How to use this calculator
- Enter or choose i have.
- Enter or choose young’s modulus E (optional).
- The poisson’s ratio ν updates as you type. Use Copy result or Share to keep it.
Method
ν = −ε_lat ÷ ε_ax; ε_v ≈ ε_ax + 2 ε_lat; G = E ÷ (2(1 + ν)); K = E ÷ (3(1 − 2ν))
- ε_ax
- axial strain ΔL ÷ L₀
- ε_lat
- lateral strain Δd ÷ d₀
- E
- Young’s modulus
- G
- shear modulus
- K
- bulk modulus
Worked example
- ε_ax = 0.1 ÷ 100 = 0.001.
- ε_lat = −0.003 ÷ 10 = −0.0003.
- ν = −(−0.0003) ÷ 0.001 = 0.3.
- G = 200 ÷ (2 × 1.3) = 76.92 GPa.
A 100 mm bar stretching 0.1 mm while its 10 mm diameter shrinks 0.003 mm has ν = 0.30, typical of steel.
What the result means
Most metals sit at 0.25–0.35, rubber close to 0.5 (nearly incompressible), cork near 0. A value outside −1 to 0.5 means a sign or measurement error for an isotropic material.
Assumptions and limits
- Isotropic, linear-elastic material under uniaxial load; small strains.
- Anisotropic materials (wood, composites, single crystals) have several Poisson’s ratios depending on direction.
Questions
Why the minus sign?
Lateral strain is normally opposite in sign to axial strain, so the minus sign makes ν positive for ordinary materials.
Can ν be negative?
Yes, for auxetic materials such as some foams and engineered lattices, which get wider when stretched.