Poisson's Ratio Calculator

Calculate Poisson's ratio from strain measurements or elastic moduli

Calculation Configuration

Strain-Based Calculation: Calculate Poisson's ratio from transverse and axial strains

Formula: v = εtrans / εaxial

Material Selection

Selected Material
Steel
v = 0.270
Strong and versatile structural material

Input Parameters

Calculation Results

Enter parameters to calculate Poisson's ratio
Select a material or enter custom values for calculation

Example: Steel Under Tension

Given Values

Material: Steel

Axial Strain (elongation): +0.001 (tension)

Transverse Strain (contraction): -0.00027

Calculation

v = -εtrans / εaxial

v = -(-0.00027) / 0.001

v = 0.00027 / 0.001

v = 0.27

Result

Steel has a Poisson's ratio of 0.27, which is typical for structural metals. This means that when steel is stretched by 1%, it contracts laterally by 0.27%.

Typical Poisson's Ratios

Steel
v = 0.27-0.30
Structural metals
Aluminum
v = 0.33
Lightweight alloys
Rubber
v = 0.48-0.50
Nearly incompressible
Cork
v ≈ 0.0
Minimal lateral expansion

Physical Limits

Theoretical Minimumv = -1
Most Auxetic Materialsv = -0.1 to 0
Common Rangev = 0 to 0.5
Incompressible Limitv = 0.5

Elastic Relationships

E = 2G(1 + v)
K = E/[3(1-2v)]
λ = vE/[(1+v)(1-2v)]
E = Young's modulus, G = Shear modulus,
K = Bulk modulus, λ = Lamé parameter

Physics Tips

Poisson's ratio is always positive for normal materials

v = 0.5 means incompressible (like liquids)

Negative v indicates auxetic behavior

Most engineering materials: 0.2 ≤ v ≤ 0.4

Formula: v = -εtrans / εaxial

Understanding Poisson's Ratio

What is Poisson's Ratio?

Poisson's ratio is a fundamental material property that describes how much a material contracts laterally when stretched axially, or vice versa. Named after French mathematician Siméon Denis Poisson, it quantifies the relationship between strains in perpendicular directions.

Physical Interpretation

v = -εtrans / εaxial

v: Poisson's ratio (dimensionless)

εtrans: Transverse (lateral) strain

εaxial: Axial (longitudinal) strain

The negative sign accounts for the opposite nature of transverse and axial deformations

Material Examples

Rubber (v ≈ 0.48)

When compressed from above, flows significantly sideways

Cork (v ≈ 0.0)

Changes volume with minimal lateral expansion

Auxetic Materials (v < 0)

Expand laterally when stretched longitudinally

Engineering Applications

Structural Design

Predict dimensional changes under load for proper fits and clearances

Materials Selection

Choose materials with appropriate deformation characteristics

Composite Design

Engineer anisotropic materials with tailored properties

Elastic Constants Relations

Young's & Shear Moduli

E = 2G(1 + v)

Bulk Modulus

K = E / [3(1 - 2v)]

Lamé Parameters

λ = vE / [(1+v)(1-2v)]