Hooke's Law (Spring Force) Calculator

F = −k × x. Spring force is proportional to displacement from equilibrium.

Inputs

Result

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How to use this calculator

  • Enter spring constant k and displacement x.
  • Read force and stored PE.

About this calculator

Hooke's Law: spring force is proportional to displacement from equilibrium, in the opposite direction. Valid only within elastic region — past yield point, spring deforms permanently. Energy stored = ½ k x² (parabolic in x). Used in springs (door closers, mattresses, vehicle suspensions), atomic bonds at small displacements (molecular vibrations), and any restoring system (pendulums approximate Hooke at small angles).

Frequently asked

Why negative?+
Force opposes displacement. Push spring right (positive x), force pushes back left (negative). Sign convention.
How is k determined?+
Apply known force, measure displacement: k = F/x. Or for a coil spring, designed via wire diameter, coil count, mean diameter.
When does Hooke fail?+
Beyond elastic limit (yield point). Spring deforms permanently. Real materials follow Hooke until then, then plastic deformation.
Series vs. parallel springs?+
Parallel: k_total = k₁ + k₂ (stiffer). Series: 1/k_total = 1/k₁ + 1/k₂ (softer).
Energy in spring?+
½kx² — quadratic in displacement. Doubling stretch quadruples stored energy.

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