Hooke's Law Calculator

Hooke's law states that the restoring force of a spring is proportional to its displacement from the natural length: F = k x x, where k is the spring constant and x is the stretch or compression. The stiffer the spring, the more force a given stretch produces.

Rearrange the law to k = F / x, so divide the spring force by the displacement. A 50 N force at a 0.25 m stretch gives a spring constant of 200 N/m.

Rearrange to x = F / k, dividing the force by the spring constant. A 30 N force on a 150 N/m spring stretches it 0.2 m.

The energy stored in a stretched spring is one half times the spring constant times the displacement squared, PE = 0.5 x k x x^2, in joules. The tool reports it on every result alongside the solved quantity.

Use newtons for force, newtons per meter for the spring constant and meters for displacement. With those SI inputs the energy comes out in joules. Convert centimeters to meters before entering them.

The calculator works with magnitudes and requires positive inputs, so it treats the size of the stretch and force rather than their direction. Enter the amount of compression as a positive number if you are compressing rather than stretching.

Only within the elastic limit of the spring. Stretch it too far and it deforms permanently or breaks, and the straight-line relationship F = k x x no longer applies beyond that point.

This tool models a single spring. Springs side by side (parallel) add their constants, while springs end to end (series) combine as reciprocals, giving a softer overall stiffness. Work out the effective constant first, then enter it here.

No. The algebra runs in your browser, so the values you enter are never uploaded.