Hooke's Law Calculator
From the spring constant and the displacement, get the restoring force the spring pushes back with and the elastic energy stored in it — the two numbers behind every spring.
Two inputs, two answers
Enter the spring constant and the displacement and the calculator returns the force (k × x) and the stored energy (½ × k × x²) at once.
Use SI units
Stiffness in newtons per metre (N/m), displacement in metres (m) — then the force comes back in newtons (N) and the energy in joules (J).
What is Hooke's law?
Stiffness and stretch in, force and energy out
Hooke's law is the relationship that ties together how stiff a spring is, how far it is moved, and how hard it pushes back. It says the restoring force a spring exerts equals its spring constant multiplied by its displacement from rest, written F = k × x. Once you know the spring constant and the displacement, the force is fixed — and so is the elastic potential energy stored in the spring, PE = ½ × k × x². That makes stiffness and displacement the two inputs you need for sizing suspension springs, calibrating force gauges, modelling trampolines, and almost any hands-on mechanics task.
Enter the spring constant in N/m and the displacement in metres to get the force and stored energy instantly.
Two short formulas, both built from the spring constant (k) and the displacement (x).
force = k × xThe force is simply the spring constant times the displacement (k × x). The elastic potential energy — the energy stored in the stretched or compressed spring — is half the spring constant times the displacement squared (½ × k × x²). Because the displacement is squared in the energy formula, the stored energy grows much faster than the force as the spring is moved further from rest.
Suppose a spring with a constant of 200 N/m is stretched 0.1 m.
Force
200 × 0.1 = 20 N — the restoring force the spring pushes back with.
Energy (squared displacement)
½ × 200 × 0.1² = ½ × 200 × 0.01 = 1 J — the elastic energy stored in it.
Cross-check
The energy also equals ½ × F × x = ½ × 20 × 0.1 = 1 J — the same answer two ways.
The two outputs answer two different practical questions. The force (20 N for a 200 N/m spring stretched 0.1 m) is how hard the spring pushes back toward its rest position — it tells you the load the spring will support or the pull you must apply to hold it there. The energy (1 J) is how much work is stored in the spring and how much it can release when let go — it matters for catapults, trampolines, and any mechanism that uses a spring to do work. The key insight is that force grows in step with displacement, but energy grows with the square of it: a stiffer spring (higher k) needs more force for every metre of stretch, and pulling any spring twice as far doubles the force but quadruples the stored energy. This linear behaviour holds only within the elastic limit — stretch a spring beyond it and the law breaks down, the spring deforms permanently, and it no longer returns to its original shape.
The formulas are exact within a spring's elastic range, but a couple of practical points are worth keeping in mind.
Stay within the elastic limit and use SI units
Hooke's law holds only while a spring behaves elastically — below its elastic limit, where it springs back to its original length. Stretch it too far and it yields, deforms permanently, and the linear F = k × x relationship no longer applies. This tool also solves only the force and energy from the stiffness and displacement; to find the spring constant or displacement instead, rearrange the formula (k = F ÷ x, x = F ÷ k). Keep the inputs in newtons per metre and metres so the answers come back in newtons and joules.