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Young's Modulus (Elastic Modulus) Calculator

Find a material's stress, strain, and Young's modulus of elasticity, E = (F × L₀) ÷ (A × ΔL), from a tension/compression test's force, cross-section, length, and extension.

Stress
100 MPa
Strain
0.05%
Young's modulus (E)
200 GPa

How it works

Young's modulus measures how stiff a material is under tension or compression, found from a simple pull test: apply a known force to a bar of known cross-section and original length, then measure how much it stretches. Stress is force per unit area, σ = F ÷ A; strain is the fractional change in length, ε = ΔL ÷ L₀; and Young's modulus is their ratio, E = σ ÷ ε = (F × L₀) ÷ (A × ΔL). This only holds within the material's linear-elastic range — the same small-deformation assumption behind Hooke's law for a spring, F = kx.

The default values (10,000 N force, 100 mm² cross-section, 2,000 mm original length, 1 mm extension) work out to a stress of 100 MPa, a strain of 0.05%, and E = 200 GPa — steel's textbook Young's modulus, used here as a built-in sanity check. Force, area, and both lengths get this page's metric/imperial toggle; all four are converted to newtons, square meters, and meters internally before the formula runs, so the reported modulus (in GPa) is identical regardless of which unit system was used to enter the test data.

FAQ

Why does the modulus come out in GPa when I entered force in newtons and area in mm²?

Young's modulus has the same units as stress (pascals, or newtons per square meter) — the strain in its denominator is a dimensionless ratio, so it doesn't introduce units of its own. Most real materials have moduli in the tens-to-hundreds-of-billions-of-pascals range, so gigapascals (GPa) is the standard way to report the result, whether the underlying test used metric or imperial units.

Does a higher Young's modulus mean a stronger material?

Not necessarily — stiffness and strength are different properties. A high modulus means the material resists stretching (deforms less for a given stress, like steel vs. rubber), but says nothing about how much stress it can survive before permanently deforming or breaking. A material can be very stiff yet brittle (glass), or comparatively soft yet tough (many polymers).

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