Shear Modulus Calculator
Enter shear force F, area A, shear distance L and lateral displacement Δx to compute shear modulus G=F·L/(A·Δx). F=1000 N, A=1e-4 m², L=1 m, Δx=1.26e-4 m → G≈79.4 GPa (close to steel).
Input Data
Results
At a glance:Shear modulus (symbol G, also μ, modulus of rigidity): a measure of a solid's resistance to shear (angular) deformation, defined as the ratio of shear stress τ to shear strain γ, G=τ/γ=F·L/(A·Δx), in Pa. Term by term: when a force F acts tangentially over an area A, the shear stress is τ=F/A (Pa); the block of shear-plane spacing L shifts laterally by Δx, giving shear strain γ=Δx/L (dimensionless, a pure angle in radians). G is the slope of the τ–γ curve in the linear range. Physical meaning: a larger G means harder to shear (more rigid); a smaller G means softer. It relates to Young's modulus E and Poisson's ratio ν by G=E/(2(1+ν)) — for steel E=200 GPa, ν=0.3 → G=200/(2×1.3)=76.9 GPa, matching the typical 79 GPa. Typical values: steel ~79 GPa, aluminium ~26 GPa, copper ~48 GPa, glass ~30 GPa, wood ~1 GPa (along grain), rubber ~0.3 MPa. History: the elastic-modulus framework was systematised by Cauchy in the 1820s; shear modulus is core to elastic mechanics. Applications: (1) shaft and torsion design; (2) spring stiffness; (3) building seismic resistance and structural mechanics; (4) seismic-wave analysis (S-wave speed v_s=√(G/ρ)); (5) geomechanics and rock/soil testing.
Formula
Shear modulus: G = τ/γ = F·L/(A·Δx)
Shear stress: τ = F/A
Shear strain: γ = Δx/L
With E and ν: G = E/(2(1+ν))
S-wave speed: v_s = √(G/ρ)
$$G = \frac{\tau}{\gamma} = \frac{F\,L}{A\,\Delta x}, \quad G = \frac{E}{2(1+\nu)}, \quad v_s = \sqrt{\frac{G}{\rho}}$$How to Use
- Enter shear force F (N).
- Enter shear area A (m²).
- Enter shear distance L (m) and lateral displacement Δx (m).
- The tool computes shear modulus G, shear stress τ and shear strain γ.
Case Studies
Steel shaft rigidity and S-wave
A steel test block: F=1000 N, A=1e-4 m², L=1 m, Δx=1.26e-4 m → G=1000×1/(1e-4×1.26e-4)=79.4 GPa (near steel).
With ρ=7850 kg/m³, S-wave speed v_s=√(79.4e9/7850)≈3180 m/s.
G links directly to seismic S-waves — higher G layers transmit faster shear waves.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.