What is the formula for Poisson's ratio?

Poisson's ratio is ν = −ε_lat/ε_long, where ε_lat is lateral strain and ε_long is longitudinal strain.

What values are needed to calculate Poisson's ratio?

Enter lateral strain and a non-zero longitudinal strain, then select Poisson's ratio as the quantity to solve for.

What sign should lateral strain have during tension?

For tensile longitudinal strain, lateral contraction is negative, so ε_long is positive and ε_lat is negative.

What is the typical theoretical range for isotropic materials?

The theoretical isotropic range is 0 to 0.5. Typical values include steel near 0.30 and aluminum near 0.33.

Can the calculator solve for strain instead of Poisson's ratio?

Yes. It can solve for lateral strain from ν and ε_long, or longitudinal strain from ν and ε_lat.

Poisson's Ratio Calculator | Online Free Tool

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2 examples

Ratio: ε_lat=−0.0009, ε_long=0.003 → ν = 0.30

ν = −ε_lat/ε_long = −(−0.0009)/0.003 = 0.30. Typical steel.

{"result":"Poisson's ratio ν = −ε_lat/ε_long = −(−0.0009)/0.003 = 0.3000.","metadata":{"input":{"solveFor":"ratio","epsLateral":-0.0009,"epsLong":0.003},"result":{"solveFor":"ratio","poissonRatio":0.3,"lateralStrain":-0.0009,"longitudinalStrain":0.003,"isAuxetic":false}}}

Lateral: ν=0.33, ε_long=0.002 → ε_lat = −0.00066

ε_lat = −ν·ε_long = −0.33·0.002 = −0.00066. Contraction under axial tension (aluminum).

{"result":"Lateral strain ε_lat = −ν·ε_long = −0.33·0.002 = -0.000660.","metadata":{"input":{"solveFor":"lateral","nu":0.33,"epsLong":0.002},"result":{"solveFor":"lateral","poissonRatio":0.33,"lateralStrain":-0.00066,"longitudinalStrain":0.002,"isAuxetic":false}}}

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5 options

SettingsAdjust formats, ranges, numbers, and modes.5

Solve forselectOptionalPoisson's Ratio νnumberOptionalPoisson's ratio. Required when solving for lateral or longitudinal strain. Isotropic range 0–0.5. Steel ≈ 0.30, aluminum ≈ 0.33, rubber ≈ 0.49.Lateral Strain ε_latnumberOptionalTransverse (lateral) strain, dimensionless. Negative when the longitudinal strain is tensile. Required when solving for ratio or longitudinal strain.Longitudinal Strain ε_longnumberOptionalAxial (longitudinal) strain, dimensionless. Required when solving for ratio or lateral strain. Must be non-zero when solving for ratio.Decimal PlacesnumberOptional

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Examples

1. Calculate Poisson's ratio from measured strains

Materials engineering student

Background

A tensile test records a lateral strain of −0.0009 and a longitudinal strain of 0.003.

Problem

Determine the material's Poisson's ratio from the measured strain values.

How to use

Select "Poisson's ratio ν" under "Solve for," enter −0.0009 for lateral strain and 0.003 for longitudinal strain, and set decimal places to 4.

{"solveFor":"ratio","epsLateral":-0.0009,"epsLong":0.003,"decimalPlaces":4}

Outcome

The calculator returns ν = 0.3000, a value typical of steel.

2. Find lateral strain under axial tension

Mechanical design engineer

Background

An aluminum component has ν = 0.33 and experiences a longitudinal strain of 0.002.

Problem

Calculate the transverse contraction caused by the axial tensile strain.

How to use

Select "Lateral strain ε_lat," enter 0.33 for Poisson's ratio and 0.002 for longitudinal strain, and set decimal places to 6.

{"solveFor":"lateral","nu":0.33,"epsLong":0.002,"decimalPlaces":6}

Poisson's Ratio Calculator | Online Free Tool | Elysia Tools

Poisson's Ratio Calculator

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Examples

1. Calculate Poisson's ratio from measured strains

2. Find lateral strain under axial tension

FAQ

3. Solve for longitudinal strain

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