Calculate shear strain (γ) using three methods: from lateral displacement and original height, from shear stress and shear modulus, or for a shaft under torsion. Enter your known values, select a calculation mode, and get the shear strain, shear angle, and supporting results instantly.
Shear Strain (γ)
--
Shear Angle (γ in degrees)
--
Shear Angle (γ in radians)
--
Method Used
--
Shear strain (γ) is a measure of the angular deformation a material undergoes when subjected to shear forces. It represents the change in angle between two originally perpendicular lines in the material and is defined as the ratio of the lateral displacement (x) to the original height (h) of the element. Shear strain is dimensionless.
Shear strain is dimensionless — it has no unit. It is expressed as a pure number (or sometimes in radians) because it is the ratio of two lengths (displacement over height) or an angle in radians. For very small values it may be expressed in microstrain (με).
When you know the lateral displacement (x) and the original height (h) of the element, shear strain is calculated as γ = x / h. This formula applies when the displacement is small relative to the height, which is the common engineering assumption.
Using Hooke's Law for shear, shear strain equals shear stress (τ) divided by the shear modulus (G): γ = τ / G. This applies in the elastic range where the material behaves linearly. The shear modulus (also called modulus of rigidity) is a material property.
For a circular shaft under torsion, the maximum shear strain at the outer surface is γ_max = (T × r) / (J × G), where T is the torque, r is the outer radius, J is the polar moment of inertia (J = πr⁴/2 for a solid shaft), and G is the shear modulus. This calculator uses that formula for the torsion mode.
Shear strain is universally denoted by the Greek letter gamma (γ). The subscript may indicate the plane of shear, for example γ_xy for shear strain in the x-y plane. The symbol τ (tau) is used for shear stress, not strain.
Normal strain (ε) measures elongation or compression along an axis — a change in length. Shear strain (γ) measures the change in angle (angular distortion) between two lines that were originally perpendicular. Shear strain involves a change in shape without a change in volume under pure shear conditions.
Shear strain calculations are essential in mechanical and structural engineering for analyzing torsion in drive shafts, deflection of beams under shear loads, design of adhesive and bolted joints, seismic engineering (shear wave propagation in soil), and failure analysis of materials under complex loading. It is also a key input for finite element analysis validation.