Every linear dimension increases by the same percentage with a change in temperature, including holes. This assumes that the expanding material is uniform. .

In most cases the quadratic term above can be neglected since the typical expansion coefficient is on the order of parts per million per degree C. The expression then becomes

which is equivalent to the expression at left.

Over small temperature ranges, the thermal expansion is described by the coefficient of linear expansion. If the linear expansion is put in the form

then the expanded volume has the form

In most cases the quadratic and cubic terms above can be neglected since the typical expansion coefficient is on the order of parts per million per degree C. The expression then becomes