The bulk modulus is a physical constant of solids and fluids that indicates their elastic properties when they are under pressure over their entire surfaces. The bulk modulus (K) is the inverse of the compressibility. It is also called the incompressibility: if a solid or fluid (liquid or gas) has a high bulk modulus, then it is difficult to compress.

 

The bulk modulus is defined by

 

    K = -V (dP/dV)

 

where V is the volume, which is decreased when a pressure P is exerted uniformly in all directions. Usually, it is assumed that the temperature is kept constant during the compression. K can be measured directly by exerting a known pressure and measuring the change of volume – and a whole technology has grown up for producing enormous pressures without the substance leaking past the piston which compresses it. Usually the main source of error is due to the non-uniformity of the forces acting in different directions. Alternatively, the speed of propagation of sound waves through a material can be found. This depends on the compressibility, though a number of corrections have to be applied if exact values of K are required.