SIST EN ISO 14405-1:2025

SLOVENSKI STANDARD
01-november-2025
Specifikacija geometrijskih veličin izdelka - Tolerance dimenzij - 1. del: Dolžinske
mere (ISO 14405-1:2025)
Geometrical product specifications (GPS) - Dimensional tolerancing - Part 1: Linear sizes
(ISO 14405-1:2025)
Geometrische Produktspezifikation (GPS) - Dimensionelle Tolerierung - Teil 1: Lineare
Größenmaße (ISO 14405-1:2025)
Spécification géométrique des produits (GPS) - Tolérancement dimensionnel - Partie 1:
Tailles linéaires (ISO 14405-1:2025)
Ta slovenski standard je istoveten z: EN ISO 14405-1:2025
ICS:
17.040.10 Tolerance in ujemi Limits and fits
17.040.40 Specifikacija geometrijskih Geometrical Product
veličin izdelka (GPS) Specification (GPS)
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 14405-1
EUROPEAN STANDARD
NORME EUROPÉENNE
August 2025
EUROPÄISCHE NORM
ICS 17.040.40 Supersedes EN ISO 14405-1:2016
English Version
Geometrical product specifications (GPS) - Dimensional
tolerancing - Part 1: Linear sizes (ISO 14405-1:2025)
Spécification géométrique des produits (GPS) - Geometrische Produktspezifikation (GPS) -
Tolérancement dimensionnel - Partie 1: Tailles Dimensionelle Tolerierung - Teil 1: Lineare
linéaires (ISO 14405-1:2025) Größenmaße (ISO 14405-1:2025)
This European Standard was approved by CEN on 5 July 2025.

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, Türkiye 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
© 2025 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 14405-1:2025 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 14405-1:2025) has been prepared by Technical Committee ISO/TC 213
"Dimensional and geometrical product specifications and verification " in collaboration with Technical
Committee CEN/TC 290 “Dimensional and geometrical product specification and verification” the
secretariat of which is held by AFNOR.
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 February 2026, and conflicting national standards
shall be withdrawn at the latest by February 2026.
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 14405-1:2016.
Any feedback and questions on this document should be directed to the users’ national standards
body/national committee. A complete listing of these bodies can be found on the CEN website.
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, Türkiye and the
United Kingdom.
Endorsement notice
The text of ISO 14405-1:2025 has been approved by CEN as EN ISO 14405-1:2025 without any
modification.
International
Standard
ISO 14405-1
Third edition
Geometrical product specifications
2025-08
(GPS) — Dimensional tolerancing —
Part 1:
Linear sizes
Spécification géométrique des produits (GPS) — Tolérancement
dimensionnel —
Partie 1: Tailles linéaires
Reference number
ISO 14405-1:2025(en) © ISO 2025

ISO 14405-1:2025(en)
© ISO 2025
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
ii
ISO 14405-1:2025(en)
Contents Page
Foreword .v
Introduction .vii
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 2
4 General .13
4.1 Specification modifiers and symbols . 13
4.2 Linear sizes .14
5 Basic linear size specification .16
5.1 General .16
5.2 Indication of a basic linear size specification .17
5.2.1 General .17
5.2.2 Indication of the diameter symbol .17
5.2.3 Indication of a basic linear size specification on one line .17
5.2.4 Indication of a basic linear size specification on two lines .18
5.3 Tolerancing of fits on assembly drawings .19
6 Default specification operator for linear size . 19
6.1 General .19
6.2 ISO default specification operator for linear size .19
6.3 Drawing-specific default specification operator for linear size . 20
7 Special specification operator for linear size .20
7.1 Stacked linear size specifications . 20
7.2 Indication areas .21
7.3 Sequence of specification elements for the linear size specification . 22
7.4 Sequence of specification elements for the upper and left indication areas . 25
7.5 Sequence of specification elements for the right indication area . 26
8 Indication of the toleranced feature on which the size characteristic is defined .26
8.1 Default case . 26
8.2 Linear size specification applied individually to several features of linear size . 26
8.3 Linear size specification applied to several features of linear size considered as a
common toleranced feature of linear size .27
8.4 United feature of linear size . 28
8.5 Fixed restricted portion of the feature of linear size . 29
8.6 Size characteristic in specific cross-sections of a feature of linear size . 29
8.6.1 Size characteristic in one specific cross-section of a feature of linear size . 29
8.6.2 Size characteristic in several specific cross-sections of a feature of linear size . 30
9 Envelope requirement .31
9.1 Envelope requirement for external features of linear size .31
9.2 Envelope requirement for internal features of linear size .32
10 Indication of linear portion sizes .34
11 Indication of linear section sizes .34
12 Filtration .35
13 Direction feature .35
Annex A (normative) Proportions and dimensions of graphical symbols .36
Annex B (normative) Graphical rules for linear size specifications .38
Annex C (informative) Data handling with statistical sizes . 41
Annex D (normative) Linear size specification on a circle as specific section of a cone .43

