Poisson Ratio Calculator Formula
Understand the math behind the poisson ratio calculator. Each variable explained with a worked example.
Formulas Used
Poisson's Ratio (nu)
poisson = lateral_strain / axial_strainVariables
| Variable | Description | Default |
|---|---|---|
lateral_strain | Lateral Strain (epsilon_lateral) | 0.0003 |
axial_strain | Axial Strain (epsilon_axial) | 0.001 |
How It Works
Poisson's Ratio
When a material is stretched in one direction, it contracts in the perpendicular directions. Poisson's ratio quantifies this coupling between axial and lateral strains.
Formula
nu = -epsilon_lateral / epsilon_axial
By convention, the negative sign makes nu positive for normal materials (since lateral strain is opposite in sign to axial strain). For this calculator, enter both strains as positive magnitudes. Most metals have nu between 0.25 and 0.35. Rubber approaches 0.5 (nearly incompressible).
Worked Example
A steel bar shows 0.001 axial strain and 0.0003 lateral contraction strain.
- 01nu = 0.0003 / 0.001 = 0.3
- 02This is typical for steel (nu ≈ 0.28-0.33)
Frequently Asked Questions
What are typical Poisson ratio values?
Steel: 0.27-0.30, aluminum: 0.33, copper: 0.34, rubber: ~0.50, cork: ~0, concrete: 0.15-0.20. Auxetic materials have negative Poisson ratio (they expand laterally when stretched).
Can Poisson ratio exceed 0.5?
For isotropic materials, thermodynamic stability requires -1 < nu < 0.5. A value of 0.5 means the material is perfectly incompressible. Some anisotropic materials can have nu > 0.5 in certain directions.
How does Poisson ratio relate to compressibility?
Bulk modulus K = E / (3(1 - 2*nu)). As nu approaches 0.5, K approaches infinity, meaning the material becomes incompressible. Rubber (nu ≈ 0.499) is nearly incompressible.
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Open Poisson Ratio Calculator