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
| Field | What to enter |
|---|---|
| Force F | Units: kN, N, lbf, kgf |
| Cross-section area A | Units: mm², cm², m², in² |
| Initial length L₀ | Units: m, cm, mm, km, in, ft … |
| Change in length ΔL | Units: 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) |
|---|---|
| 10 | 100.2548 |
| 15 | 150.3823 |
| 20 | 200.5097 |
| 25 | 250.6371 |
| 30 | 300.7645 |
| 40 | 401.0194 |
Formula
E = σ / ε = (F/A) / (ΔL/L₀)
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.
Frequently asked questions
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.