Shear Modulus Calculator — Modulus of Rigidity (G)
Find a material's shear modulus G — its resistance to shape-changing deformation — from measured shear stress and strain, or from the material's Young's modulus and Poisson's ratio.
Calculation method
MPa
Resistance of the material to shape-changing (shear) deformation
- 1
Shear stress τ and shear strain γ
τ = 50 MPa, γ = 0.002 - 2
Shear modulus G = τ ÷ γ
50 ÷ 0.002 = 25,000G equals shear stress divided by the dimensionless angular deformation.
How does this calculator work?
Shear modulus G measures a material's resistance to shear deformation. Calculate it as G = τ/γ (shear stress ÷ shear strain) or, for isotropic materials, as G = E / [2(1+ν)] from Young's modulus and Poisson's ratio. Reference: steel ≈ 79 GPa, aluminium ≈ 26 GPa, rubber ≈ 0.002 GPa.
Formula
How this is calculated
The shear modulus G (also called the modulus of rigidity) is a fundamental elastic constant describing how a material resists deformation when a shear force is applied parallel to a surface. Defined as the ratio of shear stress τ (force per unit area, Pa or MPa) to shear strain γ (angular deformation, dimensionless): G = τ / γ. A stiffer material has a higher G and deforms less for the same applied stress.
For isotropic elastic materials, G is also related to Young's modulus E and Poisson's ratio ν through G = E / [2(1 + ν)]. Poisson's ratio for most engineering materials lies between 0 and 0.5 (steel ≈ 0.29, aluminium ≈ 0.33, rubber ≈ 0.49). This identity is exact within linear elasticity — small strains, homogeneous, isotropic material. For anisotropic materials such as composites or wood, G depends on the loading direction and the two formulas may give different values.
Typical reference values (approximate): structural steel ≈ 79 GPa, aluminium alloys ≈ 26 GPa, copper ≈ 45 GPa, glass ≈ 26 GPa, concrete ≈ 12–14 GPa, rubber ≈ 0.001–0.003 GPa. The shear modulus appears in torsion problems, beam shear deflection, and shear wave velocity (Vs = √(G/ρ)).
Frequently asked questions
Young's modulus E describes resistance to axial (tensile or compressive) deformation — stretching or squashing along the load axis. The shear modulus G describes resistance to shear deformation — sliding of parallel planes. For isotropic materials, they are related by G = E / [2(1 + ν)], so knowing two of the three elastic constants determines the third.
Structural steel: ~79 GPa; aluminium alloys: ~26 GPa; copper: ~45 GPa; glass: ~26 GPa; concrete: ~12 GPa; rubber: ~0.001–0.003 GPa; wood (along grain): ~1–6 GPa. A higher G means the material is stiffer against shear — steel is about 26 000 times stiffer than typical rubber.
These limits follow from thermodynamic stability: elastic energy must be positive for any deformation state, which constrains ν to (−1, 0.5) for isotropic solids. In practice, nearly all engineering materials have 0 < ν < 0.5; exotic auxetic materials (ν < 0) exist but are rare. Values outside the range are physically impossible and produce a negative shear modulus.
TG we-Calculate Editorial Team. (2026). Shear Modulus Calculator — Modulus of Rigidity (G) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/shear-modulus-calculator
TG we-Calculate Editorial Team. "Shear Modulus Calculator — Modulus of Rigidity (G)." TG we-Calculate. 2026. https://we-calculate.com/calculator/shear-modulus-calculator.
TG we-Calculate Editorial Team, "Shear Modulus Calculator — Modulus of Rigidity (G)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/shear-modulus-calculator
@misc{wecalculate_shear_modulus_calculator, title = {Shear Modulus Calculator — Modulus of Rigidity (G)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/shear-modulus-calculator}}, year = {2026}, note = {TG we-Calculate} }
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