EN ISO 80000-1:2013

SLOVENSKI STANDARD
01-junij-2013
1DGRPHãþD
SIST ISO 1000+A1:2008
SIST ISO 31-0+A1+A2:2007
9HOLþLQHLQHQRWHGHO6SORãQR,623RSUDYHN
Quantities and units - Part 1: General (ISO 80000-1:2009 + Cor 1:2011)
Größen und Einheiten - Teil 1: Allgemeines (ISO 80000-1:2009 + Cor 1:2011)
Grandeurs et unités - Partie 1: Généralités (ISO 80000-1:2009 + Cor 1:2011)
Ta slovenski standard je istoveten z: EN ISO 80000-1:2013
ICS:
01.060 9HOLþLQHLQHQRWH Quantities and units
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 80000-1
NORME EUROPÉENNE
EUROPÄISCHE NORM
April 2013
ICS 01.060
English Version
Quantities and units - Part 1: General (ISO 80000-1:2009 + Cor
1:2011)
Grandeurs et unités - Partie 1: Généralités (ISO 80000- Größen und Einheiten - Teil 1: Allgemeines (ISO 80000-
1:2009 + Cor 1:2011) 1:2009 + Cor 1:2011)
This European Standard was approved by CEN on 14 March 2013.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member.

This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same
status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United
Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2013 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 80000-1:2013: E
worldwide for CEN national Members.

Contents Page
Foreword . 3

Foreword
The text of ISO 80000-1:2009 + Cor 1:2011 has been prepared by Technical Committee ISO/TC 12
“Quantities and units” of the International Organization for Standardization (ISO) and has been taken over as
This European Standard shall be given the status of a national standard, either by publication of an identical
text or by endorsement, at the latest by October 2013, and conflicting national standards shall be withdrawn at
the latest by October 2013.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech
Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece,
Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
Endorsement notice
The text of ISO 80000-1:2009 + Cor 1:2011 has been approved by CEN as EN ISO 80000-1:2013 without any
modification.
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
ISO 80000-1:2009(E)
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ii © ISO 2009 – All rights reserved

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

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
iv © ISO 2009 – All rights reserved

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

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
vacuum) is defined to be equal to 1, i.e. of dimension one; in the CGS-EMU system, the magnetic constant µ
(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).
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
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”).
2 © ISO 2009 – All rights reserved

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 .
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.
4 © ISO 2009 – All rights reserved

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]
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 units, based on a given system of quantities, in which the measurement unit for each derived
quantity is a coherent derived unit
EXAMPLE Set of coherent SI units and relations between them.
NOTE 1 A system of units can be coherent only with respect to a system of quantities and the adopted base units.
NOTE 2 For a coherent system of units, numerical value equations have the same form, including numerical factors, as
the corresponding quantity equations. See examples of numerical value equations in 3.25.
NOTE 3 Adapted from ISO/IEC Guide 99:2007, definition 1.14, in which Note 2 is different.
3.15
off-system measurement unit
off-system unit
measurement unit that does not belong to a given system of units
–19
EXAMPLE 1 The electronvolt (≈ 1,602 18 × 10 J) is an off-system measurement unit of energy with respect to the
SI.
EXAMPLE 2 Day, hour, minute are off-system measurement units of time with respect to the SI.
NOTE Adapted from ISO/IEC Guide 99:2007, definition 1.15, in which Example 1 is different and in which “off-system
unit” is given as an admitted term.
6 © ISO 2009 – All rights reserved

