# Tolerance

The term tolerance, in the context of measurement, refers to a maximum allowable variation in a physical dimension, typically of some manufactured object.

Tolerance is used in areas such as quality control. When mass producing objects such as bolts, it is understandable that the process may result in some variation in the size of the bolt, even if they are intended to have a standard size, such as a ¼ inch diameter. The tolerance in such an example is the amount that the diameter of the bolt can vary from its intended ¼ inch diameter, and still be able to be used for its intended purpose.

Tolerance is specified by writing the standard dimension ± the tolerance.

Example

Given that the standard length of the rectangle below is 50 cm, and that it cannot be larger than 53 cm or smaller than 47 cm to perform its function, specify the tolerance of the rectangle.

The black border on the rectangle depicts the regular size of the rectangle. The lightly shaded rectangle shows the acceptable size range of the rectangle. Based on this, we can specify the tolerance of the rectangle as:

50 cm ± 3 cm

## Tolerance vs allowance

Although tolerance and allowance have very similar definitions in the English language, the terms cannot be used interchangeably in an engineering context.

Tolerance is a planned limit of acceptable, unintended variation from a given standard. When specifying a tolerance, the standard value is the desired value, but there is typically a small range of values close to the desired value that are acceptable. As long as the value falls within the given range, the value is acceptable, but the variation is not intended.

On the other hand, allowance is a intentional variation from the standard. Consider the example of manufacturing a cylinder with a 5 cm diameter, that has a tolerance of ± 0.01 cm. This means that the acceptable range of diameters for the manufactured cylinder is 4.99-5.01 cm.

If the cylinder were designed to be inserted into a hole, the hole could not have the same dimensions and tolerance, or there would be a number of cases where the cylinder would not fit. As such, the hole may be designed to have a diameter of 5.03 cm ± 0.01 cm, meaning that the smallest acceptable hole would have a diameter of 5.02 cm. Since the largest acceptable diameter for the cylinder is 5.01 cm, this leaves an allowance of 0.01 cm, ensuring that the cylinder will fit.