How it works
Hooke's law is the simplest rule in elasticity: the force a spring pushes back with is proportional to how far you stretch or squash it. Double the stretch and you double the force. The constant of proportionality, k, is the spring's stiffness — a stiff spring has a large k, a floppy one a small k.
The same stretch also stores energy. Because force builds up linearly, the elastic potential energy is one-half k times the extension squared — energy that snaps back the instant you let go. That stored-and-released energy is what powers a bow, a trampoline, a wind-up toy and a car's suspension over every bump.
The law holds only up to the elastic limit. Stretch a spring or wire too far and it deforms permanently or breaks — beyond that point the neat straight-line relationship fails. Within the limit, though, Hooke's law is astonishingly accurate and underlies almost every force sensor ever built.
Use it in real life
Weighing scales: a spring (or a strain gauge) stretches in proportion to the weight, so the displacement reads off directly as force or mass — Hooke's law turned into a dial.
Vehicle suspension: springs with a chosen k soak up bumps by trading road force for stored energy, then release it in a controlled way through the dampers.
Trampolines and bows: stretch stores elastic potential energy (½kx²) that launches the jumper or arrow when released — the more you draw, the more energy you bank.
Frequently asked questions
What is the spring constant k?
It is the stiffness of the spring — the force needed per metre of stretch, in newtons per metre. A car suspension spring might be tens of thousands of N/m; a soft pen spring only a few.
How much energy does a stretched spring store?
The elastic potential energy is ½kx², which this calculator returns alongside the force. Because of the square, stretching twice as far stores four times the energy.
When does Hooke's law break down?
Beyond the elastic limit. Stretch a spring or material too far and it yields — deforming permanently or snapping — and force no longer rises in proportion to extension.