For a solid, one can ignore the effects of pressure on the material, and the volumetric (or cubical) thermal expansion coefficient can be written:
where  is the volume of the material, and  is the rate of change of that volume with temperature.
This means that the volume of a material changes by some fixed fractional amount. For example, a steel block with a volume of 1 cubic meter might expand to 1.002 cubic meters when the temperature is raised by 50 K. This is an expansion of 0.2%. If a block of steel has a volume of 2 cubic meters, then under the same conditions, it would expand to 2.004 cubic meters, again an expansion of 0.2%. The volumetric expansion coefficient would be 0.2% for 50 K, or 0.004% K.
If the expansion coefficient is known, the change in volume can be calculated
where  is the fractional change in volume (e.g., 0.002) and  is the change in temperature (50 °C).
The above example assumes that the expansion coefficient did not change as the temperature changed and the increase in volume is small compared to the original volume. This is not always true, but for small changes in temperature, it is a good approximation. If the volumetric expansion coefficient does change appreciably with temperature, or the increase in volume is significant, then the above equation will have to be integrated:
where  is the volumetric expansion coefficient as a function of temperature T, and  and  are the initial and final temperatures respectively.