Shear Strain Calculator — γ = Δx/L or γ = τ/G
Calculate the shear strain γ — the angular distortion of a material element under shear load — using the geometric definition (Δx/L) or Hooke's shear law (τ/G).
Calculation method
mm
mm
Dimensionless angular deformation — ratio of lateral displacement to perpendicular height
- 1
Lateral displacement Δx and height L
Δx = 5 mm, L = 100 mm - 2
Shear strain γ = Δx ÷ L
5 ÷ 100 = 0.050000
How does this calculator work?
Shear strain γ = Δx / L is the angular distortion of a material element under shear load: lateral displacement divided by perpendicular height. Alternatively, γ = τ / G from Hooke's shear law. It is dimensionless; typical elastic metal values are below 0.005.
Formula
How this is calculated
Shear strain γ (gamma) quantifies how much a material element distorts angularly when shear forces act on it. Geometrically, it equals the lateral displacement Δx divided by the perpendicular dimension L — equivalently, the tangent of the shear angle φ formed between the deformed and undeformed element sides. For the small deformations typical in engineering (φ < ~5°), γ ≈ tan φ ≈ φ in radians, which is an excellent approximation.
For an elastic material obeying Hooke's shear law, shear stress τ and shear strain γ are proportional: τ = G γ, where G is the shear modulus. Rearranging gives γ = τ / G. This linear relationship holds only in the elastic range; beyond the shear yield strength the material deforms plastically and the proportionality breaks down.
Shear strain is dimensionless (mm/mm = m/m). Values in elastic metal components under service loads are typically well below 0.01 (< 1%). Large shear strains occur in rubber bearings, adhesive joints and geological fault zones. The shear angle output lets you verify small-strain assumptions: if φ exceeds a few degrees, geometric nonlinearity should be accounted for in the structural model.
Frequently asked questions
Shear strain is dimensionless — it is the ratio of a displacement to a length (mm/mm). Some texts write it in 'rad' to emphasise its angular interpretation, but no unit conversion is required. Multiplying γ by G (in MPa) recovers shear stress τ (in MPa).
Normal strain ε = ΔL / L measures elongation or compression along the load axis — a square element remains square but changes length. Shear strain γ = Δx / L measures the angular distortion — a square element skews into a parallelogram. The two types of strain appear simultaneously in general loading and are combined using the strain tensor.
In the elastic range, shear stress and shear strain are proportional: τ = G γ. This is the shear analogue of the axial form σ = E ε. G is the shear modulus (modulus of rigidity): steel G ≈ 79 GPa (79 000 MPa), aluminium ≈ 26 GPa, rubber ≈ 0.001–0.003 GPa. Beyond the elastic limit, the linear relationship no longer holds.
TG we-Calculate Editorial Team. (2026). Shear Strain Calculator — γ = Δx/L or γ = τ/G [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/shear-strain-calculator
TG we-Calculate Editorial Team. "Shear Strain Calculator — γ = Δx/L or γ = τ/G." TG we-Calculate. 2026. https://we-calculate.com/calculator/shear-strain-calculator.
TG we-Calculate Editorial Team, "Shear Strain Calculator — γ = Δx/L or γ = τ/G," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/shear-strain-calculator
@misc{wecalculate_shear_strain_calculator, title = {Shear Strain Calculator — γ = Δx/L or γ = τ/G}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/shear-strain-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?