oSIST prEN ISO 80000-1:2017

Quantities and units - Part 1: General (ISO/DIS 80000-1:2017)

2018-10-09: WI abandoned to follow cancellation of corresponding WI in ISO (ISO notification to dataservice on 2018-10-09).

Größen und Einheiten - Teil 1: Allgemeines (ISO/DIS 80000-1:2017)

Grandeurs et unités - Partie 1: Généralités (ISO/DIS 80000-1:2017)

Veličine in enote - 1. del: Splošno (ISO/DIS 80000-1:2017)

General Information

• Status: Not Published
• Public Enquiry End Date: 02-Jul-2017
• ICS: 01.060 - Quantities and units
• Technical Committee: TRS - Technical drawings, quantities, units, symbols and graphical symbols
• Current Stage: 98 - Abandoned project (Adopted Project)
• Start Date: 29-Jan-2019
• Due Date: 03-Feb-2019
• Completion Date: 29-Jan-2019
• Ref Project: prEN ISO 80000-1 - Quantities and units - Part 1: General (ISO/DIS 80000-1:2017)

Relations

• Revised: SIST EN ISO 80000-1:2013 - Quantities and units - Part 1: General (ISO 80000-1:2009 + Cor 1:2011)
• Effective Date: 18-Jan-2023
• Revised: SIST EN ISO 80000-1:2013 - Quantities and units - Part 1: General (ISO 80000-1:2009 + Cor 1:2011)
• Effective Date: 01-Jun-2017

Overview

prEN ISO 80000-1 (ISO/DIS 80000-1:2017) is the draft first part of the ISO 80000 series, titled Quantities and units - Part 1: General. The document defines fundamental concepts and rules for expressing physical quantities and units, including the International System of Quantities (ISQ) and the International System of Units (SI). Note: the CEN work item was abandoned following cancellation of the corresponding ISO work item (ISO notification 2018-10-09); the draft circulated for comment in 2017 and remains a draft/cancelled work item in the CEN/ISO record.

Key Topics

The draft covers authoritative, general requirements and editorial rules used across the ISO 80000 series:

• Concepts and terminology: definitions for quantity, kind of quantity, base and derived quantities (Terms and definitions; Sections 3–4).
• Systems of quantities and dimensions: ISQ, quantity calculus and dimensional treatment (Sections 4–5).
• Units and numerical values: rules for units, coherent unit systems, and relations between quantity equations and numerical-value equations (Section 6).
• SI specifics: SI base units, SI derived units, SI prefixes, the unit “one” and other commonly used units (Section 6.5).
• Printing and notation rules: symbols for quantities and units, use of subscripts, combination of symbols, expressions for quantities, and spelling conventions (Section 7).
• Numeric presentation: conventions for decimal sign, multiplication/division, rounding, error and uncertainty presentation (Sections 7.3, Annex B).
• Special topics: logarithmic quantities and their units, chemical element/nuclide notation, Greek alphabet usage (Annex C, Sections 7.4–7.5).
• Normative and informative annexes: terms in names of physical quantities, rounding, and lists of international organizations involved in quantities and units.

Applications

This standard (and the ISO 80000 family) is intended for consistent, interoperable expression of measurements and calculations across:

• Engineering and scientific publications and reports
• Metrology and calibration laboratories
• Technical documentation, product specifications and CAD/CAM data
• Standards development, regulatory and conformity assessment texts
• Education, textbooks and data interchange platforms

Typical users include engineers, scientists, metrologists, technical editors, standards writers and software developers implementing unit handling or unit-aware computations.

Related standards

• ISO 80000 series (other parts covering specific quantities)
• The International System of Units (SI) and related ISO/IEC editorial guidance
• ISO/IEC Directives referenced for drafting and presentation rules

This draft provides a foundational, normative framework for how quantities, dimensions and units should be defined, printed and used consistently across technical and scientific domains.

