Hooke's Law Calculator
Calculate restoring force, force magnitude and elastic energy from spring constant and displacement.
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Relate spring displacement to restoring force and energy
Enter a positive spring constant and signed displacement from equilibrium. The calculator applies Hooke's law to show restoring force with direction, its magnitude and the elastic potential energy stored in the ideal spring. The negative force sign makes the return toward equilibrium explicit, while the energy output remains nonnegative because it depends on displacement squared.
Stay inside the spring's linear working region
Real springs follow the simple proportional rule only over a limited range. Preload, coil binding, hysteresis, temperature and permanent deformation can change the measured relationship. Use a tested stiffness and displacement convention for design work, and do not treat this educational result as a load rating or proof that a spring remains safe.
Frequently asked questions
Why is restoring force negative?
The sign indicates that the ideal spring force points opposite the signed displacement.
Can displacement be negative?
Yes. Its sign selects the side of equilibrium, while stored energy remains nonnegative.
Does Hooke's law apply to every extension?
No. It applies only within the spring's approximately linear elastic range.