ISO 2692:2021

INTERNATIONAL ISO
STANDARD 2692
Fourth edition
2021-06
Geometrical product specifications
(GPS) — Geometrical tolerancing
— Maximum material requirement
(MMR), least material requirement
(LMR) and reciprocity requirement
(RPR)
Spécification géométrique des produits (GPS) — Tolérancement
géométrique — Exigence du maximum de matière (MMR), exigence
du minimum de matière (LMR) et exigence de réciprocité (RPR)
Reference number
©
ISO 2021
© ISO 2021
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Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Maximum material requirement (MMR) and least material requirement (LMR) .5
4.1 General . 5
4.1.1 MMVS or LMVS specification . 5
4.1.2 Indirect determination of MMVS or LMVS . 5
4.1.3 Direct indication of MMVS or LMVS . 6
4.1.4 MMR or LMR applied to several toleranced features . 7
4.1.5 Simultaneous requirement . 7
4.1.6 MMR or LMR on a datum without MMR or LMR on the toleranced feature . 7
4.2 Maximum material requirement (MMR) . 7
4.2.1 MMR for toleranced features with indirect determination of virtual size . 7
4.2.2 MMR for related datum features with indirect determination of virtual size . 8
4.2.3 MMR for toleranced features with direct indication of virtual size .10
4.2.4 MMR for related datum features with direct indication of virtual size .10
4.3 Least material requirement (LMR) .11
4.3.1 LMR for toleranced features with indirect determination of virtual size .11
4.3.2 LMR for related datum features with indirect determination of virtual size .12
4.3.3 LMR for toleranced features with direct indication of virtual size .13
4.3.4 LMR for related datum features with direct indication of virtual size .14
5 Reciprocity requirement (RPR) .15
5.1 General .15
5.2 Reciprocity requirement (RPR) and maximum material requirement (MMR) .15
5.3 Reciprocity requirement (RPR) and least material requirement (LMR) .15
Annex A (informative) Examples of tolerancing with , and .16
Annex B (informative) Former practice.48
Annex C (informative) Concept diagram .49
Annex D (informative) Use of symbols for geometrical characteristics with or .51
Annex E (informative) Relation to the GPS matrix model.53
Bibliography .54
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 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 fourth edition cancels and replaces the third edition (ISO 2692:2014), which has been technically
revised.
The main changes to the previous edition are as follows:
— direct indication of maximum material or least material virtual size has been added (see 4.1.3);
— the use of SZ or CZ symbols has been added (see 4.1.4);
— the use of SIM symbol has been added (see 4.1.5).
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 2021 – All rights reserved

Introduction
0.1  General
This document is a geometrical product specification (GPS) standard and is to be regarded as a general
GPS standard (see ISO 14638). It influences the chain links A, B and C of the chain of standards on size,
form, orientation and location.
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 specifications made in accordance with this
document, unless otherwise indicated.
For more detailed information on the relation of this document to the GPS matrix model, see Annex E.
This document deals with some frequently occurring workpiece functional cases in design and
tolerancing. The “maximum material requirement” (MMR) can cover, for example, “assemblability” and
the “least material requirement” (LMR) can cover, for example, “minimum wall thickness” of a part.
MMR and LMR requirements can accurately simulate the intended function of the workpiece by allowing
the combination of two independent requirements into one collective requirement or to directly define
maximum material virtual condition (MMVC) or least material virtual condition (LMVC) (see Annex C).
In some cases of both MMR and LMR, the “reciprocity requirement” (RPR) can be added.
NOTE 1 In GPS standards, threaded features are often considered as a type of cylindrical feature of size.
However, no rules are defined in this document for how to apply MMR, LMR and RPR to threaded features.
Consequently, application of the tools defined in this document for threaded features is risky.
NOTE 2 A geometrical tolerance value of 0 (0 or 0 ) can be used to avoid non-conformity of parts that can
be assembled, in the case of MMR, or have minimum wall thickness, in the case of LMR.
