What is tolerance?

Tolerance means the range of acceptable measurements for something.

In manufacturing, designs are drawn up to an exact size. But the process of cutting or moulding real materials means that some of the pieces will be a tiny amount larger than intended and some will be a tiny amount smaller than intended.

When the pieces are being assembled it is vital that they fit together properly. If the battery cover at the base of a mobile phone was too big for the phone, it would fall off. If it was too small it would also not fit together with the phone.

As it is impossible to make it to an exact size there must be a range of possible sizes that are acceptable. Sizes that are not too big or too small to fit together or work properly.

This range of acceptable sizes is called the tolerance.


A machine needs a part which is \(45\,mm\) long. However the part will still fit if it is \(0.2\,mm\) too big or too small.

This can be written as \(45 \pm 0.2 = 45.2\,mm.\)

The plus and minus symbols are written together. We read this as \(45\) plus or minus \(0.2.\)

This means that the largest acceptable size is \(45 + 0.2 = 45.2\,mm\).

The smallest acceptable size is \(45 - 0.2 = 44.8\,mm\).


The tolerance of a machine part is \(56 \pm 0.7\,cm.\)

What are the largest and smallest acceptable size of the part.

\[56 + 0.7 = 56.7\,cm \]

\[56 - 0.7 = 55.3\,cm\]


The tolerance of part of a curtain rail is \(78.4 \pm 0.3\,cm \)

What are the largest and smallest acceptable sizes of the part.

\[78.4 + 0.3 = 78.7\,cm\]

\[78.4 - 0.3 = 78.1\,cm\]