Bulk Modulus (K)

The bulk modulus, denoted $K$, is the modulus of elasticity that applies to hydraulic (volume) stress and the corresponding volume strain -- the elastic constant governing how strongly a body resists a uniform change in its volume when subjected to a uniform pressure change over its entire surface, with no accompanying change in its overall shape. By Hooke's law, but with a deliberately inserted minus sign,

where $\Delta P$ is the (uniform) increase in pressure applied to the body and $\Delta V/V$ is the resulting fractional change in its volume.

The minus sign here is not arbitrary -- it exists to keep $K$ itself a positive quantity for ordinary matter. Squeezing a body harder (increasing $\Delta P$, so $\Delta P > 0$) always makes its volume shrink ($\Delta V < 0$); without the minus sign, the ratio $\Delta P/(\Delta V/V)$ would itself always come out negative, which would be an awkward, unintuitive way to report an elastic constant that is supposed to represent how strongly a material resists compression. With the minus sign in place, $K$ comes out positive, and a larger value of $K$ correctly represents a material that resists compression more strongly (a smaller fractional volume change for a given pressure increase), matching the intuitive meaning shared by $Y$ and $\eta$.

The reciprocal of the bulk modulus is called the compressibility of the material, usually denoted $C$ (or sometimes $\beta$ or $k$ in other texts):

Compressibility directly measures how easily a material's volume changes under pressure -- a highly compressible material (large $C$, small $K$) shrinks readily under pressure, while a nearly incompressible material (small $C$, large $K$) barely shrinks at all, however hard it is squeezed. …