Quantities and units - Part 1: General (ISO 80000-1:2009 + Cor 1:2011)

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.

Größen und Einheiten - Teil 1: Allgemeines (ISO 80000-1:2009 + Cor 1:2011)

ISO 80000-1 gibt allgemeine Informationen und Definitionen bezüglich Größen, Größensystemen, Einheiten, Formelzeichen für Größen und Einheiten sowie kohärenten Einheitensystemen, speziell des Internationalen Größensystems ISQ und des Internationalen Einheitensystems SI.
Die in ISO 80000-1 festgelegten Prinzipien sind für allgemeinen Gebrauch innerhalb der unterschiedlichen Gebiete von Wissenschaft und Technik gedacht sowie als Einführung in andere Teile dieser Internationalen Norm.
Ordinalmerkmale und Nominalmerkmale sind außerhalb des Anwendungsbereichs von ISO 80000-1.

Grandeurs et unités - Partie 1: Généralités (ISO 80000-1:2009 + Cor 1:2011)

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 (ISO 80000-1:2009 + Popravek 1:2011)

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 tehnologije ter kot uvod v druge dele tega mednarodnega standarda. Vrstilne veličine in nominalne lastnosti ne spadajo na področje uporabe standarda ISO 80000-1.

General Information

Status
Published
Publication Date
02-Apr-2013
Technical Committee
Current Stage
6060 - Definitive text made available (DAV) - Publishing
Due Date
03-Apr-2013
Completion Date
03-Apr-2013

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SLOVENSKI STANDARD
SIST EN ISO 80000-1:2013
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
SIST EN ISO 80000-1:2013 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 80000-1:2013
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SIST EN ISO 80000-1:2013
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.
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SIST EN ISO 80000-1:2013
EN ISO 80000-1:2013 (E)
Contents Page

Foreword ....................................................................................................................................................... 3

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SIST EN ISO 80000-1:2013
EN ISO 80000-1:2013 (E)
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

EN ISO 80000-1:2013.

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.
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SIST EN ISO 80000-1:2013
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SIST EN 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 EN ISO 80000-1:2013
ISO 80000-1:2009(E)
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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,

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Published in Switzerland
ii © ISO 2009 – All rights reserved
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SIST EN 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

© ISO 2009 – All rights reserved iii
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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
iv © ISO 2009 – All rights reserved
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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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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.

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

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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SIST EN ISO 80000-1:2013
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)
wavelength, λ wavelength of the sodium D radiation, λ or λ(Na; D)
energy, E kinetic energy, T kinetic energy of particle i in a given system, T
heat, Q heat of vaporization of sample i of water, Q
electric charge, Q electric charge of the proton, e
electric resistance, R electric resistance of resistor i in a given circuit, R

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,

C(Erys; B )
Rockwell C hardness of steel sample i, HRC (150 kg)
Rockwell C hardness (150 kg load),
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

EXAMPLE 1 In the ISQ, the quantity dimension of force is denoted by dim F = LMT .

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EXAMPLE 2 In the same system of quantities, dim ρ = ML is the quantity dimension of mass concentration of

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() =
−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 syste
...

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