Young's Modulus Calculator (Stress & Strain)
Find a material's Young's modulus from an axial load, cross-section and stretch — plus the stress and strain behind it.
How it works
E = stress ÷ strain = (F ÷ A) ÷ (ΔL ÷ L₀)
Young's modulus measures a material's stiffness in the elastic range: how much stress (force per unit area) it takes to produce a given strain (fractional stretch). A high modulus means a stiff material that barely deforms — steel is about 200 GPa, aluminium about 70 GPa, rubber only a few MPa. The relationship stays linear only up to the proportional limit; beyond it the material yields and this formula no longer applies.
Worked example
A 1,000 N pull on a rod of 1 cm² (0.0001 m²) cross-section that is 2 m long stretches it by 1 mm (0.001 m). Stress = 1000/0.0001 = 10 MPa. Strain = 0.001/2 = 0.0005. E = 10×10⁶ / 0.0005 = 2×10¹⁰ Pa = 20 GPa.
Sources: Young's modulus — Wikipedia
Frequently asked questions
What units does Young’s modulus use?
It has units of pressure — pascals (Pa) — because stress is a pressure and strain is dimensionless. Engineering values are usually quoted in gigapascals (GPa); 1 GPa = 10⁹ Pa.
Does a thicker or longer sample change the modulus?
No. Young’s modulus is a property of the material, not the specimen. The geometry (area and length) is divided out; a fat short bar and a thin long wire of the same steel share the same modulus.
Is this valid past the elastic limit?
Only within the elastic region where stress is proportional to strain. Once the material yields or necks, deformation is permanent and the stress–strain curve bends away from the straight line this calculator assumes.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.