0.2  Information about MMR
The assembly of parts depends on the combined effect of:
a) the size (of one or more features of size), and
b) the geometrical deviation of the features and their derived features, such as the pattern of bolt
holes in two flanges and the bolts securing them.
The minimum assembly clearance occurs when each of the mating features of size is at its maximum
material size (MMS) (e.g. the largest bolt size and the smallest hole size) and when the geometrical
deviations (e.g. the form, orientation and location deviations) of the features of size and their derived
features (median line or median surface) are also fully consuming their tolerances. Assembly clearance
increases to a maximum when the sizes of the assembled features of size are furthest from their MMSs
(e.g. the smallest shaft size and the largest hole size) and when the geometrical deviations (e.g. the
form, orientation and location deviations) of the features of size and their derived features are zero.
It therefore follows that to manage the assemblability, the effect of the dimensional and geometrical
variation can be dealt with by a specification using the maximum material concept. This requirement is
indicated on the drawing by the symbol .
Furthermore, it can be useful to add to the datum indicator in the datum section when the datum is
a feature of linear size and the clearance between the datum and the counterpart is favourable to the
assembly of the part.
0.3  Information about LMR
The LMR is designed to control, for example, the minimum wall thickness, thereby preventing burst
(due to pressure in a tube), or the maximum width of a series of slots. To manage the material strength
function, the effect of the dimensional and geometrical variation can be dealt with by a specification
using the minimum material concept. This requirement is indicated on drawings by the symbol .
0.4  Information about RPR
The RPR is an additional modifier, which may be used together with the MMR or with the LMR in cases
where it is permitted – taking into account the function of the toleranced feature(s) – to enlarge the
size tolerance when the geometrical deviation on the actual workpiece does not take full advantage of,
respectively, the MMVC or the LMVC.
The RPR is indicated on drawings by the symbol .
0.5  General information about terminology and figures
The terminology and tolerancing concepts in this document have been updated to conform to GPS
terminology, notably that in ISO 286-1, ISO 14405-1, ISO 17450-1 and ISO 17450-3.
vi © ISO 2021 – All rights reserved

INTERNATIONAL STANDARD ISO 2692:2021(E)
Geometrical product specifications (GPS) — Geometrical
tolerancing — Maximum material requirement (MMR),
least material requirement (LMR) and reciprocity
requirement (RPR)
1 Scope
This document defines the maximum material requirement (MMR), the least material requirement
(LMR) and the reciprocity requirement (RPR). These requirements can only be applied to linear
features of size of cylindrical type or two parallel opposite planes type.
These requirements are often used to control specific functions of workpieces where size and geometry
are interdependent, for example to fulfil the functions “assembly of parts” (for MMR) or “minimum wall
thickness” (for LMR). However, the MMR and LMR can also be used to fulfil other functional design
requirements.
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 1101:2017, Geometrical product specifications (GPS) — Geometrical tolerancing — Tolerances of form,
orientation, location and run-out
ISO 5458, Geometrical product specifications (GPS) — Geometrical tolerancing — Pattern and combined
geometrical specification
ISO 5459:2011, Geometrical product specifications (GPS) — Geometrical tolerancing — Datums and datum
systems
ISO 14405-1, Geometrical product specifications (GPS) — Dimensional tolerancing — Part 1: Linear sizes
ISO 17450-1:2011, Geometrical product specifications (GPS) — General concepts — Part 1: Model for
geometrical specification and verification
ISO 17450-3, Geometrical product specifications (GPS) — General concepts — Part 3: Toleranced features
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 5459, ISO 14405-1, ISO 17450-1
and ISO 17450-3 and the following apply.
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/
3.1
integral feature
geometrical feature belonging to the real surface of the workpiece or to a surface model
Note 1 to entry: An integral feature is intrinsically defined, for example skin of the workpiece.
[SOURCE: ISO 17450-1:2011, 3.3.5, modified — Notes 2 and 3 to entry removed.]
