Hooke's law says a spring's extension is proportional to the force stretching it: F = k·x. Drag the sliders below to change the applied force and the spring constant, and watch the extension, force, stored energy and the force-vs-extension graph respond in real time.
A car's suspension coil can carry well over a tonne, yet the same spring barely resists your fingers over the first centimetre — because a spring's push is not fixed, it builds. Drag the Applied force, F slider and watch the extension grow with it: the readout for Extension x tracks x = F/k, so doubling the force doubles the stretch. The restoring force starts at zero at the natural length and climbs in step with the pull, which is exactly what F = k·x encodes on the Force-vs-extension graph — a straight line rising from the origin. The stored elastic potential energy follows E = 1/2·k·x², so its readout climbs even faster than the force, growing with the extension squared.
Now hold the force steady and raise the Spring constant, k. Here is where intuition trips: a stiffer spring does not stretch more, it stretches less. Because x = F/k, a bigger k shrinks the Extension x for the same load, and the Force-vs-extension graph tilts steeper — its slope simply is k. Halve a spring's stiffness and the same pull stretches it twice as far.
Push F far enough and the elastic-limit indicator trips. Up to the limit of proportionality the graph stays a straight line and F = k·x holds; push a spring past its elastic limit, though, and it no longer springs back — it stays permanently stretched once the load comes off. Put numbers to your own coil with the Hooke's law calculator, or take the controls for a spin across our collection of hands-on physics simulations.
Hooke's law states that the extension of a spring is proportional to the force stretching it: F = k·x, where k is the spring constant. It holds up to the limit of proportionality; the stored elastic energy is E = ½·k·x².
Less. Since x = F/k, a larger spring constant k means a smaller extension for the same force. A stiffer spring resists more, so it stretches less — halve the stiffness and the same pull stretches it twice as far.
The elastic limit is the point beyond which a spring no longer returns to its natural length — stretch it past that and it stays permanently deformed. It sits at or just beyond the limit of proportionality, the point where the force-extension line stops being straight and F = k·x no longer holds. Between the two the spring is non-linear but still springs back.
For a graph of force (vertical) against extension (horizontal), the straight-line slope is the spring constant k. A steeper line means a stiffer spring. The area under the line equals the elastic potential energy stored.