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
Input Parameters
Calculation Results
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
Physical Limits
Elastic Relationships
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)]