3.2
feature of linear size
geometrical feature, having one or more intrinsic characteristics, only one of which may be considered
as variable parameter, that additionally is a member of a “one parameter family”, and obeys the
monotonic containment property for that parameter
EXAMPLE 1 A single cylindrical hole or shaft is a feature of linear size. Its linear size is its diameter.
EXAMPLE 2 Two parallel opposite plane surfaces are a feature of linear size. Their linear size is the distance
between the two parallel opposite planes.
[SOURCE: ISO 17450-1:2011, 3.3.1.5.1, modified — Notes to entry removed; EXAMPLE 2 replaced.]
3.3
derived feature
geometrical feature, which does not exist physically on the real surface of the workpiece and which is
not natively a nominal integral feature (3.1)
Note 1 to entry: A derived feature can be established from a nominal integral surface, an associated integral
surface or an extracted integral surface. It is qualified respectively as a nominal derived feature, an associated
derived feature or an extracted derived feature.
Note 2 to entry: The centre point, the median line and the median surface defined from one or more integral
features (3.1) are types of derived features.
EXAMPLE 1 The median line of a cylinder is a derived feature obtained from the cylindrical surface, which is
an integral feature (3.1). The axis of the nominal cylinder is a nominal derived feature.
EXAMPLE 2 The median surface of two parallel opposite planes is a derived feature obtained from the two
parallel opposite planes, which constitute an integral feature (3.1). The median plane of the nominal two parallel
opposite planes is a nominal derived feature.
[SOURCE: ISO 17450-1:2011, 3.3.6, modified.]
3.4
maximum material size
MMS
value equal to the upper limit of size (ULS) or to the largest ULS in case
of multiple size specifications
Note 1 to entry: An MMS can be defined for any of the size characteristics in ISO 14405-1.
Note 2 to entry: ULS is defined in ISO 14405-1.
3.5
maximum material size
MMS
value equal to the lower limit of size (LLS) or to the smallest LLS in
case of multiple size specifications
Note 1 to entry: An MMS can be defined for any of the size characteristics in ISO 14405-1.
Note 2 to entry: LLS is defined in ISO 14405-1.
3.6
least material size
LMS
value equal to LLS or to the smallest LLS in case of multiple size
specifications
Note 1 to entry: An LMS can be defined for any of the size characteristics in ISO 14405-1.
2 © ISO 2021 – All rights reserved

Note 2 to entry: LLS is defined in ISO 14405-1.
3.7
least material size
LMS
value equal to ULS or to the largest ULS in case of multiple size
specifications
Note 1 to entry: An LMS can be defined for any of the size characteristics in ISO 14405-1.
Note 2 to entry: ULS is defined in ISO 14405-1.
3.8
maximum material virtual size
MMVS
value equal to the size of the maximum material virtual condition (3.9)
Note 1 to entry: MMVS can be directly indicated (see 4.1.3) or calculated from the maximum material size (3.4,
3.5) and the geometrical tolerance (see 4.1.2)
3.9
maximum material virtual condition
MMVC
state of associated feature with size equal to maximum material virtual size (3.8)
Note 1 to entry: MMVC is a perfect form condition of the feature of linear size (3.2).
Note 2 to entry: MMVC includes an orientation constraint (in accordance with ISO 1101 and ISO 5459) of the
associated feature when the geometrical specification is an orientation specification (see Figure A.3). MMVC
includes a location constraint (in accordance with ISO 1101 and ISO 5459) of the associated feature when the
geometrical specification is a location specification (see Figure A.4).
Note 3 to entry: See examples in Annex A.
3.10
least material virtual size
LMVS
value equal to the size of the least material virtual condition (3.11)
Note 1 to entry: LMVS can be directly indicated (see 4.1.3) or calculated from the least material size (3.6, 3.7) and
the geometrical tolerance (see 4.1.2)
3.11
least material virtual condition
LMVC
state of associated feature of least material virtual size (3.10)
Note 1 to entry: LMVC is a perfect form condition of the feature of linear size (3.2).
