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# Poisson's Ratio Calculator

Lateral strain and axial strainYoung's modulus and shear modulus

This Poisson's ratio calculator is a tool that will help you determine the Poisson's ratio of any material. This calculator can work in two ways - either from the proportion of lateral strain and axial strain, or you can also calculate Poisson's ratio from Young's modulus and shear modulus.

## Lateral strain and axial strain

Poisson's ratio is defined as the ratio between the lateral strain and axial strain of a deformed object. Imagine it like this: if you compress a piece of rubber from above, it will "flow" sideways, increasing its width.

On the other hand, if you do the same with cork, you will discover that it merely changes its volume, with almost no increase in width observed. Rubber is an example of a material with a high Poisson's ratio, while cork has a low Poisson's ratio.

The Poisson's ratio calculator uses the following formula:

$v = \frac{\varepsilon_\text{trans}}{\varepsilon_\text{axial}}$

where:

• $v$ — Poisson's ratio (dimensionless);
• $\varepsilon_\text{trans}$ — Transverse (lateral) strain - the relative change in the dimension perpendicular to the direction of force; and
• $\varepsilon_\text{axial}$ — Axial strain - the relative change in a dimension parallel to the direction of the force.

We always assume tension (stretching) to be positive and compression to be negative. Notice that Poisson's ratio will always be positive - it is impossible to have a material that, when compressed in one direction, will automatically compress in the transverse direction as well. Most materials have Poisson's ratio between 0 and 0.5, where 0.5 corresponds to a perfectly incompressible material (one that doesn't change its volume).

## Young's modulus and shear modulus

You can also use our Poisson's ratio calculator to find Poisson's ratio based on the values of shear modulus and modulus of elasticity of isotropic and homogenous materials. These three parameters are related according to the following equation:

$E = 2 \times G (1 + v)$

where:

• $E$ — Young's modulus, in gigapascals (GPa);
• $G$ — Shear modulus, in GPa (obtain it with our shear modulus calculator); and
• $v$ — Poisson's ratio.

This equation explains how to calculate the Poisson's ratio from Young's modulus but for isotropic materials only. We suggest using GPa as the units for $E$ and $G$ as they are the most appropriate units considering the encountered magnitudes in those variables. Even so, you can use the pressure units you want as long as they're the same for both variables. Our pressure conversion tool can be useful in achieving that uniformity.

🙋 If you want to find out more about the importance of Young's modulus, check out our stress calculator.

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