Calculate the elastic potential energy stored in a spring from the spring constant and stretch, or the spring constant or stretch from the energy.
Last updated: November 8, 2026
E = ½ × k × x² and Hooke's law
A stretched or compressed spring stores energy. By Hooke's law, the spring force is proportional to the stretch: • F = k × x • E = ½ × k × x² • k = 2E ÷ x², x = √(2E ÷ k) Example: a spring with k = 200 N/m stretched 10 cm (0.1 m) stores ½ × 200 × 0.1² = 1 J and pulls back with 200 × 0.1 = 20 N. The formula holds as long as the spring stays within its elastic limit. Overstretched, it deforms permanently.
Common questions about elastic potential energy
E = ½ × k × x², with k the spring constant (N/m) and x the stretch or compression (m).
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In newtons per metre.
In metres, 10 cm = 0.1 m.