Note 2 to entry: LMVC includes an orientation constraint (in accordance with ISO 1101 and ISO 5459) of the
associated feature when the geometrical specification is an orientation specification. LMVC includes a location
constraint (in accordance with ISO 1101 and ISO 5459) of the associated feature when the geometrical
specification is a location specification (see Figure A.5).
Note 3 to entry: See Figures A.5, A.8, A.9, A.14, A.15.
3.12
maximum material requirement
MMR
requirement for a feature of linear size (3.2), defining a geometrical feature of the same type and of
perfect form, with a given value for the intrinsic characteristic (dimension) equal to the maximum
material virtual size (3.8), which limits the non-ideal feature on the outside of the material
Note 1 to entry: MMR is used to control the assemblability of a workpiece.
Note 2 to entry: See also 4.2.
3.13
least material requirement
LMR
requirement for a feature of linear size (3.2), defining a geometrical feature of the same type and of
perfect form, with a given value for the intrinsic characteristic (dimension) equal to the least material
virtual size (3.10), which limits the non-ideal feature on the inside of the material
Note 1 to entry: LMR is used, for example, to control the minimum wall thickness between two symmetrical or
coaxially located similar features of size.
Note 2 to entry: See also 4.3.
3.14
reciprocity requirement
RPR
additional requirement for a feature of linear size (3.2) indicated in addition to the maximum material
requirement (3.12) or the least material requirement (3.13) to indicate that the size tolerance is increased
by the difference between the geometrical tolerance and the actual geometrical deviation
3.15
external feature of linear size
feature of linear size (3.2) where vectors normal to the surface are directed outward from the material
in a direction opposite to the median feature
Note 1 to entry: The cylindrical surface of a shaft is considered to be an external feature of linear size.
Note 2 to entry: See Figure 1.
Key
1 external feature of linear size
2 normal vectors directed outward from the material
3 median feature (cylinder axis)
Figure 1 — Example of external feature of linear size
4 © ISO 2021 – All rights reserved

3.16
internal feature of linear size
feature of linear size (3.2) where vectors normal to the surface are directed outward from the material
in a direction toward the median feature
Note 1 to entry: The cylindrical surface of a hole is considered to be an internal feature of linear size.
Note 2 to entry: See Figure 2.
Key
1 internal feature of linear size
2 normal vectors directed outward from the material
3 median feature (cylinder axis)
Figure 2 — Example of internal feature of linear size
4 Maximum material requirement (MMR) and least material requirement (LMR)
4.1 General
4.1.1 MMVS or LMVS specification
The MMR and the LMR can be applied to a set of one or more feature(s) of size as toleranced feature(s),
datum(s) or both. The MMVS or the LMVS shall be specified by one of the two following options:
a) An MMR without direct indication of MMVS or an LMR without direct indication of LMVS but with a
size specification for the considered feature. This option is referred to as indirect determination of
virtual size in this document.
b) An MMR with direct indication of MMVS between square brackets in the tolerance indicator or
an LMR with direct indication of LMVS between square brackets in the tolerance indicator as
explained in this document. This option is referred to as direct indication of virtual size.
A geometrical specification with MMR or LMR shall be indicated as applying to a derived feature.
However, the toleranced feature considered in the rules of this document is the corresponding integral
feature.
The rules in this document shall not be applied to threaded features, even if threaded features are often
considered as cylindrical features in GPS standards.
The possible combinations of geometrical characteristic symbols and MMR or LMR are illustrated in
Annex D.
4.1.2 Indirect determination of MMVS or LMVS
When indirect determination of virtual size is selected [4.1.1 a)], the virtual size(s) introduced by the use
of maximum or least material modifier in geometrical specification shall be calculated by considering
the combination(s) of the geometrical tolerance(s) (applied to the derived feature of the feature of size)
and the upper or lower tolerance limit of the dimensional specification(s) (of the feature(s) of size).
NOTE As limited by the scope, the only derived features considered in this document are median lines and
median surfaces.
When indirect determination of virtual size is used, then the MMVS or the LMVS shall be the result of
the computations described hereafter.
