Hooke's Law Calculator
Enter force, area and specimen length to get stress, strain and elongation — or add a measured elongation to compute the material's actual modulus.
Last updated: 2026-09-28
How the calculation works
- Stress divides force by area; strain is the relative elongation.
- With a known modulus (steel 200 GPa default), the tool predicts elongation from load.
- With a measured elongation entered, it inverts the relation to compute the actual E — a tensile-test check.
Formula
σ = F / A ε = ΔL / L E = σ / ε
| Symbol | Meaning | Unit |
|---|---|---|
σ | Normal stress | MPa |
ε | Strain | — |
E | Young's modulus | GPa |
Worked example
Interpreting the result
Hooke's law is the elastic contract: stress and strain stay proportional until yield, then the relation breaks permanently. Steel's stiffness is essentially fixed — alloying changes strength dramatically but stiffness barely at all (all steels ≈ 200 GPa). That surprises people: a stronger steel does not bend less under the same load, it only survives more load. The elastic range is why springs work, and exceeding it is why bent parts stay bent.
Assumptions
- Linear-elastic behavior below yield; uniform uniaxial loading.
- Nominal (engineering) stress — necking beyond yield changes the real area.
Limitations
- No Poisson lateral contraction, no buckling for long slender members in compression.
- Temperature, strain rate and cyclic loading shift the modulus and limits.
Frequently asked questions
What is Hooke's law?
Stress is proportional to strain below yield: σ = E·ε. Double the load, double the stretch — until the elastic limit, where the proportionality ends permanently.
How do I find Young's modulus from a tensile test?
E = stress ÷ strain in the elastic region: (F/A) ÷ (ΔL/L). Enter the measured elongation here and the calculator returns E directly.