# FprEN ISO 80000-1

(Main)## Quantities and units - Part 1: General (ISO/FDIS 80000-1:2022)

## Quantities and units - Part 1: General (ISO/FDIS 80000-1:2022)

This document 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).

The principles laid down in this document are intended for general use within the various fields of science and technology, and as an introduction to other parts of this International Standard.

The ISO/IEC 80000 series does not, as yet, cover ordinal quantities and nominal properties.

## Größen und Einheiten - Teil 1: Allgemeines (ISO/FDIS 80000‑1:2022)

Dieses Dokument enthält allgemeine Informationen und Definitionen zu Größen, Größensystemen, Einheiten, Formelzeichen für Größen und Einheiten sowie zu kohärenten Einheitensystemen, insbesondere zum Internationalen Größensystem (ISQ, en: International System of Quantities).

Die in diesem Dokument festgelegten Grundsätze sind für den allgemeinen Gebrauch innerhalb der unterschiedlichen Gebiete von Wissenschaft und Technik vorgesehen sowie als Einführung in andere Teile dieser Internationalen Norm.

Ordinalmerkmale (en: ordnial quantities) und Nominalmerkmale (en: nominal properties) werden von der Normenreihe ISO/IEC 80000 bisher nicht abgedeckt.

## Grandeurs et unités - Partie 1 : Généralités (ISO/FDIS 80000-1:2022)

Le présent document 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).

Les principes établis dans le présent document 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.

La série ISO/IEC 80000 ne couvre pas, à l’heure actuelle, les grandeurs ordinales et les propriétés qualitatives.

## Veličine in enote - 1. del: Splošno (ISO/FDIS 80000-1:2022)

### General Information

### RELATIONS

### Standards Content (sample)

SLOVENSKI STANDARD

oSIST prEN ISO 80000-1:2022

01-april-2022

Veličine in enote - 1. del: Splošno (ISO/DIS 80000-1:2022)

Quantities and units - Part 1: General (ISO/DIS 80000-1:2022)

Größen und Einheiten – Teil 1: Allgemeines (ISO/DIS 80000-1:2022)

Grandeurs et unités - Partie 1 : Généralités (ISO/DIS 80000-1:2022)

Ta slovenski standard je istoveten z: prEN ISO 80000-1

ICS:

01.060 Veličine in enote Quantities and units

oSIST prEN ISO 80000-1:2022 en,fr,de

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

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oSIST prEN ISO 80000-1:2022

DRAFT INTERNATIONAL STANDARD

ISO/DIS 80000-1

ISO/TC 12 Secretariat: SIS

Voting begins on: Voting terminates on:

2022-01-28 2022-04-22

Quantities and units —

Part 1:

General

Grandeurs et unités —

Partie 1: Généralités

ICS: 01.060

This document is circulated as received from the committee secretariat.

This draft is submitted to a parallel vote in ISO and in IEC.

THIS DOCUMENT IS A DRAFT CIRCULATED

FOR COMMENT AND APPROVAL. IT IS

ISO/CEN PARALLEL PROCESSING

THEREFORE SUBJECT TO CHANGE AND MAY

NOT BE REFERRED TO AS AN INTERNATIONAL

STANDARD UNTIL PUBLISHED AS SUCH.

IN ADDITION TO THEIR EVALUATION AS

BEING ACCEPTABLE FOR INDUSTRIAL,

TECHNOLOGICAL, COMMERCIAL AND

USER PURPOSES, DRAFT INTERNATIONAL

STANDARDS MAY ON OCCASION HAVE TO

BE CONSIDERED IN THE LIGHT OF THEIR

POTENTIAL TO BECOME STANDARDS TO

WHICH REFERENCE MAY BE MADE IN

Reference number

NATIONAL REGULATIONS.