Standards Content (Sample)

SLOVENSKI STANDARD
01-junij-2017
9HOLþLQHLQHQRWHGHO6SORãQR,62',6
Quantities and units - Part 1: General (ISO/DIS 80000-1:2017)
Größen und Einheiten - Teil 1: Allgemeines (ISO/DIS 80000-1:2017)
Grandeurs et unités - Partie 1: Généralités (ISO/DIS 80000-1:2017)
Ta slovenski standard je istoveten z: prEN ISO 80000-1
ICS:
01.060 9HOLþLQHLQHQRWH Quantities and units
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

DRAFT INTERNATIONAL STANDARD
ISO/DIS 80000-1
ISO/TC 12 Secretariat: SIS
Voting begins on: Voting terminates on:
2017-04-14 2017-07-07
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 DOCUMENT IS A DRAFT CIRCULATED
This draft is submitted to a parallel vote in ISO and in IEC.
FOR COMMENT AND APPROVAL. IT IS
THEREFORE SUBJECT TO CHANGE AND MAY
NOT BE REFERRED TO AS AN INTERNATIONAL
STANDARD UNTIL PUBLISHED AS SUCH.
IN ADDITION TO THEIR EVALUATION AS
ISO/CEN PARALLEL PROCESSING
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 80000-1:2017(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 2017

ISO/DIS 80000-1:2017(E)
© ISO 2017, Published in Switzerland
All rights reserved. Unless otherwise specified, 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
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Tel. [phone]
Fax [phone]
[e-mail]
www.iso.org
ii © ISO 2017 – All rights reserved

ISO/DIS 80000-1:2017(E)
Contents
Page
Foreword . v
Introduction . vi
0.1 Quantities . vi
0.2 Units . vi
0.3 Realizing the values of units . vii
0.4 Arrangement of the tables . vii
1 Scope .1
2 Normative references .1
3 Terms and definitions .1
4 Quantities . 12
4.1 The concept of quantity . 12
4.2 Kind of quantity ─ Quantity calculus . 12
4.3 System of quantities ─ Base quantities and derived quantities . 13
4.4 Universal constants and empirical constants . 13
4.5 Constant multipliers in quantity equations . 14
4.6 International System of Quantities, ISQ . 14
5 Quantity dimensions . 14
6 Units . 15
6.1 Units and numerical values . 15
6.2 Mathematical operations . 16
6.3 Quantity equations and numerical value equations . 17
6.4 Coherent systems of units. 17
6.5 The International System of Units, SI . 18
6.5.1 General . 18
6.5.2 SI base units . 18
6.5.3 SI derived units . 18
6.5.4 SI prefixes . 21
6.5.5 The unit one . 22
6.5.6 Other units . 23
7 Printing rules . 24
7.1 Symbols for quantities . 24
7.1.1 General . 24
7.1.2 Subscripts . 25
7.1.3 Combination of symbols for quantities . 25
7.1.4 Expressions for quantities . 27
7.2 Names and symbols for units . 27
7.2.1 General . 27
7.2.2 Combination of symbols for units . 28
7.2.3 Prefixes . 28
7.2.4 English names of compound units . 28
7.2.5 Spelling of names of quantities and of units in the English and French languages . 29
iii
ISO/DIS 80000-1:2017(E)
7.3 Numbers . 29
7.3.1 General . 29
7.3.2 Decimal sign . 30
7.3.3 Multiplication and division . 30
7.3.4 Error and uncertainty . 31
7.4 Chemical elements and nuclides . 32
7.5 Greek alphabet . 33
Annex A (normative) Terms in names for physical quantities . 34
A.1 General . 34
A.2 Coefficients, factors . 34
A.3 Parameters, numbers, ratios . 35
A.4 Levels . 35
A.5 Constants . 36
A.6 Terms with general application . 36
Annex B (normative) Rounding of numbers . 39
Annex C (normative) Logarithmic quantities and their units . 41
C.1 General . 41
C.2 Logarithmic root-power quantities . 41
C.3 Logarithmic power quantities . 42
C.4 Logarithmic information-theory quantities . 42
Annex D (informative) International organizations in the field of quantities and units . 43
D.1 JCGM . 43
D.2 CGPM ― CIPM ― BIPM . 43
D.3 IEC ― IEC/TC 25 . 43
D.4 IFCC . 43
D.5 ILAC . 43
D.6 ISO ― ISO/TC 12 . 43
D.7 IUPAC . 43
D.8 IUPAP . 43
D.9 OIML ― CGML ― CIML ― BIML . 44
Bibliography . 45

