What this calculator does
Shear modulus measures how much a material resists being deformed sideways, as distinct from being stretched. Pushing the top face of a block sideways while the bottom stays fixed produces shear rather than tension.
It is typically around a third to a half of Young's modulus for common metals, and it is the property that governs torsion in shafts, deflection in beams and the behaviour of fasteners loaded across their axis.
The formula
Shear stress is the force divided by the area it acts over. Shear strain is the sideways displacement divided by the transverse length. The modulus is stress divided by strain.
| Term | Meaning |
|---|---|
| Shear modulus (G) | Shear stress divided by shear strain, also called the modulus of rigidity. |
| Shear stress (τ) | Force acting parallel to a surface, divided by that area. |
| Shear strain (γ) | Sideways displacement divided by the distance between the sheared faces. |
The inputs explained
| Field | What to enter |
|---|---|
| Shear force (N) | The shear force applied parallel to the surface, in newtons. |
| Transverse length (L) (m) | The transverse length between the fixed and moving faces, in metres. |
| Area force acts on (m²) | A number, measured in m². Starts at 0.01. |
| Displacement (Δx) (m) | A number, measured in m. Starts at 0.0005. |
When to use it
Analysing a shaft in torsion
Twist in a drive shaft depends directly on the shear modulus of its material.
Checking a fastener in shear
Bolts loaded across their axis are in shear rather than tension, which is a different calculation with different limits.
Characterising an elastomer
Rubber mounts work primarily in shear, so the shear modulus is the relevant stiffness figure.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the applied force change the calculated modulus?
The same specimen under a range of shear forces.
| Shear force | Shear modulus (GPa) | Shear stress |
|---|---|---|
| 2,500 N | 0.1000 GPa | 0.25 MPa |
| 5,000 N | 0.2000 GPa | 0.50 MPa |
| 10,000 N | 0.4000 GPa | 1.00 MPa |
Questions
How does shear differ from tension?
Tension pulls a material apart along one axis; shear slides adjacent layers past each other. They produce different deformations and are resisted by different moduli, though both are elastic properties of the same material.
How does it relate to Young's modulus?
For an isotropic material, Young's modulus equals twice the shear modulus times one plus Poisson's ratio. For steel that puts the shear modulus at roughly 40 per cent of Young's modulus.
Do fluids have a shear modulus?
Not in the elastic sense. A fluid keeps deforming under any shear stress rather than settling at a fixed strain, which is essentially what makes it a fluid. Its resistance is described by viscosity instead.
Why does it matter for shafts?
Because a shaft transmitting torque is entirely in shear. The angle of twist for a given torque depends directly on the shear modulus, so it sets how stiff the drive feels.
For tensile stiffness, see the Young's modulus calculator. For the ratio linking the two, see the Poisson's ratio calculator.