ISO/DIS 80000-1:2022(E)

RECIPIENTS OF THIS DRAFT ARE INVITED

TO SUBMIT, WITH THEIR COMMENTS,

NOTIFICATION OF ANY RELEVANT PATENT

RIGHTS OF WHICH THEY ARE AWARE AND TO

PROVIDE SUPPORTING DOCUMENTATION. © ISO 2022

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COPYRIGHT PROTECTED DOCUMENT

© ISO 2022

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on

the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below

or ISO’s member body in the country of the requester.ISO copyright office

CP 401 • Ch. de Blandonnet 8

CH-1214 Vernier, Geneva

Phone: +41 22 749 01 11

Email: copyright@iso.org

Website: www.iso.org

Published in Switzerland

© ISO 2022 – All rights reserved

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Contents Page

Foreword ........................................................................................................................................................................................................................................iv

0 Introduction ..........................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ..................................................................................................................................................................................... 1

3 Terms and definitions .................................................................................................................................................................................... 1

4 Quantities .................................................................................................................................................................................................................... 1

4.1 The concept of quantity .................................................................................................................................................................. 1

4.2 System of quantities ─ Base quantities and derived quantities ................................................................. 2

4.3 Universal constants and empirical constants ............................................................................................................ 2

4.4 Constant multipliers in quantity equations.................................................................................................................. 2

4.5 International System of Quantities, ISQ ........................................................................................................................... 3

5 Dimensions ................................................................................................................................................................................................................3

6 Units................................................................................................................................................................................................................................... 4

6.1 Units and numerical values ......................................................................................................................................................... 4

6.2 Mathematical operations .............................................................................................................................................................. 5

6.3 Quantity equations and numerical value equations ............................................................................................. 5

6.4 Coherent systems of units ............................................................................................................................................................ 6

7 Printing rules ..........................................................................................................................................................................................................6

7.1 Symbols for quantities ..................................................................................................................................................................... 6

7.1.1 General ........................................................................................................................................................................................ 6

7.1.2 Subscripts ................................................................................................................................................................................. 7

7.1.3 Combination of symbols for quantities .......................................................................................................... 7

7.1.4 Expressions for quantities ......................................................................................................................................... 8

7.1.5 Expressions for dimensions ..................................................................................................................................... 9

7.2 Numbers ....................................................................................................................................................................................................... 9

7.2.1 General ........................................................................................................................................................................................ 9

7.2.2 Decimal sign ........................................................................................................................................................................... 9

7.2.3 Multiplication and division .................................................................................................................................... 10

7.2.4 Error and uncertainty ................................................................................................................................................ 11

7.3 Chemical elements and nuclides ..........................................................................................................................................12

7.4 Greek alphabet ..................................................................................................................................................................................... 13

Annex A (normative) Specific terms used for quantities ............................................................................................................14

Annex B (normative) Rounding of numbers .............................................................................................................................................18

Bibliography .............................................................................................................................................................................................................................20

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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.The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www.iso.org/patents).Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to

the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see

www.iso.org/iso/foreword.html.This document was prepared by Technical Committee ISO/TC 12, Quantities and units in co-operation

with IEC/TC 25, Quantities and units.This second edition cancels the first edition (ISO 80000-1:2009), which has been technically revised.

The main changes are as follows:— More focus on concepts and terminology based on a system of quantities, particularly following the

recent major revision of the International System of Units (SI) and the proposed revisions of the

International vocabulary of metrology (VIM).— At the same time, sections of previous editions of this Standard which essentially reproduced content

from other sources – particularly metrological vocabulary, descriptions of SI units and compilations

of fundamental constants – have been substantially removed from the present edition, in accord

with an ISO/TC 12 CIB 2020.A list of all parts in the ISO 80000 and IEC 80000 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www.iso.org/members.html.© ISO 2022 – All rights reserved

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0 Introduction

0.1 Quantities

Systems of quantities – as defined in the ISO/IEC Guide 99 (VIM) – can be treated in many consistent,

but different, ways. Which treatment to use is partly a matter of convention.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.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.The system of quantities presented in this International Standard 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, the ISQ does appear in ISO/IEC Guide 99 and is the system

of quantities underlying the International System of Units, denoted “SI”, in all languages. It should

be realized that the ISQ is an essentially infinite and continually evolving and expanding system of

quantities and equations on which all of modern science and technology rests.0.2 Arrangement of the tables

In parts 3 to 14 of this International Standard, the quantities and relations among them, which are a

[1]subset of the ISQ, are given and the units of the SI (and some other units) are given in tables. Some

additional quantities and units are also given. The item numbers of quantities are written pp-nn.s (pp,

part number; nn, running number in the part, respectively; s, sub-number).© ISO 2022 – All rights reserved

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DRAFT INTERNATIONAL STANDARD ISO/DIS 80000-1:2022(E)

Quantities and units —

Part 1:

General

1 Scope

This document 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.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.