ISO 80000-1:2009(E)
3.16
International System of Units
SI
system of units, based on the International System of Quantities, their names and symbols, including a series
of prefixes and their names and symbols, together with rules for their use, adopted by the General Conference
on Weights and Measures (CGPM)
NOTE 1 The SI is founded on the seven base quantities of the ISQ and the names and symbols of the corresponding
base units, see 6.5.2.
NOTE 2 The base units and the coherent derived units of the SI form a coherent set, designated the “set of coherent SI
units”.
NOTE 3 For a full description and explanation of the International System of Units, see edition 8 of the SI brochure
published by the Bureau International des Poids et Mesures (BIPM) and available on the BIPM website.
NOTE 4 In quantity calculus, the quantity ‘number of entities’ is often considered to be a base quantity, with the base
unit one, symbol 1.
NOTE 5 For the SI prefixes for multiples of units and submultiples of units, see 6.5.4.
NOTE 6 Adapted from ISO/IEC Guide 99:2007, definition 1.16, in which Notes 1 and 5 are different.
3.17
multiple of a unit
measurement unit obtained by multiplying a given measurement unit by an integer greater than one
EXAMPLE 1 The kilometre is a decimal multiple of the metre.
EXAMPLE 2 The hour is a non-decimal multiple of the second.
NOTE 1 SI prefixes for decimal multiples of SI base units and SI derived units are given in 6.5.4.
NOTE 2 SI prefixes refer strictly to powers of 10, and should not be used for powers of 2. For example, 1 kbit should
not be used to represent 1024 bits (2 bits), which is a kibibit (1 Kibit).
Prefixes for binary multiples are:
Prefix
Factor Value
Name Symbol
10 8
(2 ) 1 208 925 819 614 629 174 706 176 yobi Yi

10 7
(2 ) 1 180 591 620 717 411 303 424 zebi Zi

10 6
(2 ) 1 152 921 504 606 846 976 exbi Ei

10 5
1 125 899 906 842 624 pebi Pi
(2 )
10 4
1 099 511 627 776 tebi Ti
(2 )
10 3
(2 ) 1 073 741 824 gibi Gi
10 2
(2 ) 1 048 576 mebi Mi
10 1
1 024 kibi Ki
(2 )
Source: IEC 80000-13:2008.
NOTE 3 Adapted from ISO/IEC Guide 99:2007, definition 1.17, in which Notes 1 and 2 are different.
ISO 80000-1:2009(E)
3.18
submultiple of a unit
measurement unit obtained by dividing a given measurement unit by an integer greater than one
EXAMPLE 1 The millimetre is a decimal submultiple of the metre.
EXAMPLE 2 For plane angle, the second is a non-decimal submultiple of the minute.
NOTE SI prefixes for decimal submultiples of SI base units and SI derived units are given in 6.5.4.
[ISO/IEC Guide 99:2007, 1.18]
3.19
quantity value
value of a quantity
value
number and reference together expressing magnitude of a quantity
EXAMPLE 1 Length of a given rod: 5,34 m or 534 cm
EXAMPLE 2 Mass of a given body: 0,152 kg or 152 g

−1
EXAMPLE 3 Curvature of a given arc: 112 m
EXAMPLE 4 Celsius temperature of a given sample: −5 °C
EXAMPLE 5 Electric impedance of a given circuit element at a given frequency,
where j is the imaginary unit: (7 + 3j) Ω
EXAMPLE 6 Refractive index of a given sample of glass: 1,32
EXAMPLE 7 Rockwell C hardness of a given sample (150 kg load): 43,5 HRC(150 kg)

−9
EXAMPLE 8 Mass fraction of cadmium in a given sample of copper: 3 µg/kg or 3 × 10
2+
EXAMPLE 9 Molality of Pb in a given sample of water: 1,76 µmol/kg
EXAMPLE 10 Amount-of-substance concentration of lutropin in a given 5,0 IU/l (WHO
sample of plasma (WHO international standard 80/552): International Units per litre)
NOTE 1 According to the type of reference, a quantity value is either
⎯ a product of a number and a measurement unit (see Examples 1, 2, 3, 4, 5, 8 and 9); the measurement unit one is
generally not indicated for quantities of dimension one (see Examples 6 and 8), or
⎯ a number and a reference to a measurement procedure (see Example 7), or
⎯ a number and a reference material (see Example 10).
NOTE 2 The number can be complex (see Example 5).
NOTE 3 A quantity value can be presented in more than one way (see Examples 1, 2 and 8).
NOTE 4 In the case of vector or tensor quantities, each component has a quantity value.
EXAMPLE Force acting on a given particle, e.g. in Cartesian components (F ; F ; F ) = (−31,5; 43,2; 17,0) N, where
x y z
(−31,5; 43,2; 17,0) is a numerical-value vector and N (newton) is the unit, or (F ; F ; F ) = (−31,5 N; 43,2 N; 17,0 N)
x y z
where each component is a quantity.
NOTE 5 Adapted from ISO/IEC Guide 99:2007, definition 1.19, in which Example 10 and Note 4 are different and in
which “value of a quantity” and “value” are given as admitted terms.
8 © ISO 2009 – All rights reserved

