Poisson's Ratio Calculator

Poisson's ratio measures how a material changes dimension perpendicular to an applied axial load. When a conventional material is stretched, it usually becomes narrower; when compressed, it becomes wider. The dimensionless ratio is ν = -ε_transverse / ε_longitudinal. The minus sign makes the ratio positive when axial and lateral strains have opposite signs. Engineering strain is change in length divided by original length, so both strain inputs must use the same dimensionless convention. For stable isotropic linear-elastic materials, Poisson's ratio normally lies between -1 and 0.5. Metals commonly fall near 0.25 to 0.35, rubber approaches 0.5 because it changes shape with little volume change, and cork has a value near zero. Auxetic materials can have a negative ratio and expand laterally when stretched. A calculated result outside the theoretical isotropic range often indicates inconsistent signs, measurement noise, anisotropy, plastic deformation, or conditions outside the small-strain elastic regime. When Young's modulus E is known, Poisson's ratio links the other elastic constants. Shear modulus is G = E / [2(1 + ν)], describing resistance to shear distortion. Bulk modulus is K = E / [3(1 - 2ν)], describing resistance to uniform compression. This calculator accepts E in pascals and reports both derived moduli in gigapascals for readability. These relationships assume a homogeneous isotropic material; composites, crystals, wood, laminates, and direction-dependent materials may require a full stiffness matrix instead. Use strain values from the same load step and specimen region. Tensile longitudinal strain is ordinarily positive while the corresponding contraction is negative. If an instrument reports contraction only as a positive magnitude, add the negative sign before calculation. Young's modulus should come from the slope of the linear elastic stress-strain region, not from a secant through yielding or damage. Temperature, strain rate, porosity, moisture, and processing history can all change measured properties. The results support material-science exercises, tensile-test checks, preliminary finite-element inputs, and comparisons with handbook data. They do not replace a validated material test program for safety-critical design. Confirm whether plane stress, plane strain, anisotropic behavior, or nonlinear constitutive models apply before transferring these values into an engineering analysis.