Poisson’s Ratio
Relate lateral strain to longitudinal strain under uniaxial loading.
Try this formula
Calculate poisson ratio or choose another supported quantity.
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Try this formula
Calculate poisson ratio or choose another supported quantity.
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Poisson ratio
Enter the known values to see the result.
Use small strains and a homogeneous, linearly elastic material. Loads are static or slowly applied; remain below the proportional limit. Use a uniaxial stress state and strains measured in perpendicular directions. For stable isotropic linear elasticity, −1 < ν < 0.5.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, mechanics, and consistent SI units
Source
Donney Fan — MECH 360 — Mechanics of MaterialsReference equation: Axial Load — Poisson's Ration. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Definition
Most materials contract laterally when stretched longitudinally. The minus sign gives a positive Poisson ratio for this behavior; auxetic materials can instead have a negative ratio.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Poisson ratio | ||
| Signed lateral engineering strain | ||
| Signed longitudinal engineering strain |
Real-World Applications
Material testing
Estimate Poisson ratio from two strain measurements.
Lateral deformation
Predict contraction across a tensile specimen.
Worked Example
Problem
A specimen has longitudinal strain 0.001 and lateral strain −0.0003. Find its Poisson ratio.
Given
Solution
Final Answer
Contents
Info
Tools
Source & review
Reference equation: Axial Load — Poisson's Ration. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Assumptions
- • Use small strains and a homogeneous, linearly elastic material.
- • Loads are static or slowly applied; remain below the proportional limit.
- • Use a uniaxial stress state and strains measured in perpendicular directions.
- • For stable isotropic linear elasticity, −1 < ν < 0.5.
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