Poisson's Ratio Calculator

Poisson's ratio describes how a material thins sideways as it stretches.

How the Math Works

Poisson's ratio (ν) quantifies how a material deforms when stretched or compressed. When a material is subjected to an axial force, it elongates in one direction while contracting laterally. The formula ν = -lateral strain ÷ axial strain captures this relationship: lateral strain is the proportional change in width (or diameter), while axial strain is the proportional change in length. The negative sign ensures the ratio is positive, since stretching causes contraction in perpendicular directions. For example, if a rod stretches by 2% in length (axial strain = 0.02) and narrows by 1% in diameter (lateral strain = -0.01), Poisson's ratio equals 0.5, indicating moderate deformation behavior.

Practical Applications

Engineers use Poisson's ratio to predict how materials behave under load in structural design. When creating bridges, buildings, or mechanical components, knowing this ratio helps determine if a material will squash, stretch, or maintain its shape under stress. For instance, concrete has a lower Poisson's ratio (~0.15-0.25) than rubber (~0.5), meaning it deforms less laterally when compressed. This calculation becomes crucial when selecting materials for applications like earthquake-resistant structures, where precise deformation predictions prevent catastrophic failures.

Day-to-Day Use

While you may not calculate Poisson's ratio daily, this concept influences items you encounter regularly. The flexibility of your smartphone case, the bounce of a tennis ball, or even the comfort of your running shoes all depend on material deformation properties described by Poisson's ratio. When architects design earthquake-proof buildings, they ensure materials won't collapse unexpectedly due to lateral spreading during ground motion. Understanding this ratio also explains why metal cans crumple predictably when stepped on, and why some packaging materials compress without tearing.

Worked example

−0.0009 lateral over 0.003 axial → ν = 0.3.

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