Spring Potential Energy Calculator

A compressed or stretched spring stores elastic potential energy. Release it and that energy converts to kinetic energy, launching whatever the spring pushes against.

The stored energy follows Hooke’s Law:

PE = (1/2) x k x x²

Where k is the spring constant (stiffness, in N/m) and x is the displacement from the spring’s natural length (in meters). The energy scales with the square of displacement — double the compression, quadruple the energy stored.

Hooke’s Law also gives the restoring force:

F = k x x

A spring with k = 1000 N/m compressed 0.05 m stores 1.25 J of energy and exerts a force of 50 N. That stored energy can launch a 0.1 kg ball to a speed of v = sqrt(2 × 1.25 / 0.1) = 5 m/s, ignoring friction.

Spring constants in practice:

• Soft springs (mattresses, door closers): 1–100 N/m
• Stiff mechanical springs (automotive valve springs): 10,000–100,000 N/m
• Very stiff materials (steel beam modeled as a spring): millions of N/m
• A human Achilles tendon during running: approximately 4,000 N/m

The law breaks down at large deformations — when the spring is stretched or compressed beyond its elastic limit. Past that point, the spring yields permanently and does not return to its original length. Hooke’s Law only applies within the elastic region.

Simple harmonic motion period for a mass-spring system: T = 2π × sqrt(m/k). A heavier mass and a softer spring both slow the oscillation.