Poisson’s Ratio Calculator
Calculate Poisson’s ratio ν from lateral and axial strain or from Young’s and shear modulus, and get the related shear modulus G, bulk modulus K and volume change for an isotropic material.
How it works
ν = −ε_lateral / ε_axial · isotropic relations: G = E / (2(1 + ν)), K = E / (3(1 − 2ν)), ν = E/(2G) − 1 · volume strain ΔV/V ≈ ε_axial·(1 − 2ν) · stable range −1 < ν < 0.5
When a bar is stretched it gets longer and thinner. Poisson’s ratio is the ratio of the sideways contraction strain to the lengthwise extension strain (the minus sign in the definition makes it positive for ordinary materials). For an isotropic linear-elastic material only two of the constants E, G, K and ν are independent, so knowing ν and E gives the shear and bulk moduli. Most metals sit near 0.3, rubber approaches 0.5 (volume is conserved) and cork is close to 0. Relations follow Gere & Goodno, Mechanics of Materials, and ASTM E132 (Poisson’s ratio at room temperature).
Worked example
A steel bar (E = 200 GPa) shows an axial strain of 0.002 and a lateral strain of 0.0006. ν = 0.0006 / 0.002 = 0.3000. Then G = 200 / (2 × 1.3) = 76.92 GPa and K = 200 / (3 × 0.4) = 166.67 GPa. The volume grows by 0.002 × (1 − 0.6) = 0.0800%, and 0.3 is typical of metals.
Sources: ASTM E132 — Standard Test Method for Poisson’s Ratio at Room Temperature · Wikipedia — Poisson’s ratio (typical values and elastic relations)
Frequently asked questions
What is a typical Poisson’s ratio?
Steel about 0.27–0.30, aluminium 0.33, copper 0.34, concrete 0.15–0.20, glass 0.22, rubber 0.49–0.50 and cork close to 0.
Why can’t Poisson’s ratio exceed 0.5?
At 0.5 the volume does not change under load and the bulk modulus becomes infinite. Above 0.5 an isotropic material would gain energy when compressed, which is not physically stable.
Can Poisson’s ratio be negative?
Yes, in auxetic materials such as some foams and engineered lattices, which get fatter when stretched. Enter E and G (moduli mode) to compute a negative value; the strain mode uses magnitudes.
How is Poisson’s ratio measured?
With a tensile test fitted with two strain gauges or an extensometer — one along the load axis and one across it — in the elastic range, as described in ASTM E132.
Related calculators
Results assume the idealised textbook model stated above; real systems have losses and tolerances, so verify safety-critical values with measurements or a qualified engineer.