To a first approximation, the change in length measurements of an object (linear dimension as opposed to, for example, volumetric dimension) due to thermal expansion is related to temperature change by a linear expansion coefficient. It is the fractional change in length per degree of temperature change. Assuming negligible effect of pressure, we may write:
αL = 1/L dL/dT
where L is a particular length measurement and dL/dT is the rate of change of that linear dimension per unit change in temperature. From the definition of the expansion coefficient, the change in the linear dimension ΔLΔL over a temperature range ΔTΔT can be estimated to be:
ΔL/L = αLΔT.
This equation works well as long as the linear-expansion coefficient does not change much over the change in temperature. If it does, the equation must be integrated.