Poisson's Ratio Calculator

How to use this Poisson's ratio calculator

What this calculator does

This calculator estimates the dimensionless Poisson's ratio, ν, from either a pair of strain measurements or a pair of elastic moduli. The strain route uses the ratio of transverse strain magnitude to axial strain magnitude. The modulus route uses the isotropic linear-elastic identity E = 2G(1 + ν), rearranged to ν = E/(2G) – 1. When both pairs are present, the calculator also compares the two independently derived values so you can spot inconsistent measurements or assumptions. It is a compact engineering calculator, not a material-certification tool: the E – G relationship is intended for homogeneous, isotropic, linear-elastic behavior, and real test data can depart from those assumptions.

When to use it

Use it when reducing a uniaxial tensile or compression test, checking whether measured lateral and axial deformation are mutually plausible, converting between common isotropic elastic constants, or sanity-checking material data before a preliminary model. For a concise explanation of strain sign conventions and the conventional Poisson definition, see the engineering reference on stress, strain, and Poisson's ratio.

How to calculate

1. The calculator opens with a complete demonstration: transverse strain 0.0003, axial strain 0.001, E = 200 GPa, and G = 76.9230769231 GPa. The result is ν = 0.3000 and the example XLSX is immediately available.
2. Replace either pair with your own data. Editing a strain field makes the strain pair the active result source; editing E or G makes the modulus pair active. If one pair is incomplete but the other remains complete, the complete pair is used automatically.
3. Read the large Poisson's ratio value first. The two smaller method values show the independently computed results when both pairs are available, while the status message reports whether they agree closely.
4. Select Download Excel to export the current validated model to a real XLSX workbook containing Summary, Inputs, and Checks sheets. Select Reset to clear the demonstration data. Reset intentionally leaves the inputs empty and can disable Excel export until at least one complete valid input pair is entered again.

Input guide

Transverse strain (εtrans) is a conditionally required, dimensionless decimal. Enter a nonnegative strain magnitude such as 0.0003. Scientific notation such as 3e-4 is accepted; grouping separators and unit text are not. A larger transverse strain at fixed axial strain raises ν. Do not paste a percent sign or a length change in millimeters – the field expects strain, which is change divided by original dimension.

Axial strain (εaxial) is the paired dimensionless axial strain magnitude and must be greater than zero when the strain route is used. A realistic example is 0.001. At fixed transverse strain, a larger axial strain lowers ν. Avoid zero because the ratio would require division by zero. This interface uses positive magnitudes to reproduce the positive-ratio convention; if you work with signed tensile/compressive strains, the conventional definition includes a minus sign.

Modulus of elasticity (E) is Young's modulus. It is conditionally required with G, must be positive, and is entered here in GPa; 200 GPa is the demonstration value. Increasing E while holding G fixed raises the modulus-derived ν. The most common mistake is mixing units between E and G. The formula only cancels units when both values use the same pressure unit.

Shear modulus (G) is conditionally required with E, must be positive, and is entered in GPa; the example uses 76.9230769231 GPa. Increasing G while E is fixed lowers the modulus-derived ν. Do not substitute bulk modulus or shear strength: G is the elastic shear modulus. COMSOL's documentation on isotropic elastic property pairs illustrates why E, G, and ν can be used as related material constants under isotropic assumptions.

Output guide

Poisson's ratio (ν) is the primary dimensionless result. The active complete pair drives it: ν = εtrans/εaxial for the magnitude-based strain route, or ν = E/(2G) – 1 for the modulus route. Values near 0 indicate little lateral response relative to axial deformation; values around 0.3 are common for many metals; values approaching 0.5 indicate nearly incompressible isotropic behavior. A negative modulus-derived value can occur mathematically and can be associated with auxetic behavior under appropriate constitutive assumptions. A high, low, or unusual result is a prompt to check material assumptions and measurements rather than a recommendation by itself.

The ν from strains and ν from E and G cards show each route separately when the necessary inputs are present. Their difference is a consistency check, not a third formula. Small differences can arise from rounding or experimental uncertainty; a larger difference means the four supplied values do not describe exactly the same ideal isotropic state.

Worked example

With the startup strain values, ν = 0.0003 ÷ 0.001 = 0.3000. Independently, E/(2G) – 1 = 200 ÷ (2 × 76.9230769231) – 1 ≈ 0.3000. Because both routes produce the same displayed result, the status begins in the agreement state. The downloadable workbook stores the underlying numeric values rather than rounded screen text, so the same inputs and calculation checkpoints remain reproducible.