The specification above is incomplete, because for any object or system the magnitude of the compressibility depends strongly on whether the process is isentropic or isothermal. Accordingly, isothermal compressibility is defined:
where the subscript  indicates that the partial differential is to be taken at constant temperature.
Isentropic compressibility is defined:
where  is entropy. For a solid, the distinction between the two is usually negligible.
Since the density  of a material is inversely proportional to its volume, it can be shown that in both cases