SIST EN ISO 80000-3:2013

SLOVENSKI STANDARD
SIST EN ISO 80000-3:2013
01-junij-2013
1DGRPHãþD
SIST ISO 31-1+A1:2007
SIST ISO 31-2+A1:2007
9HOLþLQHLQHQRWHGHO3URVWRULQþDV,62
Quantities and units - Part 3: Space and time (ISO 80000-3:2006)
Größen und Einheiten - Teil 3: Raum und Zeit (ISO 80000-3:2006)
Grandeurs et unités - Partie 3: Espace et temps (ISO 80000-3:2006)
Ta slovenski standard je istoveten z: EN ISO 80000-3:2013
ICS:
01.060 9HOLþLQHLQHQRWH Quantities and units
07.030 Fizika. Kemija Physics. Chemistry
SIST EN ISO 80000-3:2013 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------

SIST EN ISO 80000-3:2013

---------------------- Page: 2 ----------------------

SIST EN ISO 80000-3:2013


EUROPEAN STANDARD
EN ISO 80000-3

NORME EUROPÉENNE

EUROPÄISCHE NORM
April 2013
ICS 01.060
English Version
Quantities and units - Part 3: Space and time (ISO 80000-
3:2006)
Grandeurs et unités - Partie 3: Espace et temps (ISO Größen und Einheiten - Teil 3: Raum und Zeit (ISO 80000-
80000-3:2006) 3:2006)
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 80000-3:2013: E
worldwide for CEN national Members.

---------------------- Page: 3 ----------------------

SIST EN ISO 80000-3:2013
EN ISO 80000-3:2013 (E)
Contents Page
Foreword . 3

2

---------------------- Page: 4 ----------------------

SIST EN ISO 80000-3:2013
EN ISO 80000-3:2013 (E)
Foreword
The text of ISO 80000-3:2006 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 80000-3:2013.
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 80000-3:2006 has been approved by CEN as EN ISO 80000-3:2013 without any modification.

3

---------------------- Page: 5 ----------------------

SIST EN ISO 80000-3:2013

---------------------- Page: 6 ----------------------

SIST EN ISO 80000-3:2013
INTERNATIONAL ISO
STANDARD 80000-3
First edition
2006-03-01
Quantities and units —
Part 3:
Space and time
Grandeurs et unités —
Partie 3: Espace et temps

Reference number
ISO 80000-3:2006(E)
©
ISO 2006

---------------------- Page: 7 ----------------------

SIST EN ISO 80000-3:2013
ISO 80000-3:2006(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but shall
not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the
unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2006
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56  CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
©
ii ISO 2006 – All rights reserved

---------------------- Page: 8 ----------------------

SIST EN ISO 80000-3:2013
ISO 80000-3:2006(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Names, symbols and definitions . 1
Annex A (informative) Units in the CGS system with special names . 16
Annex B (informative) Units based on the foot, pound, second, and some other related units . 17
Annex C (informative) Other non-SI units given for information, especially regarding the conversion
factors . 19
©
ISO 2006 – All rights reserved iii

---------------------- Page: 9 ----------------------

SIST EN ISO 80000-3:2013
ISO 80000-3:2006(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 this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 80000-3 was prepared by Technical Committee ISO/TC 12, Quantities, units, symbols, conversion factors,
in collaboration with IEC/TC 25, Quantities and units, and their letter symbols.
This first edition cancels and replaces the second edition of ISO 31-1:1992 and of ISO 31-2:1992. The major
technical changes from the previous standards are the following:
— the presentation of numerical statements has been changed;
— the remark on logarithmic quantities and their units in the Introduction has been changed;
— the normative references have been changed;
— the quantities radial distance, position vector, displacement and rotation have been added to the list of
quantities.
ISO 80000 consists of the following parts, under the general title Quantities and units:
— Part 1: General
— Part 2: Mathematical signs and symbols for use 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
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
©
iv ISO 2006 – All rights reserved

