Hooke's Law formula
| Symbol | Quantity | SI unit | Meaning |
|---|---|---|---|
| F | Spring force | N | Force applied to (or exerted by) the spring |
| k | Spring constant | N/m | Spring constant (stiffness) |
| x | Extension / compression | m | Extension or compression from natural length |
What is Hooke's Law?
Hooke's Law: The force needed to stretch or compress a spring is proportional to the displacement from its natural length. — Robert Hooke, 1678
Hooke's law describes linear elastic behaviour. Hooke summarised it as "ut tensio, sic vis" — as the extension, so the force. The restoring force exerted by the spring is −kx, which points back toward equilibrium. The calculator works with magnitudes.
Hooke's law holds up to the elastic limit. In materials science it generalises to stress = Young's modulus × strain. It also underpins simple harmonic motion, with period T = 2π√(m/k).
How to use this calculator
- Choose the quantity you want to find in the Calculate menu. It is highlighted as the result field.
- Enter the known values. Scientific notation such as
1.6e-11is accepted. - Select a unit for each value. Units are converted to SI automatically.
- The answer updates as you type. Open Show calculation steps to see the working, or use Copy result to share a link with your inputs.
Worked example
A spring with k = 250 N/m is stretched 4 cm.
- F = 250 × 0.04 = 10 N.
- Stored energy = ½ × 250 × 0.04² = 0.2 J.
Frequently asked questions
How do springs combine?
In series, 1/k = 1/k₁ + 1/k₂ (the combination is softer). In parallel, k = k₁ + k₂ (stiffer).
What happens beyond the elastic limit?
The spring deforms permanently and no longer returns to its original length, so F = kx stops applying.