Hooke's Law Calculator

Find the restoring force and stored energy of a stretched spring.

Inputs

N/m
m
Formulas
F = k·x
E = ½·k·x²

Results

Restoring force N
Elastic PE J

Hooke's law

Hooke's law states that the force needed to stretch or compress a spring is proportional to the extension: F = kx. The spring constant k measures stiffness; a larger k means a stiffer spring that resists deformation more strongly. The spring pushes or pulls back with an equal and opposite restoring force.

F = k·x

Elastic potential energy

Stretching a spring stores energy in it, equal to E = ½kx². This elastic potential energy is released when the spring returns to its natural length. This calculator returns both the restoring force and the stored energy. Hooke's law only holds up to the elastic limit, beyond which the spring deforms permanently.

Frequently asked questions

What is the spring constant?

It is the stiffness of a spring, measured in newtons per metre. It tells you how much force is needed to stretch the spring by one metre.

When does Hooke's law stop working?

Beyond the elastic limit. If a spring is stretched too far it deforms permanently and no longer obeys the linear F = kx relationship.

Read the full guide