Spring Potential Energy Calculator
Find the elastic energy stored in a spring from its stiffness and stretch, plus the spring force and the launch speed it can give a mass.
How it works
PE = ½ · k · x² · Spring force F = k·x · Launch speed v = √(2·PE ÷ m)
A spring obeying Hooke’s law stores energy equal to ½kx², the area under its linear force-versus-stretch line. Because the displacement is squared, stretching a spring twice as far stores four times the energy — while the force it pushes back with only doubles. If that energy is released into a mass, energy conservation (½kx² = ½mv²) sets the launch speed, which is how spring guns, trampolines and catapults work.
Worked example
A spring with k = 200 N/m compressed by x = 0.10 m stores PE = ½ × 200 × 0.10² = ½ × 200 × 0.01 = 1 J and pushes back with F = 200 × 0.10 = 20 N. Released into a 0.5 kg mass, that 1 J becomes kinetic energy: v = √(2 × 1 / 0.5) = √4 = 2 m/s.
Sources: Elastic energy — Wikipedia
Frequently asked questions
How is this different from the elastic potential energy calculator?
It uses the same ½kx² law but focuses on a spring: it also reports the restoring force k·x and, if you enter a mass, the launch speed the stored energy would give it via energy conservation.
Does it matter whether the spring is stretched or compressed?
No. The energy depends on x², so a stretch and a compression of the same size store the same energy. This calculator uses the magnitude of the displacement.
What if the spring is stretched past its elastic limit?
Then Hooke’s law no longer holds and ½kx² overestimates the stored energy. The formula is valid only in the linear elastic region where force is proportional to stretch.
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This calculator is for educational purposes. Double-check important results before acting on them.