
Engineering tolerance is the permissible limit or limits of variation in:
# a physical
dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coor ...
;
# a measured value or
physical property
A physical property is any Property (philosophy), property that is Measurement, measurable, whose value describes a state of a physical system. The changes in the physical properties of a system can be used to describe its changes between momenta ...
of a material,
manufactured object, system, or service;
# other measured values (such as temperature, humidity, etc.);
# in
engineering
Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...
and
safety, a physical
distance or space (tolerance), as in a
truck
A truck or lorry is a motor vehicle designed to transport cargo, carry specialized payloads, or perform other utilitarian work. Trucks vary greatly in size, power, and configuration, but the vast majority feature body-on-frame constructi ...
(lorry),
train or
boat
A boat is a watercraft of a large range of types and sizes, but generally smaller than a ship, which is distinguished by its larger size, shape, cargo or passenger capacity, or its ability to carry boats.
Small boats are typically found on i ...
under a
bridge
A bridge is a structure built to span a physical obstacle (such as a body of water, valley, road, or rail) without blocking the way underneath. It is constructed for the purpose of providing passage over the obstacle, which is usually somethi ...
as well as a train in a
tunnel (see
structure gauge and
loading gauge);
# in
mechanical engineering, the
space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually con ...
between a
bolt
The BOLT Browser was a web browser for mobile phones including feature phones and smartphones that can run Java ME applications. The BOLT Browser was offered free of charge to consumers and by license to mobile network operators and handset manuf ...
and a
nut or a hole, etc.
Dimensions, properties, or conditions may have some variation without significantly affecting functioning of systems, machines, structures, etc. A variation beyond the tolerance (for example, a temperature that is too hot or too cold) is said to be noncompliant, rejected, or exceeding the tolerance.
Considerations when setting tolerances
A primary concern is to determine how wide the tolerances may be without affecting other factors or the outcome of a process. This can be by the use of scientific principles, engineering knowledge, and professional experience. Experimental investigation is very useful to investigate the effects of tolerances:
Design of experiments
The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...
, formal engineering evaluations, etc.
A good set of engineering tolerances in a
specification, by itself, does not imply that compliance with those tolerances will be achieved. Actual production of any product (or operation of any system) involves some inherent variation of input and output. Measurement error and statistical uncertainty are also present in all measurements. With a
normal distribution
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is
:
f(x) = \frac e^
The parameter \mu i ...
, the tails of measured values may extend well beyond plus and minus three standard deviations from the process average. Appreciable portions of one (or both) tails might extend beyond the specified tolerance.
The
process capability of systems, materials, and products needs to be compatible with the specified engineering tolerances.
Process controls must be in place and an effective
Quality management system, such as
Total Quality Management, needs to keep actual production within the desired tolerances. A
process capability index is used to indicate the relationship between tolerances and actual measured production.
The choice of tolerances is also affected by the intended statistical
sampling plan and its characteristics such as the Acceptable Quality Level. This relates to the question of whether tolerances must be extremely rigid (high confidence in 100% conformance) or whether some small percentage of being out-of-tolerance may sometimes be acceptable.
An alternative view of tolerances
Genichi Taguchi
was an engineer and statistician. From the 1950s onwards, Taguchi developed a methodology for applying statistics to improve the quality of manufactured goods. Taguchi methods have been controversial among some conventional Western statisticians, ...
and others have suggested that traditional two-sided tolerancing is analogous to "goal posts" in a
football game: It implies that all data within those tolerances are equally acceptable. The alternative is that the best product has a measurement which is precisely on target. There is an increasing loss which is a function of the deviation or variability from the target value of any design parameter. The greater the deviation from target, the greater is the loss. This is described as the
Taguchi loss function or ''quality loss function'', and it is the key principle of an alternative system called ''inertial tolerancing''.
