Young’s modulus tells you how stiff a material is — how much it stretches under load. This reference lists Young’s modulus, shear modulus, and Poisson’s ratio for common materials and computes elastic strain from an applied stress using Hooke’s law.
How it works
In the elastic region stress and strain are proportional, and the constant of proportionality is Young’s modulus E:
strain = stress / EFor an isotropic material the three elastic constants are linked by:
E = 2 * G * (1 + ν)so the shear modulus G and Poisson’s ratio ν are not independent of E. The
calculator takes a stress in MPa, divides by E (converted to MPa), and reports
the dimensionless strain and its percent elongation. A 250 MPa stress in steel
(E ≈ 200000 MPa) gives a strain of 250 / 200000 = 0.00125, about 0.125 percent.
Material comparisons at a glance
The wide range of Young’s modulus values across materials is one of the key reasons engineers choose one over another for a given application. A few illustrative points:
| Material | Young’s modulus (approx.) | Character |
|---|---|---|
| Diamond | ~1000 GPa | Stiffer than any common engineering material |
| Steel (carbon and alloy) | ~200 GPa | The backbone of structural engineering |
| Titanium alloys | ~110 GPa | Half the stiffness of steel at ~60% the density |
| Aluminium alloys | ~69 GPa | One-third the stiffness of steel; much lighter |
| Concrete | ~30 GPa | Stiff in compression, weak in tension |
| Wood (along grain) | 8–15 GPa | Highly direction-dependent |
| Rubber | ~0.01–0.1 GPa | Four to five orders of magnitude softer than steel |
This spread explains, for example, why an aluminium aircraft structure deflects measurably more than an equivalent steel one under the same aerodynamic load, and why composite designs mix fibres with very different moduli.
Worked example
For example, a steel rod with cross-section 10 mm × 10 mm carries a tensile load of 25 kN. Stress = 25,000 N ÷ (0.01 m × 0.01 m) = 250 MPa. With E = 200,000 MPa, strain = 250 ÷ 200,000 = 0.00125, or 0.125 percent elongation. A 1-metre section of that rod would stretch by 1.25 mm under that load.
Running the same calculation with aluminium (E ≈ 69,000 MPa) gives a strain of ~0.0036 and 3.6 mm of stretch — nearly three times more deflection under the same force.
Tips and notes
- Stay in the elastic region: Hooke’s law only holds below the yield stress. Computing a large strain does not mean the material behaves that way — it means it has yielded or fractured.
- All carbon and alloy steels share roughly 200 GPa — alloying changes strength and toughness far more than it changes stiffness.
- Most metals have Poisson’s ratio near 0.3; rubber approaches the incompressible limit of 0.5; cork is near zero.
- Modulus drops slowly with temperature. The calculator gives a room-temperature value; use a corrected figure for high-temperature or cryogenic service.