For external features of linear size except for a datum feature with MMR when rule F is fulfilled [see
4.2.2 b)], the MMVS is given by Formula (1):
σ = σ + δ (1)
MMVS MMS
For internal features of linear size except for a datum feature with MMR when rule F is fulfilled [see
4.2.2 b)], the MMVS is given by Formula (2):
σ = σ − δ (2)
MMVS MMS
For external features of linear size except for a datum feature with LMR when rule M is fulfilled [see
4.3.2 b)], the LMVS is given by Formula (3):
σ = σ − δ (3)
LMVS LMS
For internal features of linear size except for a datum feature with LMR when rule M is fulfilled [see
4.3.2 b)], the LMVS is given by Formula (4):
σ = σ + δ (4)
LMVS LMS
For a datum feature with MMR when rule F is fulfilled [see 4.2.2 b)], the MMVS for external and internal
features of size is given by Formula (5):
σ = σ (5)
MMVS MMS
For a datum feature with LMR when rule M is fulfilled (see 4.3.2 b)], the LMVS for external and internal
features of size is given by Formula (6):
σ = σ (6)
LMVS LMS
where
σ is the MMVS;
MMVS
σ is the MMS;
MMS
σ is the LMVS;
LMVS
σ is the LMS;
LMS
δ is the geometrical tolerance.
4.1.3 Direct indication of MMVS or LMVS
When direct indication of virtual size is selected [4.1.1 b)], then the MMVS or the LMVS shall be indicated
between square brackets in the tolerance indicator and the virtual size is equal to this value as stated in
the rules of this document. If a size is also specified for the considered feature, it shall be considered as
an independent specification according to ISO 14405-1. No collective requirement is created between
6 © ISO 2021 – All rights reserved

the two specifications (size specification and geometrical specification) in the case of direct indication
of MMVS or LMVS.
NOTE It is the responsibility of the designer to select compatible values for the size of the feature and the
MMVS or LMVS as they can conflict.
4.1.4 MMR or LMR applied to several toleranced features
When an MMR or LMR applies to several toleranced features, the symbols CZ or SZ shall always be
indicated in the zone section of the tolerance indicator following the sequence order specified in
ISO 1101.
NOTE See Annex B for former practice.
4.1.5 Simultaneous requirement
A simultaneous requirement can be useful for example for MMR or LMR with same datum indication
containing MMR or LMR.
When a simultaneous requirement is needed, the SIM symbol possibly followed by an identification
number (SIMi) without a space shall be indicated in the adjacent indication area of each related
geometrical specification in accordance with ISO 5458.
The use of the SIM modifier transforms a set of more than one geometrical specification with MMR
or LMR into a combined specification. The corresponding MMVC or LMVC are locked together with
location and orientation constraints according to the rules of this document. The datum system is also
constrained to be the same for each specification in the same SIM group.
Figure A.17 shows an example of simultaneous requirement.
4.1.6 MMR or LMR on a datum without MMR or LMR on the toleranced feature
When an MMR or LMR is applied to the datum only (see Figure A.19), then the rules for datum fully
apply (see 4.2.2, 4.2.4 and 4.3.2, 4.3.4). In addition, the constraints on the MMVC(s) of the datum(s) and
the MMVC(s) of the toleranced feature(s) stated in rule D [see 4.2.1 d)] or in rule K (see 4.3.1 d)] are
replaced with the corresponding constraints applied on the MMVC(s) of the datum(s) and the tolerance
zone as defined in ISO 1101 and ISO 5459.
4.2 Maximum material requirement (MMR)
4.2.1 MMR for toleranced features with indirect determination of virtual size
When the MMR applies to the toleranced feature and the indirect determination of virtual size is
selected, it shall be indicated on drawings by the symbol placed after the geometrical tolerance of
the derived feature of the feature of linear size (toleranced feature) in the tolerance indicator with no
size indicated in square brackets.
