This Hooke’s law calculator solves F = k × x for springs: find the restoring force, the spring constant, or the extension/compression — plus the elastic potential energy stored, ½kx².
What Is Hooke’s Law?
Hooke’s law states that a spring’s restoring force is proportional to how far it is stretched or compressed: F = k × x, where k is the spring constant — the spring’s stiffness fingerprint. Double the stretch, double the force. Robert Hooke published it in 1676 (as an anagram, “ceiiinosssttuv”, revealed later as ut tensio, sic vis — “as the extension, so the force”) and it remains the first model of every elastic system. The force quantities plug straight into our Force Calculator; this tool is part of our Physics Calculators collection.
Worked Example (Verified)
A spring with k = 200 N/m stretched 0.1 m (10 cm):
- Restoring force: F = 200 × 0.1 = 20 N (about the weight of a 2 kg mass)
- Energy stored: ½ × 200 × 0.1² = 1 J — released if you let go, via the Work Calculator‘s energy bookkeeping
- Stretch it twice as far (0.2 m): force doubles to 40 N, but energy quadruples to 4 J — energy goes with x², a fact that matters for bow limbs, bungee cords and car suspensions.
Reading Spring Constants
| System | Typical k |
|---|---|
| Slinky | ≈1 N/m |
| Pen spring | ≈10–50 N/m |
| Screen-door spring | ≈100–300 N/m |
| Car suspension (per wheel) | ≈20,000–40,000 N/m |
Measure an unknown spring’s k by hanging a known weight and measuring the stretch: k = F ÷ x — the “Spring constant” solve mode above does it directly.
The Elastic Limit — Where Hooke’s Law Ends
The proportionality holds only within the elastic limit. Stretch beyond it and the spring deforms permanently (or snaps): k stops being constant, and the spring never returns to its original length. Materials scientists map this boundary on stress–strain curves, where Hooke’s law is the straight initial segment; the slope there, Young’s modulus, is the material-level version of k.
Related Tools
- Force Calculator — F = ma and weights
- Work Calculator — energy transfers
- Physics Calculators — the full collection
Frequently Asked Questions
What is the formula for Hooke’s law?
F = kx — force equals spring constant times displacement from equilibrium. Strictly, the spring’s force is −kx (opposite the stretch); magnitudes are what most problems need.
What is the spring constant?
k, in newtons per meter: the force needed to stretch the spring by one meter. Bigger k, stiffer spring.
How do I find the spring constant experimentally?
Hang a known force (a weight: mass × 9.81) and measure the extension; k = F ÷ x. Use the calculator’s “Spring constant” mode.
How much energy is stored in a stretched spring?
PE = ½kx². It grows with the square of the stretch — doubling extension quadruples stored energy.
Does Hooke’s law apply to rubber bands?
Only approximately and only for small stretches. Rubber is famously non-linear — its force curve bends — so Hooke’s law is a first approximation there, unlike for metal coil springs where it is excellent.
Is this Hooke’s law calculator free?
Yes — free, instant, no sign-up.