The ISO 80000 series does not, as yet, cover ordinal quantities and nominal properties.

2 Normative referencesThe 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, International vocabulary of metrology — Basic and general concepts and associated

terms (VIM)3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO/IEC Guide 99 apply.

4 Quantities4.1 The concept of quantity

In this International Standard, it is accepted that things (including physical bodies and phenomena,

substances, events, etc.) are characterized by properties, according to which things can be compared,

in terms of having the same property or not, as is the case for rigid bodies about their shape and for

human beings about having the same blood type or not. Some properties make things comparable

also by order, so that for example winds can be compared by their strength and earthquakes can be

compared by their magnitude. Finally, some properties make things comparable not only in terms of

equivalence and order, but also in more complex ways, and in particular by ratio, as is the case for most

physical quantities, according to which the mass or the electric charge of a body might be twice the

mass or the electric charge of another body, and so on.Not all properties, and more specifically quantities, can be compared with each other. For example,

while the diameter of a cylindrical rod can be compared to the height of a block, the diameter of a rod

cannot be compared to the mass of a block.[2]

Quantities that are comparable are said to be of the same kind and are instances of the same general

quantity. Hence diameters and heights are quantities of the same kind, being instances of the general

quantity length.© ISO 2022 – All rights reserved

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It is customary to use the same term, "quantity", to refer to both general quantities, such as length, mass,

etc., and their instances, such as given lengths, given masses, etc. Accordingly, we are used to saying

both that length is a quantity and that a given length is a quantity, by maintaining the specification –

"general quantity" or "individual quantity" – implicit and exploiting the linguistic context to remove the

ambiguity.4.2 System of quantities ─ Base quantities and derived quantities

General quantities are related through equations that express laws of nature or define new general

quantities. Each equation between quantities is called a quantity equation.It is convenient to consider some quantities of different kinds as mutually independent. Such quantities

are called base quantities. Other quantities, called derived quantities, are defined or expressed in terms

of base quantities by means of equations.It is a matter of choice how many and which quantities are considered to be base quantities. It is also a

matter of choice which equations are used to define the derived quantities. Each set of non-contradictory

equations between quantities is called a system of quantities.4.3 Universal constants and empirical constants

Some individual quantities are considered to be constant under all circumstances. Such quantities are

called universal constants or fundamental physical constants.[3]

EXAMPLE 1 The Planck constant, ħ .

[3]

EXAMPLE 2 The Faraday constant, F .

Other quantities may be constant under some circumstances but depend on others. Their values are

generally obtained by measurement. They are called empirical constants.EXAMPLE 3

The result of measuring at a certain station the length l and the periodic time T, for each of several particle

pendulums, can be expressed by one quantity equationTC= l

where C is an empirical constant that depends on the location.

Theory shows that

C =

where g is the local acceleration of free fall, which is another empirical constant.

4.4 Constant multipliers in quantity equationsEquations between quantities sometimes contain constant multipliers. These multipliers depend on the

definitions chosen for the quantities occurring in the equations, i.e., on the system of quantities chosen.

Such multipliers may be purely numerical and are then called numerical factors.EXAMPLE 1

In a three-dimensional quantity system, where length, mass, and time are three base quantities, the kinetic

energy of a particle in classical mechanics isTm= v

where T is kinetic energy, m is mass and v is speed. This equation contains the numerical factor .

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A multiplier may include one or more universal (or empirical) constants.

EXAMPLE 2

In the three-dimensional quantity system, the Coulomb law for electric charges is

F =where F is scalar force, q and q are two electric charges, r is distance.

