Poisson's ratio calculator
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:
ν = −εtrans / εaxial
where:
- ν — Poisson's ratio (dimensionless);
- εtrans — Transverse (lateral) strain: the relative change in the dimension perpendicular to the direction of the force; and
- εaxial — 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. With this sign convention, stretching a bar (positive axial strain) makes it thinner (negative transverse strain), so the minus sign in the formula returns a positive Poisson's ratio. Most materials have a 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 homogeneous materials. These three parameters are related according to the following equation:
E = 2 × G × (1 + ν)
which we rearrange to solve for Poisson's ratio:
ν = E / (2 × G) − 1
where:
- E — Young's modulus, in gigapascals (GPa);
- G — Shear modulus, in GPa; and
- ν — Poisson's ratio.
This equation explains how to calculate 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 magnitudes encountered in those variables. Even so, you can use whichever pressure units you want as long as they're the same for both variables. When you choose the American (imperial) system, the calculator labels the moduli in ksi instead of GPa.
How to use the Poisson's ratio calculator
- Choose how you want to calculate — from lateral and axial strain, or from Young's modulus and shear modulus.
- For the strain method, enter the transverse (lateral) strain and the axial strain, following the sign convention (tension positive, compression negative).
- For the moduli method, select your unit system (metric or American) and enter the Young's modulus and shear modulus in the same units.
- Read off the Poisson's ratio instantly. In the moduli mode, the calculator also reports the bulk modulus.
Typical Poisson's ratio values
- Cork ≈ 0 — barely widens when compressed, which is why it is ideal for sealing bottles.
- Steel ≈ 0.27–0.30
- Aluminum ≈ 0.33
- Copper ≈ 0.34
- Rubber ≈ 0.50 — practically incompressible.
- Auxetic materials — rare materials with a negative Poisson's ratio: they get thicker when stretched.
FAQs
What is Poisson's ratio?
Poisson's ratio is the negative ratio of transverse (lateral) strain to axial (longitudinal) strain for a material loaded along a single axis. It describes how much a material contracts sideways when it is stretched, or expands sideways when it is compressed.
Can Poisson's ratio be negative?
Yes. Materials with a negative Poisson's ratio are called auxetic. When stretched along one axis, they expand (rather than contract) in the perpendicular direction. Such behaviour is rare but occurs in certain foams and engineered structures.
Why is the maximum Poisson's ratio 0.5?
For an isotropic material that stays elastic, a Poisson's ratio of 0.5 means the volume does not change during deformation — the material is perfectly incompressible. Values above 0.5 would imply the volume decreases when stretched, which is not physically possible for ordinary isotropic materials, so 0.5 is the upper limit.