---------------------- Page: 10 ----------------------

SIST EN ISO 80000-3:2013
ISO 80000-3:2006(E)
Introduction
0.1 Arrangement of the tables
The tables of quantities and units in this International Standard are arranged so that the quantities are
presented on the left-hand pages and the units on the corresponding right-hand pages.
All units between two full lines on the right-hand pages belong to the quantities between the corresponding full
lines on the left-hand pages.
Where the numbering of an item has been changed in the revision of a part of ISO 31, the number in the
preceding edition is shown in parenthesis on the left-hand page under the new number for the quantity; a dash
is used to indicate that the item in question did not appear in the preceding edition.
0.2 Tables of quantities
The names in English and in French of the most important quantities within the field of this International
Standard are given together with their symbols and, in most cases, their definitions. These names and symbols
are recommendations. The definitions are given for identification of the quantities in the International System of
Quantities (ISQ), listed on the left-hand pages of the table; they are not intended to be complete.
The scalar, vectorial or tensorial character of quantities is pointed out, especially when this is needed for the
definitions.
In most cases only one name and only one symbol for the quantity are given; where two or more names or two
or more symbols are given for one quantity and no special distinction is made, they are on an equal footing.
When two types of italic letters exist (for example as with ϑ and θ; ϕ and φ; a and a; g and g) only one of these
is given. This does not mean that the other is not equally acceptable. It is not recommended to give such
variants different meanings. A symbol within parenthesis implies that it is a reserve symbol, to be used when, in
a particular context, the main symbol is in use with a different meaning.
In this English edition, the quantity names in French are printed in an italic font, and are preceded by fr. The
gender of the French name is indicated by (m) for male and (f) for female, immediately after the noun in the
French name.
0.3 Tables of units
0.3.1 General
The names of units for the corresponding quantities are given together with the international symbols and the
definitions. These unit names are language-dependent, but the symbols are international and the same in all
th 1)
languages. For further information, see the SI Brochure (7 edition 1998) from BIPM and ISO 80000-1 .
The units are arranged in the following way.
a) The coherent SI units are given first. The SI units have been adopted by the General Conference on
Weights and Measures (Conférence Générale des Poids et Mesures, CGPM). The use of coherent SI units
1) To be published.
©
ISO 2006 – All rights reserved v

---------------------- Page: 11 ----------------------

SIST EN ISO 80000-3:2013
ISO 80000-3:2006(E)
is recommended; decimal multiples and submultiples formed with the SI prefixes are recommended even
though not explicitly mentioned.
b) Some non-SI units are then given, being those accepted by the International Committee for Weights and
Measures (Comité International des Poids et Mesures, CIPM), or by the International Organization of Legal
Metrology (Organisation Internationale de Métrologie Légale, OIML), or by ISO and IEC, for use with the SI.
Such units are separated from the SI units in the item by use of a broken line between the SI units and the
other units.
c) Non-SI units currently accepted by the CIPM for use with the SI are given in small print (smaller than the text
size) in the “Conversion factors and remarks” column.
d) Non-SI units that are not recommended are given only in annexes in some parts of this International
Standard. These annexes are informative, in the first place for the conversion factors, and are not integral
parts of the standard. These deprecated units are arranged in two groups:
1) units in the CGS system with special names;
2) units based on the foot, pound, second, and some other related units.
e) Other non-SI units given for information, especially regarding the conversion factors, are given in another
informative annex.
0.3.2 Remark on units for quantities of dimension one, or dimensionless quantities
The coherent unit for any quantity of dimension one, also called a dimensionless quantity, is the number one,
symbol 1. When the value of such a quantity is expressed, the unit symbol 1 is generally not written out
explicitly.
EXAMPLE Refractive index n = 1,53× 1 = 1,53
Prefixes shall not be used to form multiples or submultiples of the unit one. Instead of prefixes, powers of 10 are
recommended.
3
EXAMPLE Reynolds number Re = 1,32× 10
Considering that plane angle is generally expressed as the ratio of two lengths and solid angle as the ratio of
two areas, in 1995 the CGPM specified that, in the SI, the radian, symbol rad, and steradian, symbol sr, are
dimensionless derived units. This implies that the quantities plane angle and solid angle are considered as
derived quantities of dimension one. The units radian and steradian are thus equal to one; they may either be
omitted, or they may be used in expressions for derived units to facilitate distinction between quantities of
different kind but having the same dimension.
0.4 Numerical statements in this International Standard
The sign = is used to denote “is exactly equal to”, the sign ≈ is used to denote “is approximately equal to”, and
the sign := is used to denote “is by definition equal to”.
Numerical values of physical quantities that have been experimentally determined always have an associated
measurement uncertainty. This uncertainty should always be specified. In this International Standard, the
magnitude of the uncertainty is represented as in the following example.
EXAMPLE l = 2,347 82(32) m
In this example, l = a(b) m, the numerical value of the uncertainty b indicated in parentheses is assumed to
apply to the last (and least significant) digits of the numerical value a of the length l. This notation is used when
b represents the standard uncertainty (estimated standard deviation) in the last digits of a. The numerical
example given above may be interpreted to mean that the best estimate of the numerical value of the length l
(when l is expressed in the unit metre) is 2,347 82, and that the unknown value of l is believed to lie between
(2,347 82− 0,000 32) m and (2,347 82 + 0,000 32) m, with a probability determined by the standard
uncertainty 0,000 32 m and the probability distribution of the values of l.
©
vi ISO 2006 – All rights reserved

