Poisson's ratio tells you how a material's cross-section responds when you pull or push on it lengthwise. It's one of the three fundamental elastic constants engineers use alongside Young's modulus and shear modulus to fully describe how an isotropic material deforms under load.

Why Materials Get Thinner When Stretched

Pull on a rubber band and it visibly narrows as it stretches — that narrowing is exactly what Poisson's ratio quantifies. Most materials conserve something close to their original volume when deformed elastically, so if they elongate in one direction they must contract in the perpendicular directions to compensate. Poisson's ratio is the proportionality constant between those two strains: ν = −ε_lateral/ε_axial. A material with ν close to 0.5 (like rubber) is nearly incompressible and narrows a lot per unit of stretch relative to its volume change; a material with ν close to 0 (like cork) barely narrows at all, which is exactly why cork makes a good wine-bottle stopper — it can be compressed into the neck without bulging sideways.

One of Three Linked Elastic Constants

For an isotropic material, Young's modulus (E), shear modulus (G), and Poisson's ratio (ν) are not independent — any two determine the third via ν = E/(2G) − 1, equivalently G = E/(2(1+ν)). This calculator's second tab lets you compute ν directly from E and G when you have those values from a materials datasheet but not raw strain measurements. It's the same underlying material property either way; the two tabs will always agree for consistent inputs.

The Valid Range, and Auxetic Materials

For isotropic materials, thermodynamic stability limits Poisson's ratio to the range −1 to 0.5. Almost every everyday material falls between 0 and 0.5, with most metals clustering around 0.25–0.35. Values near 0.5 indicate near-incompressibility (rubber, biological soft tissue). A small number of engineered materials — certain foams, re-entrant honeycomb lattices, and some textiles — are auxetic: they have a negative Poisson's ratio and actually get thicker perpendicular to a stretch. This calculator accepts any input combination within the strain or modulus tabs; values outside the typical range are still computed and flagged by the interpretation text rather than rejected, since auxetic materials are a legitimate (if unusual) case.