The coefficient of compressibility ( or ) is determined by measuring the change of volume () of the material as a function of the pressure applied (), while the temperature () is held constant:
The definition includes the normalisation with respect to the volume in order to take into the account the size of the system; is therefore an intrinsic quantity.
When increases, decreases: the derivative in formula above is inherently negative.
Thus, inclusion of the minus sign guarantees that tabulated values of K are positive numbers.
Note: The compressibility is defined analogously to to the thermal expansion coefficient:
The bulk modulus is given by
The pressure can be expressed as follows by means of the first principle of thermodynamics: the internal energy () of the system under investigation can change when an amount of work ( ) is performed or when an amount of heat () is transferred to the system.
The expression above can be inserted in the definition of :
and by simplifying the notation, the bulk modulus can be obtained at the athermal limit by applying the formula
At this point, it is necessary to tabulate the energy as a function of the volume, to fit the data and to calculate .