1 2

For a rationalised four-dimensional quantity system, where at least one base quantity of an electrical nature

is added, the expression becomesF =

4πε

[1]

where ε is since the 2019 redefinition of SI base units , an empirical constant, i.e., the electric constant (it

was formerly a universal constant).A multiplier may also include one or more conventional quantity values.

Constant multipliers other than numerical factors are often called coefficients.

4.5 International System of Quantities, ISQ

The special choice of base quantities and quantity equations, including multipliers, given in ISO 80000

and IEC 80000 defines the International System of Quantities, denoted “ISQ” in all languages. Derived

quantities can be defined in terms of the base units by quantity equations. There are seven base

quantities in the ISQ: length, mass, time, electric current, thermodynamic temperature, amount of

substance, and luminous intensity.5 Dimensions

In the system of quantities under consideration, the relation between any general quantity Q and the

base quantities can be expressed by means of an equation. The equation may include a sum of terms,

each of which can be expressed as a product of powers of base quantities A, B, C, … from a chosen set,

α β γsometimes multiplied by a numerical factor ξ, i.e., ξ · A B C …, where the set of exponents α, β, γ, … is the

same for each term.The dimension of the quantity Q is then expressed by the dimensional product

α β γ

dim Q = A B C …

where A, B, C, … denote the dimensions of the base quantities A, B, C, …, respectively, and α, β, γ, … are

called the dimensional exponents.Quantities that are of the same kind (e.g., length) have the same dimension, even if they are originally

expressed in different units (such as yards and metres). If quantities have different dimensions (such as

[2,4] [5]length vs. mass), they are of different kinds and cannot be compared .

A quantity whose dimensional exponents are all equal to zero has the dimensional product denoted

0 0 0A B C … = 1, where the symbol 1 denotes the corresponding dimension. There is no agreement on how

to refer to such quantities. They have been called dimensionless quantities (although this term should

now be avoided), quantities with dimension one, quantities with dimension number, or quantities with

the unit one. Such quantities are dimensionally simply numbers. To avoid confusion, it is helpful to use

[1]explicit units with these quantities where possible, e.g., m/m, nmol/mol, rad . It is especially important

to have a clear description of any such quantity when expressing a measurement result.

NOTE 1 These quantities include those defined as a quotient of two quantities of the same dimension and

those defined as numbers of entities.© ISO 2022 – All rights reserved

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In the ISQ, with the seven base quantities length, mass, time, electric current, thermodynamic

temperature, amount of substance and luminous intensity, the dimensions of the base quantities are

denoted by L, M, T, I, Θ, N and J, respectively. Hence, in the ISQ, the dimension of a quantity Q in general

becomesα β γ δ ε ζ η

dim Q = L M T I Θ N J

EXAMPLE

Quantity Dimension

speed LT

frequency T

force LMT

2 –2

energy L MT

2 –2 –1

entropy L MT Θ

2 –3 2

electric tension L MT I

2 –2 –1

magnetic flux L MT I

illuminance L J

2 –2 –1 –1

molar entropy L MT Θ N

efficiency 1

6 Units

6.1 Units and numerical values

If a particular example of a quantity of a given kind is chosen as a reference quantity called the unit,

then any other quantity of the same kind can be expressed in terms of this unit, as a product of this unit

and a number. That number is called the numerical value of the quantity expressed in this unit.

EXAMPLE 1 The wavelength of one of the sodium spectral lines isλ ≈ 5,896 ⋅ 10 m

Here, λ is the symbol for the quantity wavelength, m is the symbol for the unit of length, the metre, and

5,896 × 10 is the numerical value of the wavelength expressed in metres.[4]

In formal treatments of quantities and units, this relation may be expressed in the form

Q = {Q } ∙ [Q]a a

where Q is the symbol for an individual quantity Q , [Q] is the symbol for the unit and {Q } is the

a a asymbol for the numerical value of the quantity Q expressed in the unit [Q]. For vectors and tensors, the

components are quantities that can be expressed as described above. Vectors and tensors can also be

expressed as a numerical value vector or tensor, respectively, multiplied by a unit.

