How to Use Poisson’s Ratio Converter
The Poisson’s Ratio Converter determines any missing elastic constants from Young’s modulus E, shear modulus G, bulk modulus K and Poisson’s ratio ν when any two of the four are known, covering the most common material-testing input pairs.
- Select input pair — choose (E, G), (E, K) or (G, K) depending on which two moduli you have measured or found in a data sheet.
- Enter the two modulus values — use consistent units throughout (MPa, GPa or psi); modulus outputs will be in the same unit.
- Read Poisson’s ratio ν — a dimensionless number; stable isotropic materials require −1 < ν < 0.5.
- Read the remaining modulus — the third modulus is computed automatically from the input pair.
- Verify physical plausibility — the result panel flags ν values outside 0–0.5 (unusual for common engineering materials) and values outside −1 to 0.5 as thermodynamically forbidden.
Formula & Theory — Poisson’s Ratio Converter
The Poisson’s Ratio Converter uses the closed-form inter-relationships between isotropic elastic constants:
ν = E/(2G) − 1 (from E, G)
ν = (3K − E)/(6K) (from E, K)
ν = (3K − 2G)/(2(3K + G)) (from G, K)
K = E / (3(1 − 2ν))
G = E / (2(1 + ν))
E = 9KG / (3K + G)| Symbol | Meaning | SI Unit |
|---|---|---|
| E | Young’s (tensile) modulus | Pa (or GPa) |
| G | Shear modulus | Pa (or GPa) |
| K | Bulk modulus | Pa (or GPa) |
| ν | Poisson’s ratio (dimensionless) | — |
Typical values: structural steel E ≈ 200 GPa, ν ≈ 0.30; aluminium alloy E ≈ 70 GPa, ν ≈ 0.33; rubber ν ≈ 0.49–0.4999 (nearly incompressible); auxetic foam ν < 0. Note that K → ∞ as ν → 0.5, meaning the material becomes volume-incompressible under hydrostatic stress.
Use Cases for Poisson’s Ratio Converter
- FEA model preparation — most finite-element solvers require (E, ν) as inputs; convert from (G, K) data-sheet values before building and meshing the model.
- Material qualification — cross-check measured ultrasonic wave speeds (from which E and G are derived via density) against reported ν for incoming material verification.
- Rock and geomechanics testing — infer in-situ horizontal stress from vertical confining pressure using elastic constant relationships for rock salt, shale or chalk.
- Polymer and elastomer characterisation — detect processing defects or anisotropy by comparing static compression and dynamic DMA modulus ratios.
- Composite material design — understand how fibre volume fraction and orientation affect apparent in-plane moduli and Poisson coupling terms in laminate theory.
- Educational structural analysis — explore how approaching ν = 0.5 (rubber-like) makes a material volume-conserving under uniaxial load, and its consequences for bearing and interference-fit calculations.