Tolerance (engineering)
Encyclopedia
Engineering tolerance is the permissible limit or limits of variation in
1. a physical dimension
Dimension
In physics and mathematics, the dimension of a 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 because only one coordinate is needed to specify a point on it...

,
2. a measured value or physical property
Physical property
A physical property is any property that is measurable whose value describes a physical system's state. The changes in the physical properties of a system can be used to describe its transformations ....

of a material, manufactured
Manufacturing
Manufacturing is the use of machines, tools and labor to produce goods for use or sale. The term may refer to a range of human activity, from handicraft to high tech, but is most commonly applied to industrial production, in which raw materials are transformed into finished goods on a large scale...

object, system, or service,
3. other measured values (such as temperature, humidity, etc.).
4. in engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...

and safety
Safety
Safety is the state of being "safe" , the condition of being protected against physical, social, spiritual, financial, political, emotional, occupational, psychological, educational or other types or consequences of failure, damage, error, accidents, harm or any other event which could be...

, a physical distance
Distance
Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...

or space (tolerance), as in a truck
Truck
A truck or lorry is a motor vehicle designed to transport cargo. Trucks vary greatly in size, power, and configuration, with the smallest being mechanically similar to an automobile...

(lorry), train
Train
A train is a connected series of vehicles for rail transport that move along a track to transport cargo or passengers from one place to another place. The track usually consists of two rails, but might also be a monorail or maglev guideway.Propulsion for the train is provided by a separate...

or boat
Boat
A boat is a watercraft of any size designed to float or plane, to provide passage across water. Usually this water will be inland or in protected coastal areas. However, boats such as the whaleboat were designed to be operated from a ship in an offshore environment. In naval terms, a boat is a...

under a bridge
Bridge
A bridge is a structure built to span physical obstacles such as a body of water, valley, or road, for the purpose of providing passage over the obstacle...

as well as a train in a tunnel
Tunnel
A tunnel is an underground passageway, completely enclosed except for openings for egress, commonly at each end.A tunnel may be for foot or vehicular road traffic, for rail traffic, or for a canal. Some tunnels are aqueducts to supply water for consumption or for hydroelectric stations or are sewers...

(see structure gauge
Structure gauge
The structure gauge, also called the minimum clearance outline, is the minimum height and width of tunnels and bridges as well as the minimum height and width of the doors that allow a rail siding access into a warehouse...

A loading gauge defines the maximum height and width for railway vehicles and their loads to ensure safe passage through bridges, tunnels and other structures...

).
5. in mechanical engineering
Mechanical engineering
Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. It is the branch of engineering that involves the production and usage of heat and mechanical power for the...

the space between a bolt
Bolt
-Fasteners:*A cap screw, as used in a bolted joint*Screw, a cylindrical threaded fastener*Dead bolt, a kind of locking mechanism*Bolt , an anchor point used in rock climbing-Weaponry:*Bolt , a mechanism used in firearms...

and a nut
Nut (hardware)
A nut is a type of hardware fastener with a threaded hole. Nuts are almost always used opposite a mating bolt to fasten a stack of parts together. The two partners are kept together by a combination of their threads' friction, a slight stretch of the bolt, and compression of the parts...

or a hole, etc..

Dimensions, properties, or conditions may vary within certain practical limits without significantly affecting functioning of equipment or a process. Tolerances are specified to allow reasonable leeway for imperfections and inherent variability without compromising performance.

A variation beyond the tolerance (for example, a temperature that's too hot or too cold) is said to be non-compliant, rejected, or exceeding the tolerance (regardless of if this breach was of the lower or the upper bound). If the tolerance is set too restrictive, resulting in most objects run by it being rejected, it is said to be intolerant.

## Tolerances

Tolerances are often set by design engineers and published in specifications or contract
Contract
A contract is an agreement entered into by two parties or more with the intention of creating a legal obligation, which may have elements in writing. Contracts can be made orally. The remedy for breach of contract can be "damages" or compensation of money. In equity, the remedy can be specific...

s. Many technical standards have tolerances agreed upon by consensus discussions and sometimes formal voting procedures.

The tolerance may be specified as a factor or percentage of the nominal value, a maximum deviation from a nominal value, an explicit range of allowed values, be specified by a note or published standard with this information, or be implied by the numeric accuracy of the nominal value. Tolerance can be symmetrical, as in 40±0.1, or asymmetrical, such as 40+0.2/−0.1.

It is often desirable to specify the largest possible tolerance while maintaining proper functionality. Closer or tighter tolerances are more difficult, and hence costly, to achieve. Conversely, larger or looser tolerances may significantly affect the operation of the device.

Tolerance is different from safety factor
Factor of safety
Factor of safety , also known as safety factor , is a term describing the structural capacity of a system beyond the expected loads or actual loads. Essentially, how much stronger the system is than it usually needs to be for an intended load...

, but an adequate safety factor will take into account relevant tolerances as well as other possible variations.

## 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
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...

, 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, the tails of measured values may extend well beyond plus and minus three standard deviations from the process average. One, or both, tails might extend beyond the specified tolerance.

