EN ISO 80000-3:2020

SLOVENSKI STANDARD
01-december-2020
Nadomešča:
SIST EN ISO 80000-3:2013
SIST ISO 80000-3:2012
Veličine in enote - 3. del: Prostor in čas (ISO 80000-3:2019)
Quantities and units - Part 3: Space and time (ISO 80000-3:2019)
Größen und Einheiten - Teil 3: Raum und Zeit (ISO 80000-3:2019)
Grandeurs et unités - Partie 3: Espace et temps (ISO 80000-3:2019)
Ta slovenski standard je istoveten z: EN ISO 80000-3:2020
ICS:
01.060 Veličine in enote Quantities and units
07.030 Fizika. Kemija Physics. Chemistry
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 80000-3
EUROPEAN STANDARD
NORME EUROPÉENNE
October 2020
EUROPÄISCHE NORM
ICS 01.060 Supersedes EN ISO 80000-3:2013
English Version
Quantities and units - Part 3: Space and time (ISO 80000-
3:2019)
Grandeurs et unités - Partie 3: Espace et temps (ISO Größen und Einheiten - Teil 3: Raum und Zeit (ISO
80000-3:2019) 80000-3:2019)
This European Standard was approved by CEN on 21 October 2020.

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, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2020 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 80000-3:2020 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
The text of ISO 80000-3:2019 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
is held by CCMC.
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 April 2021, and conflicting national standards shall be
withdrawn at the latest by April 2021.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 80000-3:2013.
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, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the
United Kingdom.
Endorsement notice
The text of ISO 80000-3:2019 has been approved by CEN as EN ISO 80000-3:2020 without any
modification.
INTERNATIONAL ISO
STANDARD 80000-3
Second edition
2019-10
Quantities and units —
Part 3:
Space and time
Grandeurs et unités —
Partie 3: Espace et temps
Reference number
ISO 80000-3:2019(E)
©
ISO 2019
ISO 80000-3:2019(E)
© ISO 2019
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
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below or ISO’s member body in the country of the requester.
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Phone: +41 22 749 01 11
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Email: copyright@iso.org
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Published in Switzerland
ii © ISO 2019 – All rights reserved

ISO 80000-3:2019(E)
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
Bibliography .10
Index .11
ISO 80000-3:2019(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.
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 collaboration
with Technical Committee IEC/TC 25, Quantities and units.
This second edition cancels and replaces the first edition (ISO 80000-3:2006), which has been
technically revised.
The main changes compared to the previous edition are as follows:
— the table giving the quantities and units has been simplified;
— some definitions and the remarks have been stated physically more precisely.
A list of all parts in the ISO 80000 and IEC 80000 series can be found on the ISO and IEC websites.
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.
iv © ISO 2019 – All rights reserved

INTERNATIONAL STANDARD ISO 80000-3:2019(E)
Quantities and units —
Part 3:
Space and time
1 Scope
This document gives names, symbols, definitions and units for quantities of space and time. Where
appropriate, conversion factors are also given.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
Names, symbols, definitions and units for quantities of space and time are given in Table 1.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
ISO 80000-3:2019(E)
2 © ISO 2019 – All rights reserved
Table 1 — Quantities and units of space and time
Item No. Quantity Unit Remarks
Name Symbol Definition
3-1.1 length l, L linear extent in space between any two points m Length does not need to be measured along a
straight line.
Length is one of the seven base quantities in the Inter-
national System of Units (ISO 80000-1).
3-1.2 width, b, B minimum length of a straight line segment m This quantity is non-negative.
between two parallel straight lines (in two
breadth
dimensions) or planes (in three dimensions)
that enclose a given geometrical shape
3-1.3 height, h, H minimum length of a straight line segment m This quantity is usually signed. The sign expresses
between a point and a reference line or refer- the position of the particular point with respect to the
depth,
ence surface reference line or surface and is chosen by convention.
altitude
The symbol H is often used to denote altitude, i.e.
height above sea level.
3-1.4 thickness d, δ width (item 3-1.2) m This quantity is non-negative.
3-1.5 diameter d, D width (item 3-1.2) of a circle, cylinder or sphere m This quantity is non-negative.
3-1.6 radius r, R half of a diameter (item 3-1.5) m This quantity is non-negative.
3-1.7 path length, s length of a rectifiable curve between two of m The differential path length at a given point of a
its points curve is:
arc length
ddsx= + ddyz+
() () ()
where x, y, and z denote the Cartesian coordinates
(ISO 80000-2) of the particular point.
There are curves which are not rectifiable, for exam-
ple fractal curves.
3-1.8 distance d, r shortest path length (item 3-1.7) between two m A metric space might be curved. An example of a
points in a metric space curved metric space is the surface of the Earth.
In this case, distances are measured along great
circles.
A metric is not necessarily Euclidean.

ISO 80000-3:2019(E)
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
3-1.9 radial distance r , ρ distance (item 3-1.8), where one point is locat- m The subscript Q denotes the point from which the
Q
ed on an axis or within a closed non self-inter- radial distance is measured.
secting curve or surface
Examples of closed non self-intersecting curves are
circles or ellipses.
Examples of closed non self-intersecting surfaces are
surfaces of spheres or egg-shaped objects.
3-1.10 position vector r vector (ISO 80000-2) quantity from the origin m Position vectors are so-called bounded vectors, i.e.
of a coordinate system to a point in space their magnitude (ISO 80000-2) and direction depend
on the particular coordinate system used.
3-1.11 displacement Δr vector (ISO 80000-2) quantity between any m Displacement vectors are so-called free vectors, i.e.
two points in space their magnitude (ISO 80000-2) and direction do not
depend on a particular coordinate system.
The magnitude of this vector is also called displace-
ment.
3-1.12 radius of curvature ρ radius (item 3-1.6) of the osculating circle of a m The radius of curvature is only defined for curves
planar curve at a particular point of the curve which are at least twice continuously differentiable.
−1
κ
3-2 curvature inverse of the radius of curvature (item 3-1.12) m The curvature is given by:
κ=
ρ
where ρ denotes the radius of curvature (item 3-1.12).
3-3 area A, S extent of a two-dimensional geometrical shape m The surface element at a given point of a surface is
given by:
dA = g du dv
where u and v denote the Gaussian surface coordi-
nates and g denotes the determinant of the metric
tensor (ISO 80000-2) at the particular point.
The symbol dσ is also used for the surface element.

ISO 80000-3:2019(E)
4 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
3-4 volume V, (
...