Young's Modulus Calculator
Young's modulus is E = σ / ε: a stress of 250 MPa at 0.125 % strain gives E = 250 ÷ 0.00125 = 200 000 MPa = 200 GPa, typical of steel (29010 ksi).
200 GPa
- In SI: E = 200000000000 Pa, σ = 250000000 Pa, ε = 0.00125
- Valid in the linear-elastic range only, below the proportional limit.
Hooke's Law and the Stress–Strain Curve
σ = E ε E = σ / ε = F L₀ / (A ΔL)
σ stress (Pa), E Young's modulus (Pa), ε strain = ΔL / L₀, F force (N), A original area (m²), L₀ gauge length, ΔL extension
On a stress–strain curve E is the slope of the initial straight line. Beyond the proportional limit and the yield point the curve bends over and Hooke's law no longer applies, so results here are only valid for elastic loading.
| Material | GPa | ksi |
|---|---|---|
| Carbon steel | 200 | 29000 |
| Stainless steel 304 | 193 | 28000 |
| Aluminium alloys | 69 | 10000 |
| Copper | 117 | 17000 |
| Titanium Ti-6Al-4V | 114 | 16500 |
| Grey cast iron | 100 | 14500 |
| Concrete | 30 | 4350 |
| Wood along the grain | 11 | 1600 |
Typical values; alloys, tempers and test methods vary by a few percent. Use the material specification for design.
Worked Examples
- Tensile test: 20 kN on a 12.5 mm specimen (A = 122.7 mm²) gives σ = 163 MPa; a 0.040 mm extension over a 50 mm gauge length is ε = 0.0008. E = σ / ε = 203.7 GPa.
- Aluminium (E = 69 GPa) at 0.1 % strain: σ = 69 000 MPa × 0.001 = 69 MPa.
- Steel (E = 200 GPa) at its S355 yield stress: ε = 355 ÷ 200 000 = 0.178 % (1775 µε).
Frequently asked questions
What is the formula for Young's modulus?
E = σ / ε, stress divided by strain in the linear-elastic region. Stress σ = F/A and strain ε = ΔL/L₀, so E = F L₀ / (A ΔL).
What are the units of Young's modulus?
The same as stress, because strain has no unit: Pa, MPa or GPa in SI, psi or ksi (and Mpsi) in US units. Steel is about 200 GPa = 29 000 ksi.
How do I enter strain in percent or microstrain?
Choose the strain unit: 0.1 % = 0.001 mm/mm = 1000 µε. The calculator converts all three to the same dimensionless strain.
Is Young's modulus the same as stiffness?
Young's modulus is a material property. The stiffness of a part (force per deflection) also depends on its shape and length: for a bar in tension, k = E A / L.
Does Young's modulus change with temperature?
Yes, it falls as temperature rises. For steel it drops by roughly 5 % between room temperature and 200 °C, so use data for the service temperature.
What is the dimensional formula of Young's modulus?
[M L⁻¹ T⁻²], the same as pressure or stress, because strain is dimensionless.
How do I find Young's modulus from a stress–strain graph?
Take two points on the straight, elastic part of the curve and divide the change in stress by the change in strain: E = Δσ / Δε. Do not use points past the proportional limit.
Is elastic modulus the same as Young's modulus?
In tension and compression, yes: 'elastic modulus' usually means Young's modulus E. Other elastic moduli are the shear modulus G and the bulk modulus K; for isotropic materials E = 2G(1 + ν).
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Young's Modulus Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/youngs-modulus/
IEEE
Scientific Converters, "Young's Modulus Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/youngs-modulus/