Young’s Modulus Calculator
Find a material’s elastic modulus (E) from stress and strain, or straight from an axial tension test.
That is close to structural steel (≈ 200 GPa). A higher modulus means a stiffer material, not a stronger one.
Young’s modulus is stiffness: divide stress by strain, E = σ ÷ ε. A stress of 100 MPa (1×10⁸ Pa) at a strain of 0.0005 gives E = 1×10⁸ ÷ 0.0005 = 2×10¹¹ Pa = 200 GPa — a value typical of steel. A higher modulus means a stiffer material, not a stronger one.
What Young’s modulus tells you
Young’s modulus (E), also called the elastic modulus, measures how much a material resists being stretched or compressed in its elastic region. It is the ratio of stress (force per unit area, σ) to strain (fractional change in length, ε). Because strain is a bare number, E carries the units of stress — pascals — and for stiff engineering materials it is quoted in gigapascals (GPa). A large E means the material barely deforms under load: steel at ≈ 200 GPa is roughly three times as stiff as aluminium and thousands of times stiffer than rubber.
E = Young’s modulus (Pa), σ = stress (Pa), ε = strain (unitless), F = force (N), A = area (m²), L₀ = original length, ΔL = change in length
Worked example
A steel rod, 1 m long with a 100 mm² cross-section, carries a 10 kN axial pull and stretches 0.5 mm. Find its Young’s modulus straight from the tension test.
- 1 Convert the area to m². 100 mm² × 1×10⁻⁶ = 1×10⁻⁴ m². Working in SI base units keeps the modulus in pascals.
- 2 Convert the elongation to metres. ΔL = 0.5 mm × 1×10⁻³ = 5×10⁻⁴ m.
- 3 Substitute into E = (F · L₀) ÷ (A · ΔL). E = (10000 N × 1 m) ÷ (1×10⁻⁴ m² × 5×10⁻⁴ m) = 10000 ÷ 5×10⁻⁸.
- 4 Compute the modulus. E = 2×10¹¹ Pa = 200 GPa — the standard stiffness of structural steel.
- 5 Cross-check with E = σ ÷ ε. σ = 10000 ÷ 1×10⁻⁴ = 100 MPa and ε = 5×10⁻⁴ ÷ 1 = 0.0005, so E = 1×10⁸ ÷ 0.0005 = 200 GPa. Same answer.
Typical Young’s modulus of common materials
Representative values for everyday engineering materials. Real figures vary with alloy, grade, grain direction, and temperature.
| Material | Young’s modulus (GPa) | Notes |
|---|---|---|
| Structural steel | ≈ 200 | Reference stiffness for beams and frames |
| Aluminium | ≈ 69 | About one-third as stiff as steel |
| Concrete | ≈ 30 | Varies widely with mix and curing |
| Wood (along grain) | ≈ 11 | Much lower across the grain |
| Rubber | ≈ 0.01–0.1 | Very low and not truly linear-elastic |
Stiffness is not strength, and it only holds in the elastic region
The single most common mistake is treating a high modulus as “strong.” Stiffness (E) is how much a material deforms under load; strength (yield or ultimate stress) is how much load it takes before it permanently deforms or breaks. Cast iron is stiffer than many steels yet more brittle; a bungee cord is very strong in the sense that it holds you, but its modulus is tiny. The two properties are independent.
Young’s modulus is only meaningful in the elastic region, where stress is proportional to strain (Hooke’s law, σ ∝ ε) and the material springs back on unloading. Graphically, E is the slope of the initial straight part of the stress–strain curve. Past the yield point the curve bends over, deformation becomes permanent, and a single modulus no longer describes the behaviour — so keep applied stress well below yield when you rely on E.