Research and development work conducted by M. Pillet and colleagues at the Savoy University has resulted in industry-specific adoption. Recently the publishing of the French standard NFX 04-008 has allowed further consideration by the manufacturing community.
Mechanical component tolerance

Dimensional tolerance is related to, but different from
fit in mechanical engineering, which is a ''designed-in'' clearance or interference between two parts. Tolerances are assigned to parts for manufacturing purposes, as boundaries for acceptable build. No machine can hold dimensions precisely to the nominal value, so there must be acceptable degrees of variation. If a part is manufactured, but has dimensions that are out of tolerance, it is not a usable part according to the design intent. Tolerances can be applied to any dimension. The commonly used terms are:
; Basic size: The nominal diameter of the shaft (or bolt) and the hole. This is, in general, the same for both components.
; Lower deviation: The difference between the minimum possible component size and the basic size.
; Upper deviation: The difference between the maximum possible component size and the basic size.
; Fundamental deviation: The ''minimum'' difference in size between a component and the basic size.
This is identical to the upper deviation for shafts and the lower deviation for holes. If the fundamental deviation is greater than zero, the bolt will always be smaller than the basic size and the hole will always be wider. Fundamental deviation is a form of
allowance, rather than tolerance.
; International Tolerance grade: This is a standardised measure of the ''maximum'' difference in size between the component and the basic size (see below).
For example, if a shaft with a nominal diameter of 10
mm is to have a sliding fit within a hole, the shaft might be specified with a tolerance range from 9.964 to 10 mm (i.e., a zero fundamental deviation, but a lower deviation of 0.036 mm) and the hole might be specified with a tolerance range from 10.04 mm to 10.076 mm (0.04 mm fundamental deviation and 0.076 mm upper deviation). This would provide a clearance fit of somewhere between 0.04 mm (largest shaft paired with the smallest hole, called the ''Maximum Material Condition'' - MMC) and 0.112 mm (smallest shaft paired with the largest hole, ''Least Material Condition'' - LMC). In this case the size of the tolerance range for both the shaft and hole is chosen to be the same (0.036 mm), meaning that both components have the same International Tolerance grade but this need not be the case in general.
When no other tolerances are provided, the
machining industry
Machining is a process in which a material (often metal) is cut to a desired final shape and size by a controlled material-removal process. The processes that have this common theme are collectively called subtractive manufacturing, which utilizes ...
uses the following standard tolerances:
[According to Chris McCauley, Editor-In-Chief of Industrial Press' Machinery's Handbook: Standard Tolerance "…''does not appear to originate with any of the recent editions (24-28) of Machinery's Handbook, although those tolerances may have been mentioned somewhere in one of the many old editions of the Handbook.''" (4/24/2009 8:47 AM)]
International Tolerance grades
When designing mechanical components, a system of standardized tolerances called International Tolerance grades are often used. The standard (size) tolerances are divided into two categories: hole and shaft. They are labelled with a letter (capitals for holes and lowercase for shafts) and a number. For example: H7 (hole,
tapped hole, or
nut) and h7 (shaft or bolt). H7/h6 is a very common standard tolerance which gives a tight fit. The tolerances work in such a way that for a hole H7 means that the hole should be made slightly larger than the base dimension (in this case for an ISO fit 10+0.015−0, meaning that it may be up to 0.015 mm larger than the base dimension, and 0 mm smaller). The actual amount bigger/smaller depends on the base dimension. For a shaft of the same size, h6 would mean 10+0−0.009, which means the shaft may be as small as 0.009 mm smaller than the base dimension and 0 mm larger. This method of standard tolerances is also known as Limits and Fits and can be found i
ISO 286-1:2010 (Link to ISO catalog)
The table below summarises the International Tolerance (IT) grades and the general applications of these grades:
An analysis of fit by
statistical interference
When two probability distributions overlap, statistical interference exists. Knowledge of the distributions can be used to determine the likelihood that one parameter exceeds another, and by how much.
