# Shear Modulus Calculator

URL: https://speedycalculator.com/calculators/physics/shear-modulus/
Last updated: 2026-10-30

> The shear modulus calculator finds a material's modulus of rigidity from the shear force, area, thickness and transverse displacement, or from shear stress and shear strain.

## Inputs

- Method
- Shear force F (N, kN, MN, mN, lbf, kgf, dyn)
- Area A (m², cm², mm², km², in², ft²)
- Initial length (height) l (m, cm, mm, km, in, ft, yd, mi)
- Transverse displacement Δx (mm, cm, m, in, µm)
- Shear stress τ (MPa, kPa, Pa, GPa, psi, ksi)
- Shear strain γ (rad)

## Results

- Shear stress τ
- Shear strain γ
- Shear modulus G

## Formula

```
G = τ / γ = (F/A) / (Δx/l)
```

## Explanation

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

FieldWhat to enterMethodChoose one: Force, area and displacement, Shear stress and strainShear force FUnits: N, kN, MN, mN, lbf, kgf …Area AUnits: m², cm², mm², km², in², ft²Initial length (height) lUnits: m, cm, mm, km, in, ft …Transverse displacement ΔxUnits: mm, cm, m, in, µmShear stress τUnits: MPa, kPa, Pa, GPa, psi, ksiShear 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)5,000507,5007510,00010012,50012515,00015020,000200

## 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.

## FAQ

**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.


## Sources

- [MIT OpenCourseWare – Mechanics of Materials](https://ocw.mit.edu/courses/2-001-mechanics-materials-i-fall-2006/)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)