Poisson's Ratio — Values for Common Materials

Overview

Poisson's ratio ($\nu$) is a fundamental material property describing how a material deforms under uniaxial stress. When a material is stretched, it contracts in the direction perpendicular to the applied load. Poisson's ratio quantifies this relationship as the negative ratio of lateral (transverse) strain to axial (longitudinal) strain. For most stable engineering materials, its value lies between 0 and 0.5. Materials with a ratio of 0.5 are considered incompressible (like rubber), while cork has a ratio near zero.

Key Formulas

The axial strain ($\varepsilon_l$) and the resulting lateral strain ($\varepsilon_t$) are defined as:

$\varepsilon_l = \frac{\Delta l}{l}$

$\varepsilon_t = \frac{\Delta d}{d}$

Poisson's ratio ($\nu$) is the negative of the ratio of these strains:

$\nu = -\frac{\varepsilon_t}{\varepsilon_l}$

For an initial cylindrical geometry, the change in radius ($\Delta r$) can be calculated if the axial deformation is known:

$\Delta r = -\nu \cdot r \cdot \frac{\Delta l}{l}$

Variables

• $l$ : Original length
• $\Delta l$ : Change in length (axial deformation)
• $d, r$ : Original diameter or radius
• $\Delta d, \Delta r$ : Change in diameter or radius (lateral deformation)
• $\varepsilon_l$ : Axial (longitudinal) strain (dimensionless)
• $\varepsilon_t$ : Lateral (transverse) strain (dimensionless)
• $\nu$ : Poisson's ratio (dimensionless)

Reference Data

Typical values for Poisson's ratio of common engineering materials are preserved in the restored original source table below.

Example Calculator

Calculate the radial contraction of an aluminum bar under tension.

Restored Original Source Tables

The following tables are restored from the original source page to preserve the complete reference data.

Poisson's Ratios common Materials

Interactive Poisson's Ratio Chart

The original diagram is preserved below. The numeric material values from the source table are also represented as an interactive chart for quick comparison; source rows expressed as ranges remain in the complete table above.

Engineering Notes

• Incompressibility: The theoretical maximum value of 0.5 corresponds to a perfectly incompressible material, where volume is conserved during deformation.
• Anisotropy: Values can vary significantly with direction in composite materials, rolled metals, or wood.
• Range of Validity: Tabulated values are for linear elastic, small-strain conditions. Plastic deformation or large strains can alter the effective ratio.
• Measurement: Poisson's ratio is often determined experimentally by measuring simultaneous axial and lateral strains during a tensile test.
• Design Impact: A higher Poisson's ratio indicates greater lateral expansion under compression, which is critical in applications like gasket design or press-fit assemblies.

References

• Original Source: Poisson's Ratio - Engineering ToolBox