The MMR for toleranced features with indirect determination of virtual size results in four independent
requirements:
— a requirement for the upper limit of the size [see rules A 1) and A 2)];
— a requirement for the lower limit of the size [see rules B 1) and B 2)];
— a requirement for the surface non-violation of the MMVC (see rule C);
— a requirement for applying constraints on MMVCs (see rule D).
When the MMR is specified for the toleranced feature with indirect determination of virtual size, then
the following rules shall be applied for the surface(s) (of the feature of linear size), and the MMVS shall
be computed from the size specification and the geometric specification according to the rules of this
document.
a) Rule A: The sizes of the toleranced feature shall be:
1) equal to or smaller than the MMS, for external features;
2) equal to or larger than the MMS, for internal features.
NOTE 1 This rule can be altered by the indication of RPR, with symbol after the symbol [see 5.2
and Figure A.1 b)].
b) Rule B: The sizes of the toleranced feature shall be:
1) equal to or larger than the LMS, for external features [see Figures A.2 a), A.3 a), A.4 a), A.6 a),
A.7 a), A.10, A.11 and A.12];
2) equal to or smaller than the LMS, for internal features [see Figures A.2 b), A.3 b), A.4 b), A.6 b),
A.7 b), A.10 to A.13, A.16 to A.19].
c) Rule C: The MMVC of the toleranced feature shall not be violated by the extracted (integral) feature
(see Figures A.2, A.3, A.4, A.6, A.7, A.10 to A.19).
NOTE 2 Use of the envelope requirement may lead to superfluous constraints, reducing the technical
and economic advantage of MMR, if the functional requirement is purely assemblability.
NOTE 3 The indication 0 applied to a form specification on a feature of linear size has the same meaning
as the envelope requirement applied to a size.
d) Rule D: The rule applies as follows:
— When the geometrical specification is an orientation or a location relative to a (primary)
datum or a datum system, the MMVC of the toleranced feature shall be in theoretically exact
orientation or location relative to the datum or the datum system, in accordance with ISO 1101
and ISO 5459 (see 3.9, Note 2 to entry, and Figures A.3, A.4, A.6 and A.7).
— Moreover, if several toleranced features are controlled by the same tolerance indication with
the CZ symbol, the MMVCs shall also be in theoretically exact orientation and location relative
to each other (see Figures A.1, A.10, A.11 and A.13).
— If several toleranced features are controlled by the same tolerance indicator with the SZ symbol,
then the MMVCs are not constrained to be in theoretically exact orientation nor location relative
to each other (see Figure A.18). In both cases (CZ or SZ indication) constraints relative to datums
remain.
— Additionally, if the symbol SIM possibly followed by an index number as required by ISO 5458 is
indicated, then the MMVCs shall be constrained in orientation and location with the MMVCs of
the SIM group.
4.2.2 MMR for related datum features with indirect determination of virtual size
When the MMR applies to the datum feature and the indirect determination of virtual size is selected,
it shall be indicated on drawings by the symbol placed after the datum letter(s) in the tolerance
indicator.
The datum letter(s) followed by the symbol result in an associated feature with a fixed size defined
by the MMVC.
NOTE 1 Virtual conditions of toleranced feature and datum feature are constrained between them in
orientation and location. The result is one combined virtual condition.
8 © ISO 2021 – All rights reserved

The MMR for datum features results in three independent requirements:
— a requirement for the surface non-violation of the MMVC (see rule E);
— a requirement for MMVS when there is no geometrical specification or when there are only
geometrical specifications whose tolerance value is not followed by the symbol (see rule F);
— a requirement for MMVS when there is a geometrical specification whose tolerance value is followed
by symbol and whose “datum” section (third and subsequent compartments) of the tolerance
indicator meets a property defined in rule G.
NOTE 2 The use of after the datum letter is only possible if the datum is obtained from a feature of linear
size.
