An elastic constant that is a measure of the compressibility of material perpendicular to applied stress, or the ratio of latitudinal to longitudinal strain. This elastic constant is named for Simeon Poisson (1781 to 1840), a French mathematician. Poisson's ratio (σ) can be expressed in terms of properties that can be measured in the field, including velocities of P-waves (V_{P}) and S-waves (V_{S}) as shown below.

σ = ½ (V_{P}^{2} − 2V_{S}^{2}) / (V_{P}^{2} − V_{S}^{2})

Note that if V_{S} = 0, then Poisson's ratio equals 0.5, indicating either a fluid, because shear waves do not pass through fluids, or a material that maintains constant volume regardless of stress, also known as an ideal incompressible material. Poisson's ratio for carbonate rocks is ~0.3, for sandstones ~0.2, and greater than 0.3 for shale. The Poisson's ratio of coal is ~0.4.