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Poisson's Ratio Calculator

Find the ratio of transverse contraction to longitudinal extension in a stretched or compressed material.

How it is calculated

The tool computes ν = |εlateral ÷ εaxial|, the absolute value of the ratio of the strain across the load to the strain along it. Strain is the change in length divided by the original length, a plain number with no unit. Enter both strains in the same form, for example both as fractions or both as percent, and the units cancel. The result has two decimals. Axial strain of zero gives no result. The sign is thrown away: the tool shows the same ν whether the strains have the same or opposite signs, and whichever way round they come. In a normal tension test the lateral strain is negative while the axial strain is positive. The tool does not limit the result, so it will show values the usual 0 to 0.5 range for ordinary solid materials would not allow.

Worked example

A bar is pulled so that its length grows by a strain of 0.0028, and its width shrinks by a strain of −0.00084. Divide lateral by axial: −0.00084 ÷ 0.0028 = −0.30. Take the absolute value. The tool shows 0.30. This is in the range typical of many metals. Entering +0.00084 for the lateral strain would also give 0.30, because the sign is dropped.

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Common mistakes

  • Mixing forms of strain, such as the lateral strain in microstrain (840) and the axial strain as a fraction (0.0028). The ratio is then off by a factor of a million.
  • Entering a change in length instead of a strain. A 0.3 mm change is not a strain until it is divided by the original length.
  • Expecting the sign to come out. The tool shows the absolute value, so it cannot tell a normal material from one that expands sideways when stretched.
  • Putting the axial strain in the lateral field. The ratio is lateral over axial, and the swap returns the inverse, 3.33 instead of 0.30.
  • Ignoring results above 0.5. Nothing is checked, so 0.01 over 0.005 returns 2.00. For an ordinary solid that signals a measurement or entry error.

About this calculator

Poisson's ratio (ν, nu), named after French mathematician Siméon Poisson, quantifies how much a material contracts in directions perpendicular to an applied load: it is defined as the negative ratio of transverse (lateral) strain to axial (longitudinal) strain during uniaxial tension or compression. Most engineering metals have a Poisson's ratio near 0.3, incompressible materials like rubber approach the theoretical upper limit of 0.5, and cork is famously close to 0, which is why it can be pushed into a bottle without bulging sideways.

Mechanical, civil, and materials engineers use Poisson's ratio alongside Young's modulus and shear modulus to fully characterize a material's elastic behavior in stress analysis, finite element modeling, and structural design — it directly affects calculations like stress concentration around holes, buckling behavior, and how pressurized pipes or vessels deform.

This calculator takes your measured lateral and axial strain from a tensile or compressive test and computes the resulting Poisson's ratio as the size of lateral ÷ axial strain, so the sign is dropped and the result is always positive (a negative ratio, as in auxetic materials, is shown as positive). The result is not checked against the usual 0 to 0.5 range, so judge it against your material yourself.

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