The shear modulus measures resistance to shape change: how much a block deforms sideways when you push its top face parallel to its base. Steel has a shear modulus of about 79 GPa, rubber less than 0.001 GPa.
How to use the Shear Modulus Calculator
- Method
- Shear force F
- Area A
- Initial length (height) l
- Transverse displacement Δx
- Shear stress τ
- Shear strain γ (rad)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the method and enter the values.
Inputs explained
| Field | What to enter |
|---|---|
| Method | Choose one: Force, area and displacement, Shear stress and strain |
| Shear force F | Units: N, kN, MN, mN, lbf, kgf … |
| Area A | Units: m², cm², mm², km², in², ft² |
| Initial length (height) l | Units: m, cm, mm, km, in, ft … |
| Transverse displacement Δx | Units: mm, cm, m, in, µm |
| Shear stress τ | Units: MPa, kPa, Pa, GPa, psi, ksi |
| Shear strain γ (rad) | A number |
Example values
How the main result changes when Shear force F changes and everything else stays at the example values above:
| Shear force F (N) | Shear modulus G (GPa) |
|---|---|
| 5,000 | 50 |
| 7,500 | 75 |
| 10,000 | 100 |
| 12,500 | 125 |
| 15,000 | 150 |
| 20,000 | 200 |
Formula
G = τ / γ = (F/A) / (Δx/l)
Worked example
Inputs — Method: Force, area and displacement; Shear force F: 10,000 N; Area A: 0.01 m²; Initial length (height) l: 0.1 m; Transverse displacement Δx: 0.001 mm.
Results — Shear stress τ = 1 MPa; Shear strain γ = 0.00001 rad; Shear modulus G = 100 GPa.
Key terms
- Modulus of rigidity
- Another name for the shear modulus.
Frequently asked questions
What is the shear modulus of steel?
About 79 GPa.
How does G relate to E?
G = E/(2(1 + ν)).
Why is shear strain in radians?
It is the angle of distortion, ≈ Δx/l for small angles.
Is G the same as the modulus of rigidity?
Yes.