Poisson's Ratio

Stretch a bar and it gets thinner; squeeze it and it bulges. Poisson's ratio is the bookkeeping for that sideways response — this calculator uses magnitudes, so a positive ν means the usual behaviour (the formal definition carries a minus sign, ν = −ε_lat/ε_ax). Pull steel to an axial strain of 0.0003 and each transverse dimension shrinks by 0.00009, giving ν = 0.30. Siméon Denis Poisson derived a universal value of exactly 1/4 in 1829 from a molecular model of matter; the model was wrong and the measurements soon proved it, but the ratio kept his name.

Thermodynamics caps isotropic materials at ν = 0.5, the incompressible limit that rubber nearly reaches — which is why a rubber block confined in a steel cavity behaves like a hydraulic fluid and will burst its container rather than squash. At the other end, cork sits near zero, which is exactly why a cork pushes into a bottle neck without fattening while a rubber bung fights you. Engineered auxetic foams even manage negative values, getting fatter when stretched. The practical trap: ν only applies in the elastic range; once a metal yields, plastic flow conserves volume and the effective ratio jumps to 0.5.