When MMR applies to all elements of the collection of surfaces of a common datum, the corresponding
sequence of letters identifying the common datum shall be indicated within parentheses (see Figure A.13
and ISO 5459:2011, rule 9) and MMVCs are by default constrained in location and orientation relative
to each other (see ISO 5459:2011, rule 7). When MMR applies only to one surface of the collection of
features involved in a common datum, the sequence of letters identifying the common datum shall not
be indicated within parentheses, and the requirement applies only to the feature identified by the letter
placed just before the modifier.
In this case, it specifies for the surface(s) (of the feature of linear size) the following rules:
a) Rule E: The MMVC of the related datum feature shall not be violated by the extracted (integral)
datum feature from which the datum is derived (see Figures A.6 and A.7). If a SIM symbol
optionally followed by an index number as required by ISO 5458 is indicated in the adjacent zone of
the corresponding tolerance indicator, then the MMVC shall be in the same orientation and location
as the MMVCs considered for the datums of the same SIM group (see Figure A.17).
b) Rule F: The MMVS of the related datum feature shall be equal to its MMS [see Formula (5)], when
the related datum feature:
— has no geometrical specification (see Figure A.6); or
— has only geometrical specifications whose tolerance value is not followed by the symbol ; or
— has no geometrical specification conforming with rule G.
NOTE 3 It is emphasized that when the related datum feature has a geometrical specification
without the symbol , then rule F is not sufficient to ensure the assemblability of the datum feature.
See the computation of MMVS in 4.1.2 and Figure A.6 c). Additionally, if the geometrical specification of
the datum feature is modified in a subsequent revision of the drawing, then the MMVS could change if
rule G becomes mandatory in this case.
c) Rule G: The MMVS of the related datum feature shall be equal to the MMS, plus (for external
features of linear size) or minus (for internal features of linear size) the geometrical tolerance, when
the datum feature is controlled by a geometrical specification whose tolerance value is followed by
the symbol , and:
1) it is a form specification, and the related datum is the primary datum of the tolerance indicator
where the symbol is indicated next to the datum letter (see Figure A.7); or
2) it is an orientation or location specification whose datum or datum system contains exactly the
same datum(s) in the same order as the one(s) called before the related datum in the tolerance
indicator where the symbol is indicated next to the datum letter (see Figures A.12 and A.13).
NOTE 4 In this case, the MMVS for external features of linear size is as given in Formula (1), and the
MMVS for internal features of linear size is as given in Formula (2). See 4.1.2.
When these properties are not observed, rule F applies.
In the case of rule G, the datum feature indicator should be directly connected to that geometrical
tolerance indicator from which the MMVC of the datum feature is controlled (see ISO 5459:2011, rule 1,
bullet 2).
NOTE 5 This recommendation was a requirement in ISO 2692:2014 (see B.3).
When several geometrical specifications on a related datum feature fulfil rule G, it is recommended
that direct indication of MMVS is used (see 4.1.3).
4.2.3 MMR for toleranced features with direct indication of virtual size
When the MMR applies to the toleranced feature and the direct indication of virtual size is selected,
then the value of MMVS shall be indicated after the symbol between square brackets in the zone,
feature and characteristic section. The value of MMVS shall be preceded by a Ø symbol for a cylinder
(see Figure 3 for a cylindrical feature). The Ø symbol shall be omitted when the feature size is not a
diameter. When direct indication of MMVS is selected, no geometrical tolerance value shall be indicated
before the symbol in the zone, feature and characteristic section (see Figures A.14 and A.15).
Key
1 zone, feature and characteristic section
2 numerical value for the MMVS
Figure 3 — Direct indication of MMVS for a toleranced feature
When the MMR is specified for the toleranced feature with the direct indication of virtual size, rules A
and B shall not be applied and rules C, D and Q shall be applied.
Rule Q: The MMVS for the toleranced feature shall be equal to the value indicated between square
brackets in the corresponding zone, feature and characteristic section.
If any size is also specified for the considered feature, it shall be considered as an independent
specification according to ISO 14405-1 (see Figures A.14 and A.15).
NOTE See 4.1.3.
