Engineering tolerance is the permissible limit or limits of variation in: # a physical

dimension In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...

; # a measured value or

physical property A physical property is any property that is 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 momentary states. Physical properties are ...

of a material,

manufactured Manufacturing is the creation or production of goods with the help of equipment, labor, machines, tools, and chemical or biological processing or formulation. It is the essence of secondary sector of the economy. The term may refer to a ran ...

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 Safety is the state of being "safe", the condition of being protected from harm or other danger. Safety can also refer to risk management, the control of recognized hazards in order to achieve an acceptable level of risk. Meanings There are ...

, a physical

distance Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...

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 construction ...

(lorry),

train In rail transport, a train (from Old French , from Latin , "to pull, to draw") is a series of connected vehicles that run along a railway track and Passenger train, transport people or Rail freight transport, freight. Trains are typically pul ...

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 inl ...

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 A tunnel is an underground passageway, dug through surrounding soil, earth or rock, and enclosed except for the entrance and exit, commonly at each end. A pipeline is not a tunnel, though some recent tunnels have used immersed tube cons ...

(see

structure gauge A structure gauge, also called the minimum clearance outline, is a diagram or physical structure that sets limits to the extent that bridges, tunnels and other infrastructure can encroach on rail vehicles. It specifies the height and width of pl ...

and

loading gauge A loading gauge is a diagram or physical structure that defines the maximum height and width dimensions in railway vehicles and their loads. Their purpose is to ensure that rail vehicles can pass safely through tunnels and under bridges, and ke ...

); # in

mechanical engineering Mechanical engineering is the study of physical machines that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, and ...

, 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 consider ...

between a bolt and a

nut Nut often refers to: * Nut (fruit), fruit composed of a hard shell and a seed, or a collective noun for dry and edible fruits or seeds * Nut (hardware), fastener used with a bolt Nut or Nuts may also refer to: Arts, entertainment, and media Co ...

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 A specification often refers to a set of documented requirements to be satisfied by a material, design, product, or service. A specification is often a type of technical standard. There are different types of technical or engineering specificati ...

, 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 ...

, 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 The process capability is a measurable property of a process to the specification, expressed as a process capability index (e.g., Cpk or Cpm) or as a process performance index (e.g., Ppk or Ppm). The output of this measurement is often illustra ...

of systems, materials, and products needs to be compatible with the specified engineering tolerances.

Process control An industrial process control in continuous production processes is a discipline that uses industrial control systems to achieve a production level of consistency, economy and safety which could not be achieved purely by human manual control. I ...

s 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 The process capability index, or process capability ratio, is a statistical measure of process capability: the ability of an engineering process to produce an output within specification limits. The concept of process capability only holds meani ...

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 In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt ...

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 The Taguchi loss function is graphical depiction of loss developed by the Japanese business statistician Genichi Taguchi to describe a phenomenon affecting the value of products produced by a company. Praised by Dr. W. Edwards Deming (the business ...

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 uses the following standard tolerances:According to Chris McCauley, Editor-In-Chief of Industrial Press'

Machinery's Handbook ''Machinery's Handbook'' ''for machine shop and drafting-room; a reference book on machine design and shop practice for the mechanical engineer, draftsman, toolmaker, and machinist'' (the full title of the 1st edition) is a classic reference ...

: Standard Tolerance "…''does not appear to originate with any of the recent editions (24-28) of

, although those tolerances may have been mentioned somewhere in one of the many old editions of the Handbook.''" (4/24/2009 8:47 AM) Limits and Fits

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

) 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 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 active el ...

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

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 ...

s of standard types, and some small

inductor An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...

s, 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)

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, sewage ...

, clearance refers to the difference between the

and the

in the case of

railroad car A railroad car, railcar (American and Canadian English), railway wagon, railway carriage, railway truck, railwagon, railcarriage or railtruck (British English and UIC), also called a train car, train wagon, train carriage or train truck, is a ...

s or

tram A tram (called a streetcar or trolley in North America) is a rail vehicle that travels on tramway tracks on public urban streets; some include segments on segregated right-of-way. The tramlines or networks operated as public transport are ...

s, 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), wa ...

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 for ...

of a

as well as the

air draft Air draft (or air draught) is the distance from the surface of the water to the highest point on a vessel. This is similar to the " deep draft" of a vessel which is measured from the surface of the water to the deepest part of the hull below th ...

under a

, the width of a

lock Lock(s) may refer to: Common meanings *Lock and key, a mechanical device used to secure items of importance *Lock (water navigation), a device for boats to transit between different levels of water, as in a canal Arts and entertainment * ''Lock ...

or diameter of a tunnel in the case of

watercraft Any vehicle used in or on water as well as underwater, including boats, ships, hovercraft and submarines, is a watercraft, also known as a water vessel or waterborne vessel. A watercraft usually has a propulsive capability (whether by sail, ...

. In addition there is the difference between the deep draft and the

stream bed A stream bed or streambed is the bottom of a stream or river (bathymetry) or the physical confine of the normal water flow (Channel (geography), channel). The lateral confines or channel margins are known as the stream Bank (geography), banks ...

sea bed The seabed (also known as the seafloor, sea floor, ocean floor, and ocean bottom) is the bottom of the ocean. All floors of the ocean are known as 'seabeds'. The structure of the seabed of the global ocean is governed by plate tectonics. Most of ...

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 b ...

Notes

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