iii
ISO 14405-1:2025(en)
Annex E (normative) Linear size specification on circles as any longitudinal sections of a torus .44
Annex F (normative) Linear size specifications on parallel opposite lines as any longitudinal
sections in half planes .45
Annex G (informative) Former practices .46
Annex H (informative) Sequence of the specification elements .51
Annex I (informative) Relationship to the ISO GPS matrix model .52
Bibliography .54

iv
ISO 14405-1:2025(en)
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 document 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).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
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 213, Dimensional and geometrical product
specifications and verification, in collaboration with the European Committee for Standardization (CEN)
Technical Committee CEN/TC 290, Dimensional and geometrical product specification and verification, in
accordance with the Agreement on technical cooperation between ISO and CEN (Vienna Agreement).
This third edition cancels and replaces the second edition (ISO 14405-1:2016), which has been technically
revised.
The main changes are as follows:
— the use of linear size specifications for cones, torus and two opposite circles is now reduced to the cases
described in Annexes D, E and F;
— the syntax is changed, and is now defined with several indication areas, and a sequence of specification
elements in each area;
— linear size specifications can be stacked upon each other and the rules for stacked specifications are
defined;
— the indication k×/n× is now possible, in order to facilitate stacking with geometrical specifications;
— the graphical rules are modified;
— the specification element “/0” to mean “any restricted portion whose length is equal to zero” has been
removed to use the modifier “ACS”;
— when different specification operators applied for the upper and the lower specification limits of size
characteristic, the new rule is to indicate two different size specifications;
— the indication of several linear size specifications on the same dimension line or reference line with
brackets is removed;
— it is now required to use the “between” symbol to indicate that a linear size specification applies to a
fixed restricted portion of a feature of linear size;

v
ISO 14405-1:2025(en)
— it is now required to indicate “SCS” with the identifier of the section for a specific cross-section;
— the rank-order size specification is now called statistical size specification.
A list of all parts in the ISO 14405 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.

vi
ISO 14405-1:2025(en)
Introduction
This document is a geometrical product specification (GPS) standard and is to be regarded as a general GPS
standard (see ISO 14638). It influences chain links A to C of the chain of standards on size.
The ISO GPS matrix model given in ISO 14638 gives an overview of the ISO GPS system of which this document
is a part. The fundamental rules of ISO GPS given in ISO 8015 apply to this document and the default decision
rules given in ISO 14253-1 apply to the specifications made in accordance with this document, unless
otherwise indicated.
For more detailed information on the relationship of this document to other standards and the ISO GPS
matrix model, see Annex I.
This document deals with linear size specifications on the following features of linear size:
— cylinders;
— spheres;
— two parallel opposite planes.
It also deals with the following cases:
— circles as sections of a cone;
— circles as sections of a torus;
— parallel opposite lines as longitudinal sections of cylindrical tubes.
Different specification elements allow specifying local linear sizes or global linear sizes of different types,
and, for example, specifications on several features of linear size, specifications in sections and specifications
on portions. The many specification elements allow for specifying a variety of functional needs.
Annex D provides the definition of a size for a circle as section of a cone. Annex E provides the definition
of sizes for circles as sections of a torus. Annex F provides the definition of sizes for parallel opposite lines
as longitudinal sections of cylindrical tubes in half planes containing a specified axis. Annex H gives an
overview of the sequence of specification elements for linear size specifications.
ISO 14405-2 gives the difference between linear size, angular size and dimensions other than linear or
angular sizes. ISO 14405-2 relies on this document for the rules about indication.

