Poisson's Ratio Calculator (from length and width changes)

Understanding the Poisson's ratio calculator — concept and principle

This calculator finds Poisson's ratio from a tensile or compression test: the change in length and the change in width of a specimen. It also gives the axial and lateral strains, the volume change and, with Young's modulus, the shear and bulk moduli. Materials and mechanical engineering students use it in lab work.

For every 1,000 µε of stretch the bar narrows by 300 µε, so its volume still grows a little.

How it is calculated

Axial strain ε_a = ΔL ÷ L₀; lateral strain ε_l = Δd ÷ d₀

ν = −ε_l ÷ ε_a

Volume change ΔV/V ≈ ε_a (1 − 2ν)

G = E ÷ (2(1 + ν)); K = E ÷ (3(1 − 2ν))

Lengths in mm; strains shown in microstrain (1 µε = 10⁻⁶); E in GPa.

The principle

When a bar is stretched it gets longer and, to some degree, thinner. Poisson's ratio measures how much thinner, as a fraction of the stretch. The minus sign makes ν positive for ordinary materials, which shrink sideways when pulled. If ν were 0.5 the volume would not change at all; most solids have smaller values, so their volume grows slightly in tension. For isotropic materials ν links Young's modulus to the shear and bulk moduli.

Worked example

Default inputs: L₀ = 100 mm, ΔL = +0.10 mm, d₀ = 10 mm, Δd = −0.003 mm, E = 200 GPa.

ε_a = 0.10 ÷ 100 = 1,000 µε; ε_l = −0.003 ÷ 10 = −300 µε.
ν = 300 ÷ 1,000 = 0.3, in the typical range.
ΔV/V = 0.001 × (1 − 0.6) = 0.04%.
G = 200 ÷ 2.6 = 76.92 GPa; K = 200 ÷ 1.2 = 166.7 GPa.

Each point is the calculator re-run with only “Change in length (mm, + if longer)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Change in length (mm, + if longer)	Poisson's ratio ν
0.025	1.2
0.05	0.6
0.075	0.4
0.1	0.3
0.125	0.24
0.15	0.2
0.2	0.15

How to read the result

Most metals are near 0.3, rubber near 0.5 and cork near 0. Values outside 0–0.5 for an ordinary material usually point to a measurement error, although special auxetic materials have negative ν. Lateral changes are tiny, so precise measurement, usually with strain gauges, is essential.

Common mistakes

Dropping the minus sign, which gives a negative ν for a normal material.
Measuring beyond the elastic range, where ν changes.
Using a caliper for lateral changes of a few micrometres.

Keep in mind: Use small elastic deformations and calibrated instruments. Design values should come from material standards.

Frequently asked questions

What is a typical Poisson's ratio for steel?

About 0.3.

Why is rubber close to 0.5?

It deforms at almost constant volume.

Can Poisson's ratio be negative?

Yes, in specially structured auxetic materials.

What is a microstrain?

One millionth of a unit strain, or 1 µm per metre.

Sources: MIT OpenCourseWare 2.001 Mechanics & Materials I (Fall 2006), lecture 13 notes

Checked 9 Nov 2026. MIT OpenCourseWare 2.001 Mechanics & Materials I (Prof. C. Livermore, Fall 2006), lecture 13 notes: ε_lateral = −ν ε_axial, typical ν ≈ 0.3 and 0 ≤ ν ≤ 0.5, G = E/(2(1 + ν)), K = E/(3(1 − 2ν)), ΔV/V ≈ ε_xx + ε_yy + ε_zz.

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