The process capability
Process capability
A process is a unique combination of tools, materials, methods, and people engaged in producing a measurable output; for example a manufacturing line for machine parts...

of systems, materials, and products needs to be compatible with the specified engineering tolerances. Process control
Process control
Process control is a statistics and engineering discipline that deals with architectures, mechanisms and algorithms for maintaining the output of a specific process within a desired range...

s must be in place and an effective Quality management system
Quality management system
A quality management system can be expressed as the organizational structure, procedures, processes and resources needed to implement quality management.-Elements of a Quality Management System:# Organizational structure# Responsibilities# Methods...

, such as Total Quality Management
Total Quality Management
Total quality management or TQM is an integrative philosophy of management for continuously improving the quality of products and processes....

, 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
Genichi Taguchi
is an engineer and statistician. From the 1950s onwards, Taguchi developed a methodology for applying statistics to improve the quality of manufactured goods...

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
Taguchi loss function
The Taguchi Loss Function is a 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...

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
Engineering fit
Fit refers to the mating of two mechanical components. Manufactured parts are very frequently required to mate with one another. They may be designed to slide freely against one another or they may be designed to bind together to form a single unit...

in mechanical engineering, which is a designed-in clearance or interference between two parts. 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 basic size and the minimum possible component size.
• Upper deviation: the difference between the basic size and the maximum possible component 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
Allowance (engineering)
In engineering and machining, an allowance is a planned deviation between an actual dimension and a nominal or theoretical dimension, or between an intermediate-stage dimension and an intended final dimension. The unifying abstract concept is that a certain amount of difference allows for some...

, 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") and 0.112 mm (smallest shaft paired with the largest hole). 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
Machining
Conventional machining is a form of subtractive manufacturing, in which a collection of material-working processes utilizing power-driven machine tools, such as saws, lathes, milling machines, and drill presses, are used with a sharp cutting tool to physical remove material to achieve a desired...

industry uses the following standard tolerances:
 1 decimal place (.x): ±0.2 2 decimal places (.0x): ±0.01 3 decimal places (.00x): ±0.005 4 decimal places (.000x): ±0.0005

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
Nut (hardware)
A nut is a type of hardware fastener with a threaded hole. Nuts are almost always used opposite a mating bolt to fasten a stack of parts together. The two partners are kept together by a combination of their threads' friction, a slight stretch of the bolt, and compression of the parts...

) and h7 (shaft or bolt). H7/h6 is a very common standard tolerance which gives a rather tight fit, but not so tight that you can't put the shaft in the hole, or turn the nut on the bolt, by hand. 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 is the opposite of H7. This method of standard tolerances is also known as Limits and Fits and can be found in 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
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....

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
Resistor
A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...

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 Ω to 101 Ω 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
Resistor
A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...

s and capacitor
Capacitor
A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...

s of standard types, and some small inductor
Inductor
An inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...

s, are often marked with coloured bands
Electronic color code
The electronic color code is used to indicate the values or ratings of electronic components, very commonly for resistors, but also for capacitors, inductors, and others...

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 Allowance (engineering)#Confounding of the engineering concepts of allowance and tolerance.

• Backlash (engineering)
Backlash (engineering)
In mechanical engineering, backlash, sometimes called lash or play, is clearance between mating components, sometimes described as the amount of lost motion due to clearance or slackness when movement is reversed and contact is re-established...

• Geometric dimensioning and tolerancing
Geometric dimensioning and tolerancing
Geometric dimensioning and tolerancing is a system for defining and communicating engineering tolerances. It uses a symbolic language on engineering drawings and computer-generated three-dimensional solid models for explicitly describing nominal geometry and its allowable variation...

• Key relevance
Key relevance
In master locksmithing, key relevance is the measurable difference between an original key and a copy made of that key, either from a wax impression or directly from the original, and how similar the two keys are in size and shape...

• Margin of error
Margin of error
The margin of error is a statistic expressing the amount of random sampling error in a survey's results. The larger the margin of error, the less faith one should have that the poll's reported results are close to the "true" figures; that is, the figures for the whole population...

• Process capability
Process capability
A process is a unique combination of tools, materials, methods, and people engaged in producing a measurable output; for example a manufacturing line for machine parts...

• Specification (technical standard)
Specification (technical standard)
A specification is an explicit set of requirements to be satisfied by a material, product, or service. Should a material, product or service fail to meet one or more of the applicable specifications, it may be referred to as being out of specification;the abbreviation OOS may also be used...

• Statistical process control
Statistical process control
Statistical process control is the application of statistical methods to the monitoring and control of a process to ensure that it operates at its full potential to produce conforming product. Under SPC, a process behaves predictably to produce as much conforming product as possible with the least...

• Taguchi methods
Taguchi methods
Taguchi methods are statistical methods developed by Genichi Taguchi to improve the quality of manufactured goods, and more recently also applied to, engineering, biotechnology, marketing and advertising...

• Tolerance stacks
• Tolerance coning
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...

• Verification and validation‎
• Probabilistic design
Probabilistic design
Probabilistic design is a discipline within engineering design. It deals primarily with the consideration of the effects of random variability upon the performance of an engineering system during the design phase. Typically, these effects are related to quality and reliability...