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Poisson's Ratio

ν=εlatεax\nu = \frac{\varepsilon_{lat}}{\varepsilon_{ax}}
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Worked example: lateral 90 ue / axial 300 ue → nu = 0.30. Press Try an example to run it live, then adjust anything.

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Relation Between E, G and νThermal Shock Resistance Parameter RThermal Shock Resistance Parameter R′
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See also

Normal Strain (ε = δ/L): Both use axial strain.Relation Between E, G and ν: Both use Poisson's ratio.Young's Modulus (E = σ/ε): Both use axial strain.Thermal Shock Resistance Parameter R: Both use Poisson's ratio.Thermal Shock Resistance Parameter R′: Both use Poisson's ratio.True Stress from Engineering Stress: Both use axial strain.
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Poisson's Ratio explained

εaxεlatν

Stretch a bar and it gets thinner; squeeze it and it bulges. Poisson's ratio is the bookkeeping for that sideways response: this calculator uses magnitudes, so a positive ν means the usual behaviour (the formal definition carries a minus sign, ν = −ε_lat/ε_ax). Pull steel to an axial strain of 0.0003 and each transverse dimension shrinks by 0.00009, giving ν = 0.30. Siméon Denis Poisson derived a universal value of exactly 1/4 in 1829 from a molecular model of matter; the model was wrong and the measurements soon proved it, but the ratio kept his name.

Thermodynamics caps isotropic materials at ν = 0.5, the incompressible limit that rubber nearly reaches, which is why a rubber block confined in a steel cavity behaves like a hydraulic fluid and will burst its container rather than squash. At the other end, cork sits near zero, which is exactly why a cork pushes into a bottle neck without fattening while a rubber bung fights you. Engineered auxetic foams even manage negative values, getting fatter when stretched. The practical trap: ν only applies in the elastic range; once a metal yields, plastic flow conserves volume and the effective ratio jumps to 0.5.

Poisson's Ratio formula

ν=εlatεax\nu = \frac{\varepsilon_{lat}}{\varepsilon_{ax}}
Where
  • ν\nu= Poisson's ratio
  • εlat\varepsilon_{lat}= Lateral strain (magnitude) (m/m)
  • εax\varepsilon_{ax}= Axial strain (magnitude) (m/m)
In this toolkit

Stress, strain and the elastic constants

9 formulasNormal and shear stress, strain, axial deformation, and the four elastic constants E, G, K and ν that link them.

Revised 31 October 2026
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formula.expert. (2026, October 31). Poisson's Ratio Formula & Calculator. https://formula.expert/solvers/poissons-ratio

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