Poisson's Ratio Calculator
Calculate Poisson's ratio (ν) from transverse and axial strain or Young's and shear modulus. Free physics tool with material classification, bulk modulus, and charts.
About This Calculator
Poisson's ratio (ν) is a fundamental material property that describes how a material deforms in directions perpendicular to the applied load. Named after French mathematician Siméon Denis Poisson, this ratio is essential in mechanical engineering, civil engineering, materials science, and solid mechanics for predicting material behavior under stress.
The calculator supports two complementary calculation modes. In Strain-Based mode, Poisson's ratio is computed directly as ν = -εtransverse / εaxial, where transverse strain represents lateral deformation and axial strain represents longitudinal deformation. In E & G-Based mode, it uses the elasticity relationship ν = E / (2G) - 1, where E is Young's modulus and G is the shear modulus. The calculator also derives the bulk modulus K = E / (3(1 - 2ν)) in this mode, and classifies the material based on the computed value.
Typical Poisson's ratios range from 0 (cork, no lateral expansion) to 0.5 (rubber, perfectly incompressible). Most structural metals like steel (0.27-0.30), aluminum (0.33), and titanium (0.34) fall in the middle range. Some engineered auxetic materials exhibit negative Poisson's ratios, expanding laterally when stretched — a property useful in body armor, medical stents, and smart textiles.
The calculator includes a built-in material reference with Young's modulus and Poisson's ratio values for common engineering materials including steel, aluminum, copper, brass, titanium, concrete, glass, nylon, rubber, gold, and more. For isotropic and homogeneous materials, the relationships between elastic constants — E, G, K, and ν — are governed by the theory of linear elasticity, making this tool valuable for stress analysis, finite element modeling, and structural design.
Frequently Asked Questions
What is Poisson's ratio?
Poisson's ratio (ν) is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse (lateral) strain to axial (longitudinal) strain. Most engineering materials have Poisson's ratios between 0 and 0.5.
How do I calculate Poisson's ratio from strain?
Enter the transverse strain (lateral deformation) and axial strain (longitudinal deformation) into the calculator. Poisson's ratio is computed as ν = -ε_transverse / ε_axial. The negative sign accounts for the fact that axial tension typically causes lateral contraction.
How do I calculate Poisson's ratio from Young's modulus and shear modulus?
For isotropic materials, Poisson's ratio is related to Young's modulus (E) and shear modulus (G) by ν = E / (2G) - 1. This relationship is derived from the fundamental elasticity equations for homogeneous materials.
What is a typical Poisson's ratio for steel?
Steel typically has a Poisson's ratio of approximately 0.27 to 0.30. This means when steel is stretched axially, it contracts laterally by about 27-30% of the axial strain magnitude.
What materials have a Poisson's ratio close to 0.5?
Rubber and many elastomers have Poisson's ratios very close to 0.5 (approximately 0.49-0.50). These are nearly incompressible materials — they change shape but maintain nearly constant volume under deformation.
Can Poisson's ratio be negative?
Yes, some materials called auxetics exhibit negative Poisson's ratios. These materials expand laterally when stretched, opposite to conventional materials. Auxetic behavior is rare in nature but can be engineered in metamaterials for specialized applications.
What is the relationship between Poisson's ratio, Young's modulus, and bulk modulus?
The bulk modulus K relates to Young's modulus E and Poisson's ratio ν through K = E / (3(1 - 2ν)). This shows that when ν approaches 0.5, the bulk modulus becomes very large, indicating incompressibility. This calculator computes the bulk modulus alongside Poisson's ratio in the E & G mode.
What is cork's Poisson's ratio?
Cork has a Poisson's ratio very close to zero (approximately 0.00). This unique property means cork barely expands laterally when compressed, making it ideal for sealing applications like wine bottle stoppers.