# Poisson’s Ratio Calculator

> Calculate Poisson’s ratio ν = −ε_lateral ÷ ε_axial from dimension changes or measured strains, plus volumetric strain and shear and bulk moduli from E.

Category: Science & engineering · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/poisson-ratio-calculator

Stretch a bar and it gets thinner. Poisson’s ratio is how much: ν = −(lateral strain) ÷ (axial strain), about 0.3 for most metals.

Also called: Poisson’s ratio calculator.

## Inputs
- I have (options: Dimension changes, Strains; default dimensions)
- Original length (unit mm; default 100)
- Change in length (+ longer) (unit mm; default 0.1)
- Original width or diameter (unit mm; default 10)
- Change in width (− thinner) (unit mm; default -0.003)
- Axial strain (default 0.001)
- Lateral strain (default -0.0003)
- Young’s modulus E (optional) (unit GPa; default 200; optional)

## Results
- Poisson’s ratio ν
- Axial strain
- Lateral strain
- Volumetric strain (small-strain)
- Shear modulus G
- Bulk modulus K

## Formula

```
ν = −ε_lat ÷ ε_ax;  ε_v ≈ ε_ax + 2 ε_lat;  G = E ÷ (2(1 + ν));  K = E ÷ (3(1 − 2ν))
```

Where:
- ε_ax: axial strain ΔL ÷ L₀
- ε_lat: lateral strain Δd ÷ d₀
- E: Young’s modulus
- G: shear modulus
- K: bulk modulus

## Worked example
1. ε_ax = 0.1 ÷ 100 = 0.001.
2. ε_lat = −0.003 ÷ 10 = −0.0003.
3. ν = −(−0.0003) ÷ 0.001 = 0.3.
4. G = 200 ÷ (2 × 1.3) = 76.92 GPa.

**Result:** 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.

## Related calculators
- [Young’s Modulus, Stress and Strain Calculator](https://calculators.geekmidst.com/calculators/young-modulus-strain-calculator)
- [Torsion Stress Calculator](https://calculators.geekmidst.com/calculators/torsion-stress-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/poisson-ratio-calculator