Young's Modulus Calculator
Enter a force, a cross-sectional area, an original length, and how much it stretches to get the stiffness of a material in pascals — plus the stress.
Stiffness and stress at once
This Young's modulus calculator returns the modulus of elasticity (stress ÷ strain) in pascals and the tensile stress (F ÷ A) in pascals together.
Use SI units
Force in newtons, area in square metres, and lengths in metres give the modulus in pascals — convert millimetres to metres before you start.
What is Young's modulus?
A measure of stiffness
The Young's modulus calculator turns four measurements into the stiffness of a material — how strongly it resists being stretched. Young's modulus, also called the modulus of elasticity, is the ratio of tensile stress (the force spread over the cross-sectional area) to tensile strain (the relative change in length). A stiff material like steel needs a large stress to stretch even slightly, so it has a high modulus; a soft material like rubber stretches easily and has a low one. The result comes back in pascals, the same unit as pressure, and is the number engineers use to predict how much a beam, cable, or rod will deform under load.
Enter the force, the cross-sectional area, the original length, and the change in length to get Young's modulus in pascals and the stress instantly.
Young's modulus is the tensile stress divided by the tensile strain. Stress is the force divided by the area, and strain is the change in length divided by the original length.
E = (F × L₀) ÷ (A × ΔL)Equivalently, E = stress ÷ strain, where the stress is F ÷ A and the strain is ΔL ÷ L₀. Because strain is a small fraction for a stiff material, the modulus is a very large number — usually quoted in gigapascals (1 GPa = 1,000,000,000 Pa). Keep force in newtons, area in square metres, and lengths in metres so the result lands in pascals.
Suppose a 1000 N force pulls on a steel-like bar with a cross-sectional area of 0.0001 m² and an original length of 2 m, stretching it by 0.001 m.
Find the stress
1000 ÷ 0.0001 = 10,000,000 Pa — the force spread over the area.
Find the strain
0.001 ÷ 2 = 0.0005 — the relative stretch, a dimensionless ratio.
Divide stress by strain
10,000,000 ÷ 0.0005 = 20,000,000,000 Pa (20 GPa) — Young's modulus.
The formula is exact, but a couple of practical points are worth keeping in mind.
Elastic region and consistent units
Young's modulus only applies within the elastic region, where stress and strain stay proportional (Hooke's law) and the material springs back to its original shape. Past the elastic limit the material deforms permanently and a single modulus no longer describes it. Keep your units consistent — newtons, square metres, and metres — or the pascals will be wrong: convert millimetres to metres by dividing by 1000 before you enter a length.