ISO 80000-1:2009(E)
3.20
numerical quantity value
numerical value of a quantity
numerical value
number in the expression of a quantity value, other than any number serving as the reference
NOTE 1 For quantities of dimension one, the reference is a measurement unit which is a number and this is not
considered as a part of the numerical quantity value.
EXAMPLE In an amount-of-substance fraction equal to 3 mmol/mol, the numerical quantity value is 3 and the unit is
mmol/mol. The unit mmol/mol is numerically equal to 0,001, but this number 0,001 is not part of the numerical
quantity value, which remains 3.
NOTE 2 For quantities that have a measurement unit (i.e. those other than ordinal quantities), the numerical value
{Q} of a quantity Q is frequently denoted {Q} = Q/[Q], where [Q] denotes the measurement unit.
EXAMPLE For a quantity value of m = 5,721 kg, the numerical quantity value is {m} = (5,721 kg)/kg = 5,721. The
same quantity value can be expressed as 5 721 g in which case the numerical quantity value
{m} = (5 721 g)/g = 5 721. See 3.19.
NOTE 3 Adapted from ISO/IEC Guide 99:2007, definition 1.20, in which Note 2 is different and in which “numerical
value of a quantity” and “numerical value” are given as an admitted terms.
3.21
quantity calculus
set of mathematical rules and operations applied to quantities other than ordinal quantities
NOTE In quantity calculus, quantity equations are preferred to numerical value equations because quantity equations
are independent of the choice of measurement units, whereas numerical value equations are not (see also 4.2 and 6.3).
[ISO/IEC Guide 99:2007, 1.21]
3.22
quantity equation
mathematical relation between quantities in a given system of quantities, independent of measurement units
EXAMPLE 1 Q = ζ Q Q where Q , Q and Q denote different quantities, and where ζ is a numerical factor.

1 2 3 1 2 3
EXAMPLE 2 T = (1/2) mv , where T is the kinetic energy and v is the speed of a specified particle of mass m.
EXAMPLE 3 n = It / F where n is the amount of substance of a univalent component, I is the electric current and t is
the duration of the electrolysis, and F is the Faraday constant.
[ISO/IEC Guide 99:2007, 1.22]
3.23
unit equation
mathematical relation between base units, coherent derived units or other measurement units
EXAMPLE 1 For the quantities in Example 1 of item 3.22, [Q ] = [Q ] [Q ] where [Q ], [Q ] and [Q ] denote the
1 2 3 1 2 3
measurement units of Q , Q and Q , respectively, provided that these measurement units are in a coherent system of
1 2 3
units.
2 2
EXAMPLE 2 J := kg m /s , where J, kg, m, and s are the symbols for the joule, kilogram, metre, and second,
respectively. (The symbol := denotes “is by definition equal to” as given in ISO 80000-2:2009, item 2-7.3.)
EXAMPLE 3 1 km/h = (1/3,6) m/s.
NOTE Adapted from ISO/IEC Guide 99:2007, definition 1.23, in which the Example 2 is different.
ISO 80000-1:2009(E)
3.24
conversion factor between units
ratio of two measurement units for quantities of the same kind
EXAMPLE km/m = 1 000 and thus 1 km = 1 000 m.
NOTE The measurement units may belong to different systems of units.
EXAMPLE 1 h/s = 3 600 and thus 1 h = 3 600 s.
EXAMPLE 2 (km/h)/(m/s) = (1/3,6) and thus 1 km/h = (1/3,6) m/s
[ISO/IEC Guide 99:2007, 1.24]
3.25
numerical value equation
numerical quantity value equation
mathematical relation between numerical quantity values, based on a given quantity equation and specified
measurement units
EXAMPLE 1 For the quantities in the first example in item 3.22, {Q } = ζ {Q } {Q } where {Q }, {Q } and {Q } denote the

1 2 3 1 2 3
numerical values of Q , Q and Q , respectively, provided that they are expressed in base units or coherent derived units
...