What Is Shear Strain?
Shear strain (γ, gamma) measures how much a material deforms in response to a shearing force — a force applied parallel to a surface rather than perpendicular to it. Unlike normal strain which stretches or compresses, shear strain skews the shape, turning a rectangle into a parallelogram. It is a dimensionless quantity, often expressed in radians, equal to the tangent of the deformation angle. This calculator works for any consistent unit system and applies universally across engineering and physics.
How to Use the Calculator
Choose your calculation method. If you know the physical deformation, enter the lateral displacement (Δx) and the original length (L) measured perpendicular to the applied force, and the tool computes \(\gamma = \Delta x / L\). If you instead know the loading, select stress mode and enter the shear stress (τ) and the material's shear modulus (G); the tool computes \(\gamma = \tau / G\). The result also reports the equivalent shear angle in degrees.
The Formula Explained
The two forms come from the definition of the shear modulus, also called the modulus of rigidity: \(G = \tau / \gamma\). Rearranging gives $$\gamma = \frac{\text{Shear stress } \tau \text{ (Pa)}}{\text{Shear modulus } G \text{ (Pa)}}$$ Geometrically, the same strain equals the displacement Δx of the top surface divided by the height L between the surfaces, so $$\gamma = \frac{\text{Displacement } \Delta x}{\text{Length } L}$$ For small strains, \(\gamma \approx \theta\), the angle of distortion in radians.
Worked Example
A block 50 mm tall has its top face pushed 2 mm sideways. The shear strain is $$\gamma = \Delta x / L = \frac{2}{50} = 0.04$$ The equivalent shear angle is \(\arctan(0.04) \approx 2.29^\circ\). Alternatively, if a material with shear modulus G = 25 MPa carries a shear stress τ = 1 MPa, then $$\gamma = \frac{1{,}000{,}000}{25{,}000{,}000} = 0.04$$ — the same strain.
FAQ
Is shear strain in radians or degrees? It is dimensionless but numerically equals the deformation angle in radians for small strains. We also show degrees for convenience.
What units should I use for stress and modulus? Use the same units for both (e.g. both in Pa or both in MPa); the strain is unitless so the units cancel.
Does length need specific units? No — Δx and L just need to share the same unit (mm, in, m). The ratio is dimensionless.
