# Poisson's Ratio Calculator

Calculate Poisson's ratio ν = −ε_transverse / ε_longitudinal and solve any of the three unknowns: ratio, lateral strain, or longitudinal strain. Tensile ε_long > 0 produces lateral contraction ε_lat < 0. Typical values: steel ≈ 0.30, aluminum ≈ 0.33, rubber ≈ 0.49, cork ≈ 0. Theoretical isotropic range 0 ≤ ν ≤ 0.5.

> Canonical page: https://elysiatools.com/en/tools/poisson-ratio-calculator

- **Category:** Math & Numbers

- **Keywords:** poisson's ratio, lateral strain, transverse strain, longitudinal strain, nu = -eps_lat/eps_long, axial strain, auxetic, elastic constants, mechanics of materials

## Overview

Calculate Poisson's ratio, lateral strain, or longitudinal strain using the relationship ν = −ε_lat/ε_long. Enter the known strain values or ratio, choose the quantity to solve for, and set the desired decimal places.

## Inputs

- **Solve for** (select)
- **Poisson's Ratio ν** (number): Poisson's ratio. Required when solving for lateral or longitudinal strain. Isotropic range 0–0.5. Steel ≈ 0.30, aluminum ≈ 0.33, rubber ≈ 0.49.
- **Lateral Strain ε_lat** (number): Transverse (lateral) strain, dimensionless. Negative when the longitudinal strain is tensile. Required when solving for ratio or longitudinal strain.
- **Longitudinal Strain ε_long** (number): Axial (longitudinal) strain, dimensionless. Required when solving for ratio or lateral strain. Must be non-zero when solving for ratio.
- **Decimal Places** (number)

## When to use

- Calculate Poisson's ratio from measured lateral and longitudinal strains.
- Find lateral strain for a material with a known Poisson's ratio and axial strain.
- Solve for longitudinal strain when Poisson's ratio and lateral strain are known.

## How it works

- Choose whether to solve for Poisson's ratio, lateral strain, or longitudinal strain.
- Enter the required dimensionless strain values and, when applicable, a Poisson's ratio between 0 and 0.5.
- The calculator applies ν = −ε_lat/ε_long, ε_lat = −ν·ε_long, or ε_long = −ε_lat/ν.
- Review the calculated result, input values, strain values, and auxiliary-material status in the JSON output.

## Use cases

- Checking experimental strain measurements in mechanics of materials.
- Estimating transverse contraction or expansion from axial loading data.
- Comparing calculated material behavior with reference values for steel, aluminum, rubber, or cork.

## Frequently asked questions

### What is the formula for Poisson's ratio?

Poisson's ratio is ν = −ε_lat/ε_long, where ε_lat is lateral strain and ε_long is longitudinal strain.

### What values are needed to calculate Poisson's ratio?

Enter lateral strain and a non-zero longitudinal strain, then select Poisson's ratio as the quantity to solve for.

### What sign should lateral strain have during tension?

For tensile longitudinal strain, lateral contraction is negative, so ε_long is positive and ε_lat is negative.

### What is the typical theoretical range for isotropic materials?

The theoretical isotropic range is 0 to 0.5. Typical values include steel near 0.30 and aluminum near 0.33.

### Can the calculator solve for strain instead of Poisson's ratio?

Yes. It can solve for lateral strain from ν and ε_long, or longitudinal strain from ν and ε_lat.

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