The fugacity can be deduced from measurements of volume as a function of pressure at constant temperature. In that case,
This integral can also be calculated using an equation of state.
The integral can be recast in an alternative form using the compressibility factor
Then
This is useful because of the theorem of corresponding states: If the pressure and temperature at the critical point of the gas are  and , we can define reduced properties  and . Then, to a good approximation, most gases have the same value of  for the same reduced temperature and pressure. However, in geochemical applications, this principle ceases to be accurate at pressures where metamorphism occurs.
For a gas obeying the van der Waals equation, the explicit formula for the fugacity coefficient is
This formula is based on the molar volume.  Since the pressure and the molar volume are related through the equation of state; a typical procedure would be to choose a volume, calculate the corresponding pressure, and then evaluate the right-hand side of the equation.