The shear modulus (G), also known as the modulus of rigidity, measures how strongly a material resists shape-changing deformation under a sliding or twisting force. It's a core elastic constant used in mechanical and structural engineering — from sizing shafts under torsion to predicting how a bolted joint will behave under load. This calculator computes G two ways, and solves for any missing variable.

How the Shear Modulus Calculator works

The calculator supports two independent routes to the same physical quantity. The first, G = τ / γ, uses shear stress and shear strain measured directly from a torsion or shear test — the shear analog of how Young's modulus relates tensile stress to tensile strain. The second, G = E / (2(1 + ν)), derives the shear modulus from Young's modulus and Poisson's ratio, two elastic constants that are far more commonly published on materials datasheets than direct shear-test data. For an isotropic elastic material, both formulas describe the same G and should agree closely when fed a material's true E and ν.

Inputs and what they mean

Shear stress (τ) is entered in megapascals — the tangential force per unit area causing layers of the material to slide past one another. Shear strain (γ) is a unitless ratio describing the resulting angular deformation; typical elastic values are small, often well under 1% (0.01). Young's modulus (E) is entered in gigapascals and represents tensile stiffness. Poisson's ratio (ν) is unitless and typically falls between 0.2 and 0.35 for common metals, with values near 0.5 for nearly incompressible materials like rubber.

Limits and edge cases

Both formulas assume the material is isotropic (its properties don't depend on direction) and behaves elastically — that is, within its elastic limit, not yielded or plastically deformed. The stress/strain formula is undefined when shear strain is zero. The E/ν formula is undefined at ν = −1, a value that doesn't occur for ordinary materials. Composite, anisotropic, or fiber-reinforced materials (such as wood or carbon fiber) do not have a single shear modulus that applies in every direction, so this calculator's isotropic formulas should be treated as an approximation for those materials.