vii
International Standard ISO 14405-1:2025(en)
Geometrical product specifications (GPS) — Dimensional
tolerancing —
Part 1:
Linear sizes
IMPORTANT — The figures included in this document are intended to either illustrate the text or
to provide examples of the related technical drawing specification, or both. These figures are not
fully specified, showing only the relevant general principles. As a consequence, the figures are
not a representation of a complete workpiece and are not of a quality that is required for use in
industry and, as such, are not suitable for projection for teaching purposes. Figures are simplified 2D
representations and show features that are unlikely (e.g. a minimum circumscribed cylinder with
three contact points in the same section).
1 Scope
This document specifies requirements for indicating linear sizes.
This document establishes the default specification operator (see ISO 17450-2) and defines a special
specification operator for linear sizes.
This document is applicable to the following features of linear size (see ISO 17450-1):
— cylinders;
— spheres;
— two parallel opposite planes.
This document provides a set of tools to express several types of linear size characteristics. It does not
present any information on the relationship between a function or a use and a linear size characteristic.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements 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 286-1, Geometrical product specifications (GPS) — ISO code system for tolerances on linear sizes — Part 1:
Basis of tolerances, deviations and fits
ISO 8015, Geometrical product specifications (GPS) — Fundamentals — Concepts, principles and rules
ISO 17450-1, Geometrical product specifications (GPS) — General concepts — Part 1: Model for geometrical
specification and verification
ISO 17450-2, Geometrical product specifications (GPS) — General concepts — Part 2: Basic tenets, specifications,
operators, uncertainties and ambiguities
ISO 17450-3, Geometrical product specifications (GPS) — General concepts — Part 3: Toleranced features
ISO 81714-1, Design of graphical symbols for use in the technical documentation of products — Part 1: Basic rules

ISO 14405-1:2025(en)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 286-1, ISO 8015, ISO 17450-1,
ISO 17450-2, ISO 17450-3 and the following apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
size
dimensional parameter considered variable for a feature of size that can be defined on a nominal feature or
on an associated feature
Note 1 to entry: A size is angular (e.g. angle of a cone) or linear (e.g. diameter of a cylinder). This document only applies
to linear sizes (3.2). See ISO 14405-3 for angular sizes.
Note 2 to entry: Depending on the type of feature of linear size, the terms “diameter”, “width", and “thickness” are
synonyms for size.
3.2
linear size
dimension in length units characterizing a feature of size
[SOURCE: ISO 14405-2:2018, 3.2]
3.3
size characteristic
characteristic relative to a size (3.1) and defined from an extracted integral feature
Note 1 to entry: A size can be evaluated by more than one size characteristic (e.g. the two-point diameter or the
diameter of the associated feature).
3.4
upper specification limit of size characteristic
largest permissible value for a size characteristic (3.3)
3.5
lower specification limit of size characteristic
smallest permissible value for a size characteristic (3.3)
3.6
local linear size
size characteristic (3.3) having a non-unique result of evaluation either along or around, or both, a feature of
linear size (3.2)
Note 1 to entry: For a given feature of linear size, an infinity of local linear sizes exists.
Note 2 to entry: In Figure 3, examples of local linear sizes are shown. These examples do not take into account the
statistical size (3.7.6).
3.6.1
two-point size
distance between two opposite points on an extracted integral feature of linear size (3.2)
Note 1 to entry: A two-point size on a cylinder can be called a “two-point diameter”.
Note 2 to entry: A two-point size on two parallel opposite planes can be called a “two-point thickness” or a “two-
point width”.
Note 3 to entry: The method establishing a two-point size from any kind of features of linear size is given in ISO 17450–3.

ISO 14405-1:2025(en)
Note 4 to entry: See Figure 1 for examples of two-point sizes. Figure 1 a) shows an extracted feature under
consideration, a cylinder which can be either internal or external.
a) Extracted feature under consideration
b) Two-point sizes
Key
d size
A axis of the least-squares associated cylinder with the extracted integral feature
Figure 1 — Examples of two-point sizes
3.6.2
spherical size
diameter of the maximum inscribed sphere
Note 1 to entry: The maximum inscribed sphere is used when defining the spherical size of both internal and external
features of linear size (3.2).
Note 2 to entry: The spherical size does not apply to spheres.
Note 3 to entry: See Figure 2 for examples of spherical sizes. Figure 2 a) shows an extracted feature under consideration,
a cylinder which can be either internal or external.
a) Extracted feature under consideration

