Hooke's Law Calculator
Calculate the restoring force and stored energy of a spring from its stiffness and displacement.
How it works
F = k · x and PE = ½ · k · x²
Hooke's law says the force a spring exerts is proportional to how far it is stretched or compressed, with the spring constant k as the stiffness. The force acts to restore the spring to its natural length. The work done stretching it is stored as elastic potential energy, ½·k·x².
Worked example
A spring with k = 200 N/m stretched 0.1 m pulls back with F = 200 × 0.1 = 20 N and stores PE = ½ × 200 × 0.1² = 1 J.
Frequently asked questions
What is the spring constant?
The spring constant k measures stiffness in newtons per metre — how much force is needed to stretch the spring one metre. A larger k means a stiffer spring.
Does Hooke's law always apply?
Only within the elastic limit. Stretch a spring too far and it deforms permanently or breaks, and the linear F = k·x relationship no longer holds.
Why is stored energy ½·k·x²?
The force grows 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.
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Educational estimate. Check the formula and units for your exact case.