This technique can be used for dimensioning ...
is also extremely useful: It indicates the frequency (or probability) of parts properly fitting together.
Electrical component tolerance
An electrical specification might call for a
resistor
A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias activ ...
with a nominal value of 100 Ω (
ohms), but will also state a tolerance such as "±1%". This means that any resistor with a value in the range 99–101Ω is acceptable. For critical components, one might specify that the actual resistance must remain within tolerance within a specified temperature range, over a specified lifetime, and so on.
Many commercially available
resistor
A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias activ ...
s and
capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of a ...
s of standard types, and some small
inductors, are often marked with
coloured bands to indicate their value and the tolerance. High-precision components of non-standard values may have numerical information printed on them.
Difference between ''allowance and tolerance''
The terms are often confused but sometimes a difference is maintained. See .
Clearance (civil engineering)
In
civil engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewa ...
, clearance refers to the difference between the
loading gauge and the
structure gauge in the case of
railroad cars or
trams, or the difference between the size of any
vehicle
A vehicle (from la, vehiculum) is a machine that transports people or cargo. Vehicles include wagons, bicycles, motor vehicles ( motorcycles, cars, trucks, buses, mobility scooters for disabled people), railed vehicles ( trains, trams ...
and the width/height doors, the width/height of an
overpass or the
diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid fo ...
of a
tunnel as well as the
air draft under a
bridge
A bridge is a structure built to span a physical obstacle (such as a body of water, valley, road, or rail) without blocking the way underneath. It is constructed for the purpose of providing passage over the obstacle, which is usually somethi ...
, the width of a
lock or diameter of a tunnel in the case of
watercraft. In addition there is the difference between the
deep draft and the
stream bed or
sea bed of a
waterway
A waterway is any navigable body of water. Broad distinctions are useful to avoid ambiguity, and disambiguation will be of varying importance depending on the nuance of the equivalent word in other languages. A first distinction is necessary ...
.
See also
*
Backlash (engineering)
*
Geometric dimensioning and tolerancing
*
Engineering fit
*
Key relevance
*
Loading gauge
*
Margin of error
*
Precision engineering
*
Probabilistic design
*
Process capability
*
Slack action
In railroading, slack action is the amount of free movement of one car before it transmits its motion to an adjoining coupled car. This free movement results from the fact that in railroad practice cars are loosely coupled, and the coupling is oft ...
*
Specification (technical standard)
*
Statistical process control
*
Statistical tolerance
A tolerance interval is a statistical interval within which, with some confidence level, a specified proportion of a sampled population falls. "More specifically, a 100×p%/100×(1−α) tolerance interval provides limits within which at least a ...
*
Structure gauge
*
Taguchi methods
Taguchi methods ( ja, タグチメソッド) are statistical methods, sometimes called robust design methods, developed by Genichi Taguchi to improve the quality of manufactured goods, and more recently also applied to engineering, biotechnology, ...
*
Tolerance coning Tolerance coning is the engineering discipline of creating a budget of all tolerances that potentially add/subtract to affect adequacy of a particular parameter. This is particularly critical where stages of design/manufacture precede test/use.
Fo ...
*
Tolerance interval
A tolerance interval is a statistical interval within which, with some confidence level, a specified proportion of a sampled population falls. "More specifically, a 100×p%/100×(1−α) tolerance interval provides limits within which at least a ...
*
Tolerance stacks
*
Verification and validation
Notes
Further reading
* Pyzdek, T, "Quality Engineering Handbook", 2003,
* Godfrey, A. B., "Juran's Quality Handbook", 1999,
* ASTM D4356 Standard Practice for Establishing Consistent Test Method Tolerances
External links
Limits, Fits and Tolerance Calculator (ISO System)Online calculation of fits
{{Authority control
Quality
Engineering concepts
Statistical deviation and dispersion
Mechanical standards
Metrology
Metalworking terminology
Approximations