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Chemistry & Materials Science

Poisson's Ratio Calculator

Calculate the exact Poisson's Ratio of a material by comparing the transverse strain to the axial strain during mechanical stretching.

Poisson's Ratio (ν)
0.300
Material CharacteristicStandard Solid

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The Rubber Band Effect

Take a thick rubber band and stretch it as hard as you can. What happens to its width? As it gets longer, it simultaneously gets noticeably thinner.

This universal phenomenon—where stretching an object in one direction causes it to shrink in the other directions—is mathematically defined by Poisson's Ratio (ν\nu).

The Mathematical Ratio

Poisson's Ratio is the negative ratio of Transverse Strain (the thinning) to Axial Strain (the stretching).

  • ν≈0.5\nu \approx 0.5 (Perfectly Incompressible): Materials like rubber or biological tissue bulge outward perfectly when squished.
  • ν≈0.3\nu \approx 0.3 (Standard Metals): Most steels and aluminums thin out moderately when stretched.
  • ν≈0.0\nu \approx 0.0 (Cork): Cork is unique; if you squish a wine cork from the top, the sides don't bulge outward at all. This is why corks are perfect for plugging glass bottles without shattering them!

The Equation

u=−εtransεaxial\begin{aligned} \\ u = -\frac{\varepsilon_{trans}}{\varepsilon_{axial}} \end{aligned}

Where:
ν\nu=
Poisson's Ratio
εtrans\varepsilon_{trans}=
Transverse Strain (Thinning)
εaxial\varepsilon_{axial}=
Axial Strain (Stretching)

Because transverse strain is almost always negative when you stretch an object (it gets thinner), the formula includes a negative sign to ensure Poisson's Ratio stays a positive number.

Frequently Asked Questions

Yes, but it is extremely rare! Materials with a negative Poisson's Ratio are called Auxetics. If you stretch an auxetic material, it bizarrely becomes thicker instead of thinner. They are used in advanced body armor and specialized medical stents.

A ratio of 0.5 means the material's total volume never changes, no matter how hard you stretch or squish it. If the ratio were higher than 0.5, stretching the material would mathematically cause it to lose volume and disappear into nothingness.

Poisson's Ratio is the mathematical 'bridge' between Young's Modulus (pulling), Shear Modulus (twisting), and Bulk Modulus (squishing). If you know any two of those properties, you can use Poisson's Ratio to instantly calculate the others.

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