa je osnovna enota za dolžino centimeter.
OPOMBA 2: Osnovna enota se lahko uporabi tudi za izpeljano veličino z enako dimenzijo veličine.
PRIMER: Kadar je izpeljana veličina množina dežja definirana kot površinska prostornina (prostornina na
površino), ima v sistemu SI kot koherentno izpeljano enoto meter.
OPOMBA 3: Pri številu osnovnih delcev se lahko v vsakem sistemu enot število ena, simbol 1, šteje za osnovno enoto.
Primerjaj z opombo 3 v točki 3.4.
OPOMBA 4: Prirejeno po Vodilu ISO/IEC 99:2007, definicija 1.10, v kateri je primer pri opombi 2 nekoliko drugačen. Pri
opombi 3 je dodan zadnji stavek.
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SIST ISO 80000-1 : 2013
3.11
izpeljana enota
merska enota za izpeljano veličino
PRIMERI: Meter na sekundo, simbol m/s, in centimeter na sekundo, simbol cm/s, sta v sistemu SI izpeljani enoti za hitrost.
Kilometer na uro, simbol km/h, je merska enota za hitrost zunaj sistema SI, ki pa je sprejet za uporabo z enotami SI. Vozel,
enak eni navtični milji na uro, je merska enota za hitrost zunaj sistema SI.
[Vodilo ISO/IEC 99:2007, 1.11]
3.12
koherentna izpeljana enota
izpeljana enota, ki je pri danem sistemu veličin in izbranem nizu osnovnih enot zmnožek potenc
osnovnih enot, s tem da je sorazmernostni faktor lahko samo ena
OPOMBA 1: Potenca osnovne enote je osnovna enota na eksponent.
OPOMBA 2: Soodvisnost (koherenco) je mogoče določiti samo glede na izbrani sistem veličin in na dani niz osnovnih enot.
PRIMERI: Če so meter, sekunda in mol osnovne enote, potem je meter na sekundo koherentna izpeljana enota
za hitrost, kadar je hitrost definirana z veličinsko enačbo υ = dr/dt, mol na kubični meter pa je koherentna
izpeljana enota za množinsko koncentracijo, kadar je množinska koncentracija definirana z veličinsko enačbo c
= n/V. Kilometer na uro in vozel, ki sta v točki 3.11 podana kot primera izpeljanih enot, v takem sistemu veličin
nista koherentni izpeljani enoti.
OPOMBA 3: Izpeljana enota je lahko koherentna glede na en sistem veličin, ne pa tudi glede na drugega.
PRIMER: Centimeter na sekundo je v sistemu enot CGS koherentna izpeljana enota za hitrost, ni pa
koherentna izpeljana enota v sistemu SI.
OPOMBA 4: Koherentna izpeljana enota za vsako izpeljano veličino z dimenzijo ena v danem sistemu enot je število ena s
simbolom 1. Ime in simbol za mersko enoto ena na splošno nista navedena.
[Vodilo ISO/IEC 99:2007, 1.12]
3.13
sistem enot
niz osnovnih in izpeljanih enot, njihovih večkratnikov in manjkratnikov, ki je za dani sistem veličin
definiran v skladu z danimi pravili
[Vodilo ISO/IEC 99:2007, 1.13]
3.14
koherentni sistem enot
sistem enot, temelječ na danem sistemu veličin, v katerem je merska enota za vsako izpeljano veličino
koherentna izpeljana enota
PRIMER: Niz koherentnih enot SI in povezave med njimi.
OPOMBA 1: Sistem enot je lahko koherenten samo glede na sistem veličin in na privzete osnovne enote.
OPOMBA 2: Pri koherentnem sistemu enot imajo številske enačbe enako obliko kot ustrezne veličinske enačbe, vključno s
številskimi faktorji. Glej primere številskih enačb v točki 3.25.
OPOMBA 3: Prirejeno po Vodilu ISO/IEC 99:2007, definicija 1.14, v kateri je opomba 2 drugačna.
3.15
zunajsistemska merska enota
zunajsistemska enota
merska enota, ki ne pripada danemu sistemu enot
–19
1. PRIMER: Elektronvolt (≈ 1,602 18 × 10 J) je z vidika SI zunajsistemska merska enota za energijo.
2. PRIMER: Dan, ura, minuta so z vidika SI zunajsistemske enote za čas.
OPOMBA: Prirejeno po Vodilu ISO/IEC 99:2007, definicija 1.15, v kateri je 1. primer drugačen in je izraz "zunajsistemska
enota" naveden kot dopusten izraz.
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SIST ISO 80000-1 : 2013
3.16
mednarodni sistem enot
SI
sistem enot, temelječ na mednarodnem sistemu veličin, ki ga sestavljajo imena in simboli enot, nabor
predpon z njihovimi imeni in simboli ter pravila za njihovo uporabo in ga je sprejela Generalna
konferenca za uteži in mere (CGPM)
OPOMBA 1: SI temelji na sedmih osnovnih veličinah ISQ ter na imenih in simbolih ustrezajočih osnovnih enot, glej 6.5.2.
OPOMBA 2: Osnovne enote in koherentne izpeljane enote SI tvorijo koherenten niz, imenovan "niz koherentnih enot SI".
OPOMBA 3: Za
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