iv
ISO/DIS 80000-1:2017(E) ISO/DIS 80000-1:2017(E)
7.3 Numbers . 29
7.3.1 General . 29
7.3.2 Decimal sign . 30
7.3.3 Multiplication and division . 30
7.3.4 Error and uncertainty . 31
Foreword
7.4 Chemical elements and nuclides . 32
7.5 Greek alphabet . 33
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
Annex A (normative) Terms in names for physical quantities . 34
carried out through ISO technical committees. Each member body interested in a subject for which a
A.1 General . 34
technical committee has been established has the right to be represented on that committee.
A.2 Coefficients, factors . 34
International organizations, governmental and non-governmental, in liaison with ISO, also take part in
A.3 Parameters, numbers, ratios . 35
the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all
A.4 Levels . 35
matters of electrotechnical standardization.
A.5 Constants . 36
A.6 Terms with general application . 36
The procedures used to develop this document and those intended for its further maintenance are
Annex B (normative) Rounding of numbers . 39
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
Annex C (normative) Logarithmic quantities and their units . 41
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
C.1 General . 41
C.2 Logarithmic root-power quantities . 41
Attention is drawn to the possibility that some of the elements of this document may be the subject of
C.3 Logarithmic power quantities . 42
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
C.4 Logarithmic information-theory quantities . 42
any patent rights identified during the development of the document will be in the Introduction and/or
Annex D (informative) International organizations in the field of quantities and units . 43
on the ISO list of patent declarations received (see www.iso.org/patents).
D.1 JCGM . 43
D.2 CGPM ― CIPM ― BIPM . 43
Any trade name used in this document is information given for the convenience of users and does not
D.3 IEC ― IEC/TC 25 . 43
constitute an endorsement.
D.4 IFCC . 43
D.5 ILAC . 43
For an explanation on the meaning of ISO specific terms and expressions related to conformity
D.6 ISO ― ISO/TC 12 . 43
assessment, as well as information about ISO's adherence to the World Trade Organization (WTO)
D.7 IUPAC . 43
principles in the Technical Barriers to Trade (TBT) see the following URL:
D.8 IUPAP . 43
www.iso.org/iso/foreword.html.
D.9 OIML ― CGML ― CIML ― BIML . 44
The committee responsible for this document is ISO/TC 12, Quantities and units in co-operation with
Bibliography . 45
IEC/TC 25, Quantities and units.

