Shear Modulus Calculator
The shear modulus calculator computes the modulus of rigidity (G) and related shear quantities for materials under shear loading. While Young's modulus describes resistance to stretching, shear modulus describes resistance to sliding or twisting deformations. This is critical for designing drive shafts subject to torque, bolted joints under shear loads, adhesive bonds, and structural elements resisting lateral forces. You can calculate shear modulus from shear stress and strain, from Young's modulus and Poisson's ratio, or compute the shear deformation expected under a known load. All results are shown in consistent SI units for direct use in engineering calculations.
Shear modulus formulas
G = tau / gamma = (F/A) / (delta_x / L)
G = E / (2 * (1 + nu))
Shear stress: tau = F / A [Pa]
Shear strain: gamma = delta_x / L [rad]
Shear modulus of common materials (GPa)
- Steel: approximately 80 GPa
- Aluminum: approximately 26 GPa
- Copper: approximately 48 GPa
- Titanium: approximately 44 GPa
- Glass: approximately 30 GPa
- Rubber: approximately 0.003 GPa
Shear modulus: frequently asked questions
What is the shear modulus?
The shear modulus (G), also called modulus of rigidity, is the ratio of shear stress to shear strain. It measures a material's resistance to deformation by shear forces - forces applied parallel to a surface. G = shear stress / shear strain = (F/A) / (delta_x / L). Steel has G around 80 GPa; aluminum is about 26 GPa.
How is shear modulus related to Young's modulus?
For isotropic materials: G = E / (2 * (1 + nu)), where E is Young's modulus and nu (Poisson's ratio) is typically 0.25 to 0.35 for metals. This means G is usually about 35 to 40% of E for common engineering metals. Rubber has a very low G relative to its bulk modulus due to its high Poisson's ratio (near 0.5).
What is shear stress?
Shear stress (tau) is the force applied parallel to a surface divided by the area of that surface: tau = F / A. It is measured in Pascals (Pa) or MPa. Shear stress causes angular deformation (shear strain) rather than elongation. Bolts in shear, keys in shafts, and welds all experience shear stress.
What is Poisson's ratio?
Poisson's ratio (nu) is the ratio of lateral strain to axial strain when a material is stretched: nu = -lateral strain / axial strain. A rubber band stretched lengthwise gets thinner sideways - this is Poisson's effect. For most metals nu is 0.25 to 0.35. A value of 0.5 means the material is incompressible (constant volume).
Where is shear modulus important in engineering?
Shear modulus governs torsion of shafts (how much a shaft twists under torque), deflection of springs, shear deformation of beams, design of bolted and welded joints, and earthquake resistance of buildings (shear walls). It is also critical in geotechnical engineering for soil behavior analysis.
Official sources
- NIST: NIST Materials Measurement Science Division.
- ASM International: ASM Handbook on Mechanical Properties.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.