ISO 14405-1:2025(en)
b) Spherical sizes
Key
S⌀d diameter of the maximum inscribed sphere
Figure 2 — Examples of spherical sizes
3.6.3
linear section size
global linear size (3.7) for a given section of the extracted integral feature of linear size (3.2)
Note 1 to entry: A linear section size is a global linear size for a given section and is a local linear size (3.6) for the entire
feature of linear size because it has different results of evaluation along the feature of linear size.
Note 2 to entry: On an extracted feature of linear size, which is a cylindrical surface, it is possible to define an infinite
number of cross-sections in which the diameter of the associated circle can be defined (with a specific association
criterion). This is a linear section size.
Note 3 to entry: See Figure 3 for an example of linear section size. Figure 3 a) shows an extracted feature under
consideration, a cylinder which can be either internal or external. Figure 3 b) shows a linear section size obtained
from a global linear size with maximum inscribed criterion (other criteria are possible).
a) Extracted feature under consideration
b) Linear section size obtained from a global linear size
NOTE The linear section size of Figure 3 b) in each cross-section is given by the diameter of the maximum
inscribed circle defined in that cross-section.
Figure 3 — Example of linear section size
3.6.4
linear portion size
global linear size (3.7) for a given portion of the extracted feature of linear size (3.2)
Note 1 to entry: A linear portion size is a global linear size for a given portion and is a local linear size (3.6) for the
entire feature of linear size because it has different results of evaluation along the feature of linear size.
Note 2 to entry: See Figure 4 for an example of linear portion size. Figure 4 a) shows an extracted feature under
consideration, a cylinder which can be either internal or external. Figure 4 b) shows a linear portion size obtained
from a global linear size with maximum inscribed criterion (other criteria are possible).

ISO 14405-1:2025(en)
a) Extracted feature under consideration
b) Linear portion size obtained from a global linear size
Key
L considered length of the portion of the cylinder
NOTE Only a portion of length L of the extracted feature is considered.
Figure 4 — Example of linear portion size
3.7
global linear size
size characteristic (3.3) having a unique value along and around a feature of linear size (3.2)
Note 1 to entry: A global linear size can be for a section, for a portion, or for the whole feature of linear size. See
linearsection size (3.6.3) and linearportion size (3.6.4).
Note 2 to entry: In Figures 5, 6, 7 and 8, examples of global linear sizes are shown.
3.7.1
least-squares size
global linear size (3.7) for which an associated integral feature is established from the extracted integral
feature(s) with the total least-squares objective function without constraint
Note 1 to entry: In this document, “total least-squares” objective function is referred to only as “least-squares”. This
objective function minimizes the sum of the squares of distances existing between the associated integral feature and
the extracted integral feature, see ISO 4351.
Note 2 to entry: See Figure 5 for an example of least-squares size. Figure 5 a) shows an extracted feature under
consideration, which can be either an internal or external feature and either a cylinder or two parallel opposite planes.
a) Extracted feature under consideration

ISO 14405-1:2025(en)
b) Least-squares size
Figure 5 — Example of least-squares size
3.7.2
maximum inscribed size
global linear size (3.7) for which an associated integral feature is established from the extracted integral
feature(s) with the maximum inscribed criterion
Note 1 to entry: In the case of an internal feature of linear size (3.2), the maximum inscribed size was previously called
“mating size for an internal feature”. It maximizes the size of the associated integral feature that is inscribed in the
extracted integral feature.
Note 2 to entry: See Figure 6 for an example of maximum inscribed size. Figure 6 a) shows an extracted feature under
consideration, which can be either an internal or external feature and either a cylinder or two parallel opposite planes.
a) Extracted feature under consideration
b) Maximum inscribed size
Figure 6 — Example of maximum inscribed size
3.7.3
minimum circumscribed size
global linear size (3.7) for which an associated integral feature is established from the extracted integral
feature(s) with the minimum circumscribed criterion
Note 1 to entry: In the case of an external feature of linear size (3.2), the minimum circumscribed size was previously
called “mating size for an external feature”. It minimizes the size of the associated integral feature that is circumscribed
to the extracted integral feature.
Note 2 to entry: See Figure 7 for an example of minimum circumscribed size. Figure 7 a) shows an extracted feature under
consideration, which can be either an internal or external feature and either a cylinder or two parallel opposite planes.

