By Zencalcy Editorial TeamLast reviewed About us
A stretched or compressed spring stores energy in its deformation. Because the force grows as the spring is deformed, the energy is the average force times the extension, which works out to ½kx². Doubling the extension quadruples the stored energy.
Energy stored in a stretched or compressed spring.
E = ½ k x²
E is elastic potential energy in joules, k is the spring constant in N/m and x is the extension or compression in metres. The relation assumes the spring stays within its elastic limit.
| Symbol | Meaning |
|---|---|
| E | Elastic potential energy, in joules. |
| k | Spring constant, in newtons per metre. |
| x | Extension or compression from natural length, in metres. |
E = 0.5 × 200 × 0.1² = 1 J. Compressing the same spring 20 cm stores 4 J, four times as much, because the force needed also doubles.
Continue with the Kinetic Energy Calculator, Mechanical Energy Calculator, or the Potential Energy Calculator — or browse more work, energy and power tools and all physics calculators.
The force rises linearly from zero to kx as the spring deforms. The average force is ½kx, so the work done is ½kx times x, or ½kx².
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Content updated: September 2026