If a quantity is expressed in another unit that is k times the first unit, the new numerical value becomes

1/k times the first numerical value because the quantity, which is the product of the numerical value

and the unit, is independent of the unit.© ISO 2022 – All rights reserved

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EXAMPLE 2

Changing the unit for the wavelength in the previous example from the metre to the nanometre, which is

–9 910 times the metre, leads to a numerical value which is 10 the numerical value of the quantity expressed

in metres.Thus,

–7 –7 9

λ ≈ 5,896 ⋅ 10 m = 5,896 ⋅ 10 ⋅ 10 nm = 589,6 nm

It is essential to distinguish between the quantity itself and the numerical value of the quantity

expressed in a particular unit. The numerical value of a quantity expressed in a particular unit could

be indicated by placing braces (curly brackets) around the quantity symbol and using the unit as a

subscript, e.g. {λ} . It is, however, preferable to indicate the numerical value explicitly as the ratio of

the quantity to the unit.EXAMPLE 3 λ /nm ≈ 589,6

This notation is particularly recommended for use in graphs and headings of columns in tables.

6.2 Mathematical operationsThe product and the quotient of two quantities, Q and Q , satisfy the relations

1 2

Q Q = {Q } {Q } ∙ [Q ] [Q ]

1 2 1 2 1 2

Q {}Q []Q

1 1 1

Q {}Q []Q

2 2 2

Thus, the product {Q } {Q } is the numerical value {Q Q } of the quantity Q Q , and the product [Q ] [Q ]

1 2 1 2 1 2 1 2is the unit [Q Q ] of the quantity Q Q . Similarly, the quotient {Q }/{Q } is the numerical value {Q /Q }

1 2 1 2 1 2 1 2of the quantity Q /Q , and the quotient [Q ]/[Q ] is the unit [Q /Q ] of the quantity Q /Q . Units such as

1 2 1 2 1 2 1 2[Q ] [Q ] and [Q ]/[Q ] are called compound units.

1 2 1 2

EXAMPLE 1 The speed, v, of a particle in uniform motion is given by

v=

where l is the distance travelled in the duration t.

Thus, if the particle travels a distance l = 6 m in the duration t = 2 s, the speed, v, is equal to

v = l/t = (6 m)/(2 s) = 3 m/sNOTE A quantity defined as A/B is called ‘quotient of A by B’ or ‘A per B’, but not ‘A per unit B’.

Equations between numerical values, such as {Q Q } = {Q } {Q }, are called numerical value equations.

1 2 1 2Equations between units, such as [Q Q ] = [Q ] [Q ], are called unit equations.

1 2 1 2

The arguments of exponential functions, logarithmic functions, trigonometric functions, etc., are

numbers, numerical values, or combinations of quantities with a dimensional product equal to one (see

Clause 5).EXAMPLE 2 exp(E/kT); ln(p/kPa); sin(π/3); cos(ωt + α)

6.3 Quantity equations and numerical value equations

The three types of equations introduced above, i.e., quantity equations, numerical value equations, and

unit equations, are used in science and technology. Quantity equations and numerical value equations

are generally used; unit equations are used less frequently. Numerical value equations (and of course

unit equations) depend on the choice of units, whereas quantity equations have the advantage of

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being independent of this choice. Therefore, the use of quantity equations is normally preferred and is

strongly recommended.EXAMPLE

A simple quantity equation is

v=

as given in the section Mathematical operations, example 1.

Using, for example, kilometre per hour (symbol km/h), metre (symbol m) and second (symbol s) as

the units for speed, distance, and duration, respectively, the following numerical value equation is

derived:{v} = 3,6 {l} /{t}

km/h m s

where {v} = v/(km/h).

km/h

The number 3,6 that occurs in this numerical value equation results from the particular units

chosen; with other choices, it would generally be different.Since numerical factors in numerical value equations depend on the units chosen, it is recommended

not to omit the subscripts in such equations. If subscripts are not used, the units shall be clearly stated

in the same context.6.4 Coherent systems of units

Units might be chosen arbitrarily but making an independent choice of the unit for each quantity would

lead to the appearance of additional numerical factors in the numerical value equations.

It is possible, however, and in practice more convenie**...**

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