What is shear modulus?

Shear modulus (G), also called the modulus of rigidity, measures a material's resistance to shear deformation. It is defined as the ratio of shear stress to shear strain: G = τ / γ.

How is shear modulus related to Young's modulus?

For isotropic elastic materials, G = E / (2(1 + v)), where E is Young's modulus and v is Poisson's ratio. This relationship holds because all three constants (E, G, v) describe the same elastic behavior.

What are typical shear modulus values?

Steel is about 79–81 GPa, aluminum around 26 GPa, copper near 45 GPa, rubber roughly 0.0003–0.001 GPa, and concrete in the range of 14–21 GPa.

What units does shear modulus use?

Shear modulus has the same units as pressure or stress: Pascals (Pa). Engineering problems commonly express it in MPa or GPa.

What is the valid range for Poisson's ratio?

For isotropic materials, Poisson's ratio must be between -1 and 0.5 (exclusive). Most common structural materials fall between 0.2 and 0.45.

Shear Modulus Calculator

Compute shear modulus (G) from shear stress/strain or from Young's modulus and Poisson's ratio.

Input

Calculation Method

Shear Stress (τ)

Shear Strain (γ) (dimensionless)

Common Material Values

Steel79–81 GPa Aluminum~26 GPa Copper~45 GPa Concrete14–21 GPa Glass~26 GPa Rubber0.0003–0.001 GPa

Result

Enter values and click Calculate

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Summary

The Shear Modulus Calculator computes the modulus of rigidity (G) using either the direct ratio of shear stress to shear strain (G = τ/γ), or the elastic-constants formula G = E / (2(1+v)) relating Young's modulus and Poisson's ratio. Results are shown in Pa, kPa, MPa, and GPa.

How it works

Choose the calculation method: stress/strain direct method or elastic constants method.
For direct method: enter shear stress (τ) in Pa and shear strain (γ) as a dimensionless ratio.
For elastic constants method: enter Young's modulus (E) in Pa and Poisson's ratio (v).
Click Calculate to apply the formula G = τ/γ or G = E / (2(1+v)).
The result is displayed in Pa, kPa, MPa, and GPa for easy comparison.

Use cases

Verify material properties of metals, polymers, or composites in structural analysis.
Cross-check shear modulus values for FEA material models.
Convert between different representations of elastic constants.
Quick sanity-check during mechanical engineering coursework or exam prep.
Determine stiffness under torsional or shear loading conditions.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu