# bulk modulus

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* (d*P*/d*V*)

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.