ISO 14405-1:2025(en)
a) Extracted feature under consideration
b) Minimum circumscribed size
Figure 7 — Example of minimum circumscribed size
3.7.4
minimax size
Chebyshev size
global linear size (3.7) for which an associated integral feature is established from the extracted integral
feature(s) with the minimax objective function and no material constraint
Note 1 to entry: The minimax objective function without constraint minimizes the maximum value of the set of
distances between the points of the extracted integral feature and the associated integral feature without material
constraint.
Note 2 to entry: See Figure 8 for an example of minimax size. Figure 8 a) shows an extracted feature under
consideration, which can be either an internal or external feature and either a cylinder or two parallel opposite planes.
a) Extracted feature under consideration
b) Minimax size
Key
1 places with the same minimized maximum deviation
Figure 8 — Example of minimax size

ISO 14405-1:2025(en)
3.7.5
calculated size
size (3.1) obtained by using a mathematical formula that determines an intrinsic characteristic of a feature
from one or several other dimensions of the same feature
Note 1 to entry: The calculated size is only defined for cylinders in this document.
3.7.5.1
circumference diameter
calculated size (3.7.5) giving the diameter, d, obtained from the following formula:
C
d =
π
where C is the length of the extracted and filtered integral line in a cross-section normal to the axis of the
least-squares associated cylinder
Note 1 to entry: See Figure 9, which shows an example of circumference diameter.
Note 2 to entry: The circumference diameter is a linearsection size (3.6.3).
Note 3 to entry: In cases where the feature is non-convex, the circumference diameter can be larger than the minimum
circumscribed diameter.
Note 4 to entry: A filter that builds a continuous line reduces the specification ambiguity in this case.
a) b)
Key
E extracted and filtered integral line in a cross-section, of length C
d circumference diameter, equal to C divided by π
Figure 9 — Example of circumference diameter
3.7.5.2
area diameter
calculated size (3.7.5) giving the diameter, d, obtained from the following formula:
4A
d=
π
where A is the area limited by the extracted and filtered integral line of a cross section normal to the axis of
the least-squares associated cylinder
Note 1 to entry: See Figure 10, which shows an example of area diameter.
Note 2 to entry: The area diameter is a linearsection size (3.6.3).
Note 3 to entry: A filter that builds a continuous line reduces the specification ambiguity in this case.

ISO 14405-1:2025(en)
a) b)
Key
A area inside the extracted and filtered integral line
d area diameter, calculated from A
Figure 10 — Example of area diameter
3.7.5.3
volume diameter
calculated size (3.7.5) giving the diameter, d, obtained from the following formula:
V
d=
πL
where
L is the distance between two parallel planes perpendicular to the axis of the least-squares associated
cylinder, L being the maximum distance possible such that the two parallel planes contain a complete
section of the feature;
V is the volume limited by the extracted integral cylinder and the two parallel planes.
Note 1 to entry: See Figure 11 for an example of volume diameter.
Note 2 to entry: The volume diameter is a global linear size (3.7) for the complete toleranced feature of linear size (3.2).
It can be a local linear size (3.6) when it is a linearportion size (3.6.4).

ISO 14405-1:2025(en)
Key
V volume of the extracted integral cylinder
L length of the cylinder
d volume diameter, calculated from V and L
a
Two parallel planes perpendicular to the axis of the least-squares associated cylinder with the minimum distance
between them and containing a complete section of the feature.
Figure 11 — Example of volume diameter
3.7.6
statistical size
size characteristic (3.3) defined mathematically from a homogeneous set of values of a local linear size (3.6)
Note 1 to entry: A statistical size can be used to define a global linear size (3.7) from a local linear size [two-point size
(3.6.1), spherical size (3.6.2), linearsection size (3.6.3) and linearportion size (3.6.4)].
Note 2 to entry: A statistical size can be used to define a local linear size from another local linear size, e.g. to define a
statistical linear section size from a two-point size taken in the section.
Note 3 to entry: The different types of statistical sizes defined in this document are illustrated in Figure 12.
Note 4 to entry: Annex C shows an example of a statistical size.

