Elastic Potential Energy Calculator
Calculate the energy stored in a stretched or compressed spring, plus the spring force, from its stiffness and displacement.
How it works
PE = ½·k·x² · spring force F = k·x
Stretching or compressing a spring stores energy as elastic potential energy. Because the force builds up linearly with displacement (Hooke’s law), the stored energy grows with the square of the displacement — stretch it twice as far and it holds four times the energy. That energy is released as the spring snaps back toward its natural length.
Worked example
A spring with k = 200 N/m displaced 0.1 m stores PE = ½ × 200 × 0.1² = 1 J and exerts a restoring force of 200 × 0.1 = 20 N.
Sources: Elastic energy — Wikipedia
Frequently asked questions
Why does energy depend on displacement squared?
The restoring force rises from zero to k·x as you stretch the spring, so the average force is half the maximum. Work equals average force times distance, giving ½·k·x².
Does compression store energy too?
Yes. Because x is squared, a compression stores the same energy as an equal stretch. The energy is always positive regardless of the direction of displacement.
Where is this energy used?
Everywhere springs do work: trampolines, car suspensions, clock mechanisms, bows and pogo sticks all store elastic potential energy and release it to create motion.
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Educational estimate. Check the formula and units for your exact case.