Hooke's Law Calculator
Spring force, constant, energy, period and springs combined.
About this tool
Choose whether to find the force, extension or spring constant and enter the other two. Add a mass to see how fast it would bounce on the spring, and list several spring constants to combine them in series and in parallel.
Springs and Hooke's law
Within its elastic limit, a spring's restoring force is proportional to its extension or compression: F = k × x, where k is the spring constant in N/m. A 200 N/m spring stretched 5 cm pulls back with 10 N. The energy stored is E = ½ k x², 0.25 J in that case. A mass on the spring oscillates with period T = 2π√(m ÷ k), independent of how far you pull it: 0.5 kg on a 200 N/m spring completes a cycle every 0.314 s. Springs side by side (in parallel) share the load and add stiffness, k = k₁ + k₂; springs end to end (in series) stretch more, 1/k = 1/k₁ + 1/k₂. So 200 and 300 N/m springs give 500 N/m in parallel and 120 N/m in series. The same law describes rubber bands, bending beams and even chemical bonds for small deformations. Honest limits: beyond the elastic limit springs deform permanently; real springs have mass, damping and preload, and many compression springs have a slightly non-linear rate. The pendulum calculator and the energy calculator are related.
Frequently asked questions
What is Hooke's law?
The force needed to stretch or compress a spring is proportional to the distance: F = kx.
How do I find the spring constant?
Divide the force by the extension: k = F ÷ x, in newtons per metre.
How much energy does a spring store?
E = ½kx². A 200 N/m spring stretched 5 cm stores 0.25 J.
How do springs combine in series and parallel?
Parallel: add the constants. Series: add the reciprocals, then take the reciprocal.
Is my data sent anywhere?
No. Everything is calculated in your browser, and nothing is stored or sent.