ISO 14405-1:2025(en)
a) b)
c) d)
Key
1 set of values of linear section sizes 6 median size (= 9,969)
2 position along the axis 7 mid-range size (= 10,020)
3 maximum size (= 10,497) 8 range of sizes (= 0,955)
4 minimum size (= 9,542) 9 standard deviation of sizes (=0,301)
5 average size (= 10,011) d values of local linear size
i
Figure 12 — Example of statistical sizes based on linear section sizes
3.7.6.1
maximum size
statistical size (3.7.6) defined as the maximum of the set of values of a local linear size (3.6)
3.7.6.2
minimum size
statistical size (3.7.6) defined as the minimum of the set of values of a local linear size (3.6)
3.7.6.3
average size
statistical size (3.7.6) defined as the average of the set of values of a local linear size (3.6)

ISO 14405-1:2025(en)
3.7.6.4
median size
statistical size (3.7.6) defined as the median value of the set of values of a local linear size (3.6)
Note 1 to entry: The median value allows the population of local linear size values to be split into two equal portions
(50 % above and 50 % below). Depending on the function of repartition of the population, the median size and the
average size can be identical or different.
3.7.6.5
mid-range size
statistical size (3.7.6) defined as the mean of the maximum and the minimum of the set of values of a local
linear size (3.6)
3.7.6.6
range of sizes
statistical size (3.7.6) defined as the difference between the maximum and the minimum of the set of values
of a local linear size (3.6)
3.7.6.7
standard deviation of sizes
statistical size (3.7.6) defined as the standard deviation of the set of values of a local linear size (3.6)
3.8
envelope requirement
requirement which specifies both the least material limit of the size (3.1) on the two-point size (3.6.1) and
the maximum material limit of the size on the maximum inscribed size (3.7.2) or the minimum circumscribed
size (3.7.3)
Note 1 to entry: See Clause 9.
3.9
common toleranced feature of linear size
several separate single features of linear size (3.2) on which a common tolerance is applied
Note 1 to entry: See 8.3.
3.10
united feature of linear size
set of two or more single integral features considered as one feature of linear size (3.2)
Note 1 to entry: A united feature of linear size is a sub-type of united feature. A united feature can be an integral
feature which is not a feature of linear size.
Note 2 to entry: See 8.4.
3.11
intersection plane
plane, established from an extracted feature of the workpiece, identifying one or more lines on extracted
surfaces (integral or median) or one or more points on extracted lines (integral or median)
Note 1 to entry: The use of intersection planes makes it possible to define toleranced features independent of the view.
Note 2 to entry: For areal surface texture, the intersection plane can be used to define the orientation of the evaluation
area, see ISO 25178-1.
[SOURCE: ISO 1101:2017, 3.2, modified — "a line on an extracted surface" changed to "one or more lines on
extracted surfaces" and " a point on an extracted line" changed to " one or more points on extracted lines "]

ISO 14405-1:2025(en)
3.12
direction feature
ideal feature, established from an extracted feature of the workpiece, identifying the direction
of the size characteristic (3.3)
Note 1 to entry: See Clause 13.
4 General
4.1 Specification modifiers and symbols
Rule A: For the purposes of this document, the specification modifiers (see ISO 17450-2:2012, 3.4.2) in
Tables 1 and 2 shall apply, except when the default size specification is used.
The use of these specification modifiers is described in Clauses 5 to 13. The presentation of graphical
symbols shall follow the rules given in Annex A.
The presentation of indications of linear size specifications shall follow the rules given in Annex B.
Table 1 — Specification modifiers for linear size specifications
Modifier Description Reference
Two-point size 3.6.1
Spherical size 3.6.2
Least-squares size 3.7.1
Maximum inscribed size 3.7.2
Minimum circumscribed size 3.7.3
Minimax size 3.7.4
Circumference diameter (calculated size) 3.7.5.1
Area diameter (calculated size) 3.7.5.2
Volume diameter (calculated size) 3.7.5.3
Maximum size (statistical size) 3.7.6.1
Minimum size (statistical size) 3.7.6.2
Average size (statistical size) 3.7.6.3
Median size (statistical size) 3.7.6.4
Mid-range size (statistical size) 3.7.6.5
Range of sizes (statistical size) 3.7.6.6
Standard deviation of sizes (statistical size) 3.7.6.7

ISO 14405-1:2025(en)
Table 2 — Complementary specification modifiers
Description Symbol Reference Example of indication
United feature of linear size 8.4
3.8
Envelope requirement
Clause 9
a
Any restricted portion of feature Clause 10
Any cross-s
...