---------------------- Page: 12 ----------------------

SIST EN ISO 80000-3:2013
ISO 80000-3:2006(E)
0.5 Remark on logarithmic quantities and their units
The expression for the time dependence of a damped harmonic oscillation can be written either in real notation
or as the real part of a complex notation
−δt (−δ+iω)t
F(t)= Ae cos ωt = Re(Ae ), A = F(0)
This simple relation involving δ and ω can be obtained only when e (base of natural logarithms) is used as the
base of the exponential function. The coherent SI unit for the damping coefficient δ and the angular frequency
–1
ω is second to the power minus one, symbol s . Using the special names neper, symbol Np, and radian,
symbol rad, for the units of δt and ωt, respectively, the units for δ and ω become neper per second, symbol
Np/s, and radian per second, symbol rad/s, respectively.
The corresponding variation in space is treated in the same manner
−αx −γx
F(x)= Ae cos βx = Re(Ae ), A = F(0) γ = α + iβ
where the unit for α is neper per metre, symbol Np/m, and the unit for β is radian per metre, symbol rad/m.
The taking of logarithms of complex quantities is usefully carried out only with the natural logarithm. In this
International Standard, the level L of a field quantity F is therefore defined by convention as the natural
F
logarithm of a ratio of the field quantity and a reference value F , L = In(F /F ), in accordance with decisions
0 F 0
by CIPM and OIML. Since a field quantity is defined as a quantity whose square is proportional to power when
it acts on a linear system, a square root is introduced in the expression of the level of a power quantity
�
L = In P/P =(1/2) In(P/P )
P 0 0
when defined by convention using the natural logarithm, in order to make the level of the power quantity equal
to the level of the corresponding field quantity when the proportionality factors are the same for the considered
2)
quantities and the reference quantities, respectively. See IEC 60027-3:2002, subclause 4.2.
The neper, symbol Np, and the bel, symbol B, are units for such logarithmic quantities.
The neper is the coherent unit when the logarithmic quantities are defined by convention using the natural
logarithm, 1Np = 1. The bel is the unit when the numerical value of the logarithmic quantity is expressed in
terms of decimal logarithms, 1B=(1/2) ln 10 Np≈ 1,151 293 Np. The use of the neper is mostly restricted to
theoretical calculations on field quantities, when this unit is most convenient, whereas in other cases, especially
for power quantities, the bel, or in practice its submultiple decibel, symbol dB, is widely used. It should be
emphasized that the fact that the neper is chosen as the coherent unit does not imply that the use of the bel
should be avoided. The bel is accepted by the CIPM and the OIML for use with the SI. This situation is in some
◦
respect similar to the fact that the unit degree ( ) is commonly used in practice instead of the coherent SI unit
radian (rad) for plane angle.
Generally it is not the logarithmic quantity itself, such as L or L , which is of interest; it is only the argument
F P
of the logarithm that is of interest, i.e. F /F and P /P , respectively.
0 0
To avoid ambiguities in practical applications of logarithmic quantities, the unit should always be written out
explicitly after the numerical value, even if the unit is neper, 1Np = 1. Thus, for power quantities, the level is
generally given by L = 10 lg(P /P )dB, and it is the numerical value 10 lg(P /P ) and the argument P /P that
0
P 0 0
are of interest. This numerical value is, however, not the same as the quantity L , because the unit decibel (or
P
the unit bel) is not equal to one, 1. This applies to field quantities where the level is generally given by
2
L = 10 lg(F /F ) dB.
F 0
2) IEC 60027-3:2002, Letter symbols to be used in electrical technology — Part 3: Logarithmic and related quantities, and
their units.
©
ISO 2006 – All rights reserved vii

---------------------- Page: 13 ----------------------

SIST EN ISO 80000-3:2013
ISO 80000-3:2006(E)
EXAMPLE 1 The implication of the statement that L = 3dB (= 0,3 B) for the level of a field quantity is that it is to be
F
2 2 0,3
read as meaning: lg(F /F ) = 0,3, or (F /F ) = 10 . (It also implies that L ≈ 0,3× 1,151 293 Np = 0,345 387 9 Np,
0 0 F
but this is not often used in practice.)
EXAMPLE 2 Similarly, the implication of the statement that L = 3dB (= 0,3 B) for the level of a power quantity is that it
P
0,3
is to be read as meaning: lg(P /P ) = 0,3, or (P /P )= 10 . (It also implies that
0 0
L ≈ 0,3× 1,151 293 Np = 0,345 387 9 Np, but this is not often used in practice.)
P
Meaningful measures of power quantities generally require time averaging to form a mean-square value that is
proportional to power. Corresponding field quantities may then be obtained as the root-mean-square value. For
such applications, the decimal (base 10) logarithm is generally used to form the level of field or power quantities.
However, the natural logarithm could also be used for these applications, especially when the quantities are
complex.
©
viii ISO 2006 – All rights reserved

---------------------
...