Poisson's Ratio Calculator

Poisson's ratio ($ u$) is fundamentally defined as the negative ratio of transverse strain ($Ε_t$) to axial strain ($Ε_a$) when a force is applied along one axis. Mathematically, this is expressed as $ u = -(Ε_t / Ε_a)$. Furthermore, in isotropic linear elastic materials, Poisson's ratio connects elastic properties through the equation $E = 2G(1 + u)$, where $E$ represents the modulus of elasticity (Young's modulus) and $G$ denotes the shear modulus. This allows users to cross-verify mechanical properties using different testing parameters.

Imagine a cylindrical metal rod undergoing tensile testing. The rod stretches longitudinally, resulting in an axial strain ($Ε_a$) of 0.0025. Simultaneously, its diameter narrows, creating a transverse strain ($Ε_t$) of -0.00075. To find Poisson's ratio, substitute these values into the formula: $ u = -(Ε_t / Ε_a) = -(-0.00075 / 0.0025) = 0.30$. A Poisson's ratio of 0.30 is typical for many structural steels, indicating a predictable and balanced lateral deformation under load.

Always ensure your strain units are consistent; strain is dimensionless, but input variables like Young's modulus and shear modulus must use matching pressure units such as gigapascals (GPa) or megapascals (MPa). Double-check the signs of your strains—axial stretching is positive, while transverse contraction is negative. Finally, remember that theoretical isotropic materials have a Poisson's ratio limit between -1.0 and 0.5, though most real-world engineering metals cluster around 0.25 to 0.35.