4.2.4 MMR for related datum features with direct indication of virtual size
When the MMR applies to the datum and the direct indication of virtual size is selected, then the value
of MMVS shall be indicated after the symbol between square brackets in the datum indicator (see
Figure A.16). The value of MMVS shall be preceded by a Ø symbol for a cylinder (see Figure 4 for a
cylindrical feature). The Ø symbol shall be omitted when the feature size is not a diameter.
NOTE The value indicated between square brackets is the designer's responsibility. This value can be
different from the calculated value when applying the indirect determination of MMVS.
10 © ISO 2021 – All rights reserved

Key
1 datum section
2 numerical value for the MMVS of the datum
Figure 4 — Direct indication of MMVS for a datum
In the case of a common datum with the same MMVS for each datum feature, the indication of common
datum in the datum indicator section shall be surrounded with brackets, followed by and the
indication of the MMVS in square brackets, e.g. (A-B) [d].
In the case of a common datum with different MMVSs for each datum feature, the indication of common
datum in the datum indicator section shall be surrounded with brackets, followed by and the
indication of the MMVSs in square brackets separated with a dash and surrounded with brackets, e.g.
(A-B) ([d1]-[d2]). Each MMVS value applies to each datum feature in the same order.
These two requirements apply in the same manner for more than two datum features.
When the MMR is specified for a datum with direct indication of the MMVS then rule E shall be applied,
rules F and G shall not be applied and rule O shall be applied to the surface of the feature of linear size.
Rule O: The MMVS for the related datum feature shall be equal to the value indicated between square
brackets in the corresponding datum section.
If any size is also specified for the considered feature, it shall be considered as an independent
specification according to ISO 14405-1.
4.3 Least material requirement (LMR)
4.3.1 LMR for toleranced features with indirect determination of virtual size
When the LMR applies to the toleranced feature and the indirect determination of virtual size is selected,
then it shall be indicated on the drawing by the symbol placed after the geometrical tolerance of the
derived feature of the feature of linear size (toleranced feature) in the tolerance indicator with no size
indicated in square brackets.
EXAMPLE To fully control the minimum wall thickness, the symbol can be applied to the tolerancing of
the features on both sides of the wall. LMR can be implemented in two different ways, as follows:
— The location requirements for the two different sides of the wall can refer to the same datum axis or datum
system (see Figure A.8). In this case, applies to the two toleranced features.
— The location requirement of the derived feature for one of the sides of the wall can refer to the derived feature
of the other as the datum. In this case, the tolerance for the toleranced feature and the datum letter are
followed by the symbol (see Figure A.9).
NOTE 1 This possibility only applies if the features on the two sides are features of size.
When the LMR is specified for the toleranced feature with indirect determination of virtual size, then
the following rules shall be applied to the surface(s) (of the feature of linear size), and the LMVS shall
be computed from the size specification and the geometric specification according to the rules of this
document.
a) Rule H: The sizes of the toleranced feature shall be:
1) equal to or larger than the LMS, for external features;
2) equal to or smaller than the LMS, for internal features.
NOTE 2 This rule can be altered by the indication of RPR, with the symbol after the symbol [see
5.3, Figure A.5 e) and f)].
b) Rule I: The sizes of the toleranced feature shall be:
1) equal to or smaller than the MMS, for external features [see Figures A.5 a), A.8 and A.9];
2) equal to or larger than the MMS, for internal features [see Figures A.5 b) and A.8].
c) Rule J: The LMVC of the toleranced feature shall not be violated by the extracted (integral) feature
(see Figures A.5, A.8 and A.9).
d) Rule K: The rule applies as follows:
— When the geometrical specification is an orientation or a location relative to a (primary) datum or
a datum system, the LMVC of the toleranced feature shall be in theoretically exact orientation or
location relative to the datum or the datum system, in accordance with ISO 1101 and ISO 5459 (see
3.11, Note 2 to entry, and Figures A.5, A.8 and A.9).
— Moreover, if several toleranced features are controlled by the same tolerance indication with CZ
symbol, the LMVCs shall also be in theoreticall
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