# Young’s Modulus Calculator

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

> The Young's modulus calculator finds the stiffness of a material in tension or compression from the applied force, cross-sectional area, original length and change in length.

## Inputs

- Force F (kN, N, lbf, kgf)
- Cross-section area A (mm², cm², m², in²)
- Initial length L₀ (m, cm, mm, km, in, ft, yd, mi)
- Change in length ΔL (mm, cm, m, in, µm)

## Results

- Stress σ
- Strain ε
- Young's modulus E
- Comparable to

## Formula

```
E = σ / ε = (F/A) / (ΔL/L₀)
```

## Explanation

Young's modulus measures how stiff a material is: steel is about 200 GPa, aluminium 69 GPa, rubber only about 0.01 GPa. It is found from the straight, elastic part of a tensile test.

### How to use the Young's Modulus Calculator

- **Force F**
- **Cross-section area A**
- **Initial length L₀**
- **Change in length ΔL**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the force, cross-section area, original length and the measured elongation (within the elastic range).

### Inputs explained

FieldWhat to enterForce FUnits: kN, N, lbf, kgfCross-section area AUnits: mm², cm², m², in²Initial length L₀Units: m, cm, mm, km, in, ft …Change in length ΔLUnits: mm, cm, m, in, µm

### What each result means

- **Stress σ** = [Force F]÷[Cross-section area A]
- **Strain ε** = [Change in length ΔL]÷[Initial length L₀]
- **Young's modulus E** = [Force F]÷[Cross-section area A]÷([Change in length ΔL]÷[Initial length L₀])

### Example values

How the main result changes when **Force F** changes and everything else stays at the example values above:

Force F (kN)Young's modulus E (GPa)10100.254815150.382320200.509725250.637130300.764540401.0194

## Worked example

Inputs — Force F: 20 kN; Cross-section area A: 78.54 mm²; Initial length L₀: 1 m; Change in length ΔL: 1.27 mm.

Results — Stress σ = 254.64731 MPa; Strain ε = 0.00127; **Young's modulus E = 200.5097 GPa**; Comparable to = Steel, iron.

## Key terms

- **Modulus of elasticity**: Another name for Young's modulus.

## FAQ

**What is Young's modulus of steel?**
About 200 GPa.

**Is Young's modulus the same as strength?**
No – it measures stiffness, not the stress at which a material fails.

**Does it depend on the shape?**
No – it is a material property.

**What is the elastic range?**
Loads small enough that the material returns to its original length.


## 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/)