This second edition cancels and replaces the first edition (ISO 80000-1:2009), which has been
technically revised.
A list of all parts of the ISO 80000 series can be found on the ISO website.
iv v
ISO/DIS 80000-1:2017(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.
The quantities and the relations among them are in principle 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
[8]
does appear in 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.
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
vi
ISO/DIS 80000-1:2017(E) ISO/DIS 80000-1:2017(E)
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 advice for their practical realization, are presented in the SI
[8]
Introduction
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
0.1 Quantities 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.
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 0.3 Realizing the values of units
the one that is the basis for the International System of Units, the SI (from the French: Système
To realize the value of a unit is to use the definition of the unit to make measurements that compare the
international d’unités), adopted by the General Conference on Weights and Measures, the CGPM (from
value of some quantity of the same kind as the unit with the value of the unit. This is the essential step
the French: Conférence générale des poids et mesures).
in making measurements of the value of any quantity in science. Realizing the values of the base units is
The quantities and relations among the quantities used here are those almost universally accepted for of particular importance. Realizing the values of derived units follows in principle from realizing the
use throughout the physical sciences. They are presented in the majority of scientific textbooks today base units.
and are familiar to all scientists and technologists.
There may be many different ways for the practical realization of the value of a unit, and new methods
The quantities and the relations among them are in principle infinite in number and are continually may be developed as science advances. Any method consistent with the laws of physics could be used to
evolving as new fields of science and technology are developed. Thus, it is not possible to list all these realize any SI unit. Nonetheless, it is often helpful to review experimental methods for realizing the
quantities and relations in this International Standard; instead, a selection of the more commonly used units, and the CIPM recommends such methods, which are presented as part of the SI Brochure.
quantities and the relations among them is presented.
0.4 Arrangement of the tables
It is inevitable that some readers working in particular specialized fields may find that the quantities
In parts 3 to 14 of this International Standard, the quantities and relations among them, which are a
they are interested in using may not be listed in this International Standard or in another International
subset of the ISQ, are given on the left-hand pages, and the units of the SI (and some other units) are
Standard. However, provided that they can relate their quantities to more familiar examples that are
given on the right-hand pages. Some additional quantities and units are also given on the left-hand and
listed, this will not prevent them from defining units for their quantities.
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
Most of the units used to express values of quantities of interest were developed and used long before
pp-nn.l (pp, part number; nn, running number in the part, respectively; l, sub-letter).
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
[8]
does appear in 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.
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
vi vii
DRAFT INTERNATIONAL STANDARD ISO/DIS 80000-1:2017(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 and nominal properties are outside the scope of ISO 80000-1.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. 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)
ISO/IEC Guide 98-1:2009, Uncertainty of measurement — Part 1: Introduction to the expression of
uncertainty in measurement (GUM)
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 terms and
definitions 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
Note 1 to entry: 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.
ISO/DIS 80000-1:2017(E)
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 i,
entity B, c 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 )
B i
Rockwell C hardness (150 kg load), Rockwell C hardness of steel sample i, HRC (150 kg)
i
HRC(150 kg)
Note 2 to entry: 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 to entry: 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 to entry: 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 to entry: 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 to entry: 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 to entry: Kind of quantity is often shortened to “kind”, e.g. in quantities of the same kind.
Note 2 to entry: 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 to entry: 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 to entry: Adapted from ISO/IEC Guide 99:2007, definition 1.2, in which “kind” appears as an admitted
term. Note 1 has been added, Note 4 has been omitted.
ISO/DIS 80000-1:2017(E) ISO/DIS 80000-1:2017(E)
3.3
length, l radius, r radius of circle A, r or r(A)
A
system of quantities
wavelength, λ wavelength of the sodium D radiation, λ or λ(Na; D)
D
set of quantities together with a set of non-contradictory equations relating those quantities
energy, E kinetic energy, T kinetic energy of particle i in a given system, T
