What is the formula for Bulk or Volume modulus (k) ?

Bulk or Volume modulus (k) is defined as the ratio of volume stress to volume strain within elastic limit. In other words if the Hooke’s Law is followed,  a small change in pressure produces a proportional change in volume. Bulk modulus of material indicates its resistance to change in volume. It corresponds to volumetric strain.

A body subjected to a uniform compressive force has its volume decreased and the resultant strain is a bulk or volume strain. Consider Δv as the change in volume and V is the original volume, then If F is the total compressive force acting on a total area A, then

Bulk stress = Force / Area = Pressure (P)

Bulk modulus (k) = Bulk Stress/ Bulk strain

If Pressure (P)  is the stress applied i.e. (force/unit area) then,

Bulk strain = Δv / V

The formula for Bulk or Volume modulus (k) is given as,

The unit for bulk modulus is ‘newton metre-2 (N m-2). The single term unit which is widely used for bulk modulus is ‘pascal’ with symbol ‘Pa’.