# Poisson's Ratio Calculator

Created by Luis Hoyos
Last updated: Nov 12, 2022

If you're searching for how to calculate Poisson's ratio and the equation behind it, you're in the right place. With this tool, you can obtain this quantity by two methods:

1. You can calculate the Poisson's ratio by using the transverse and axial strains; or
2. By using the Young and shear modulus to calculate it.

Apart from that, you can use this tool to calculate the shear modulus if you already know the Poisson's ratio and Young's modulus (obtain the latter with our Young's modulus calculator). You can also calculate the shear modulus with our modulus of rigidity calculator.

## What is the Poisson's ratio?

When we apply a force or stress to a deformable body, not only does it elongate in the load direction, but it also deforms laterally. This behavior is known as the Poisson effect.

The property that accounts for the Poisson effect is the Poisson's ratio, which is the ratio of the transverse strain (perpendicular to the applied load) to the axial strain (parallel to the applied load), and usually denoted by the Greek letter ν (nu). For many engineering materials, such as metals and ceramics, the Poisson's ratio is between 0.25 and 0.355, and it can be shown that its maximum value is 0.5.

## How to calculate the Poisson's ratio (equation)

According to the definition, we calculate the Poisson's ratio as the negative of the transverse to axial strain ratio:

ν = -εtrans/εaxial

, where:

• ν — Poisson's ratio;
• εtrans — Transverse strain; and
• εaxial — Axial strain.

Poisson's ratio has strain units, meaning it is a dimensionless quantity. As mentioned before, it ranges from 0 to 0.5.

💡 In tension εaxial > 0 and εtrans < 0, while in compression, εaxial < 0 and εtrans > 0. For this reason, ν is always positive.

Apart from that, this calculator also uses the following formula for the Poisson ratio, relating it to the Young's and the shear modulus:

ν = E/(2G) - 1

, where:

• ν — Poisson's ratio;
• E — Young's modulus; and
• G — Shear modulus.

In the previous Poisson ratio formula, the Young and shear modulus have pressure units, usually expressed in gigapascals (GPa) or pounds per square inch (psi). To properly use the formula, both quantities must be in the same units, for which our pressure conversion tool could be helpful.

Luis Hoyos
Input εₜᵣₐₙₛ and εₐₓ
Transverse strain (εₜᵣₐₙₛ)
Axial strain (εₐₓ)
or input E and G
Young's modulus (E)
psi
Shear modulus (G)
psi
Poisson's ratio (ν)
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