i
Note 1 to entry: Ordinal properties (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
heat, Q heat of vaporization of sample i of water, Q
i
quantities through empirical relations only.
electric charge, Q electric charge of the proton, e
Note 2 to entry: Adapted from ISO/IEC Guide 99:2007, definition 1.3, in which Note 1 is different.
electric resistance, R electric resistance of resistor i in a given circuit, R
i
3.4
amount-of-substance concentration of amount-of-substance concentration of ethanol in wine sample i,
base quantity
entity B, c c (C H OH)
B i 2 5
quantity in a conventionally chosen subset of a given system of quantities, where no quantity in the
number concentration of entity B, C number concentration of erythrocytes in blood sample i, C(Erys; B )
B i
subset can be expressed in terms of the other quantities within that subset
Rockwell C hardness (150 kg load), Rockwell C hardness of steel sample i, HRC (150 kg)
i
Note 1 to entry: The subset mentioned in the definition is termed the “set of base quantities”.
HRC(150 kg)
EXAMPLE The set of base quantities in the International System of Quantities (ISQ) is given in 3.6.
Note 2 to entry: 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 2 to entry: 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 to entry: 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 3 to entry: Adapted from ISO/IEC Guide 99:2007, definition 1.4, in which the definition is slightly different.
Note 3 has been omitted.
Note 4 to entry: 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.
3.5
derived quantity
Note 5 to entry: The concept ’quantity’ may be generically divided into, e.g. ‘physical quantity’, ‘chemical
quantity, in a system of quantities, defined in terms of the base quantities of that system
quantity’, and ‘biological quantity’, or ‘base quantity’ and ‘derived quantity’.
EXAMPLE In a system of quantities having the base quantities length and mass, mass density is a derived
Note 6 to entry: Adapted from ISO/IEC Guide 99:2007, definition 1.1, in which there is an additional note.
quantity defined as the quotient of mass and volume (length to the power three).
3.2
Note 1 to entry: Adapted from ISO/IEC Guide 99:2007, definition 1.5, in which the example is slightly different.
kind of quantity
aspect common to mutually comparable quantities
3.6
International System of Quantities
Note 1 to entry: Kind of quantity is often shortened to “kind”, e.g. in quantities of the same kind.
ISQ
system of quantities based on the seven base quantities: length, mass, time, electric current,
Note 2 to entry: The division of the concept ‘quantity’ into several kinds is to some extent arbitrary.
thermodynamic temperature, amount of substance, and luminous intensity
EXAMPLE 1 The quantities diameter, circumference, and wavelength are generally considered to be
Note 1 to entry: This system of quantities is published in the ISO 80000 and IEC 80000 series Quantities and
quantities of the same kind, namely, of the kind of quantity called length.
units, Parts 3 to 14.
EXAMPLE 2 The quantities heat, kinetic energy, and potential energy are generally considered to be
Note 2 to entry: The International System of Units (SI) (see item 3.16) is based on the ISQ.
quantities of the same kind, namely, of the kind of quantity called energy.
Note 3 to entry: Adapted from ISO/IEC Guide 99:2007, definition 1.6, in which Note 1 is different.
Note 3 to entry: 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.
3.7
quantity dimension
EXAMPLE The quantities moment of force and energy are, by convention, not regarded as being of the
dimension of a quantity
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. dimension
expression of the dependence of a quantity on the base quantities of a system of quantities as a product
Note 4 to entry: Adapted from ISO/IEC Guide 99:2007, definition 1.2, in which “kind” appears as an admitted
of powers of factors corresponding to the base quantities, omitting any numerical factor
term. Note 1 has been added, Note 4 has been omitted.
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EXAMPLE 1 In the ISQ, the quantity dimension of force is denoted by dim F = LMT .
2 3
ISO/DIS 80000-1:2017(E)
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EXAMPLE 2 In the same system of quantities, dim ρ = ML is the quantity dimension of mass concentration
B
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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
𝑙𝑙 2π
𝑇𝑇 =2π�  or  𝑇𝑇 =𝐶𝐶(𝑔𝑔)√𝑙𝑙  where  𝐶𝐶(𝑔𝑔) =
𝑔𝑔
𝑔𝑔
�
−1/2
( )
Hence dim𝐶𝐶𝑔𝑔 = T⋅ L .
Note 1 to entry: A power of a factor is the factor raised to an exponent. Each factor is the dimension of a base
quantity.
Note 2 to entry: The conventional symbolic representation of the dimension of a base quantity is a single upper
case letter in roman (upright), sans serif 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 to entry: In deriving the dimension of a quantity, no account is taken of its scalar, vector, or tensor
character.
Note 4 to entry: 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 to entry: Symbols representing the dimensions of the base quantities in the ISQ are:
Base quantity Symbol for dimension
length L
mass M
time duration 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 to entry: Adapted from ISO/IEC Guide 99:2007, definition 1.7, in which Notes 2 and 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 number
dimensionless quantity
quantity for which all the exponents of the factors corresponding to the base quantities in its quantity
dimension are zero
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EXAMPLE 2 In the same system of quantities, dim ρ =
...