Poisson's Ratio Calculator
Enter axial and lateral strain to compute Poisson's ratio ν = −ε_lateral/ε_axial, plus shear modulus and Young's modulus.
Input Data
Results
At a glance:Poisson's ratio ν is the material constant relating transverse to axial strain under uniaxial stress: ν = −ε_lateral/ε_axial (negative because stretching makes it thinner). Typical values: rubber ~0.5, steel ~0.3, cork ~0.0, auxetic materials <0. It links the elastic moduli: shear modulus G = E/(2(1+ν)) and bulk modulus K = E/(3(1−2ν)). From shear modulus G and ν, Young's modulus E = 2G(1+ν). This tool computes ν from the two strains and E from ν and G. For incompressible materials ν→0.5 (volume conserved); ν>0.5 is impossible for stable isotropic solids.
Formula
ν = −ε_lateral/ε_axial
G = E/(2(1+ν))
E = 2G(1+ν)
$$\nu = -\frac{\varepsilon_{\text{lateral}}}{\varepsilon_{\text{axial}}} = -\frac{\Delta d/d}{\Delta L/L}, \quad E = 2G(1+\nu), \quad K = \frac{E}{3(1-2\nu)}, \quad G = \frac{E}{2(1+\nu)}$$How to Use
- Enter axial strain ε_a and lateral strain ε_l.
- Optionally enter shear modulus G.
- The calculator returns ν and Young's modulus E.
Case Studies
Steel rod
ε_a = 0.001, ε_l = −0.0003.
ν = 0.3.
With G = 80 GPa, E = 2×80e9×1.3 = 208 GPa.
FAQ
Why is Poisson's ratio negative in the formula?
Axial stretch gives negative (contracting) lateral strain, so the minus sign makes ν positive for ordinary materials.
What does ν = 0.5 mean?
The material is incompressible (volume conserved under stretch, like rubber). ν cannot exceed 0.5 for stable isotropic solids; auxetics have ν<0 (widen when stretched).
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.