Hooke's law describes elastic springs and many materials under small strain.
About this calculator
Hooke's law describes elastic springs and many materials under small strain. Enter spring constant k in N/m and displacement x in metres. The calculator returns F = −kx in newtons.
Example: k = 200 N/m and x = 0.05 m (5 cm stretch) gives F = −10 N — the spring pulls back with 10 N toward equilibrium. Double the stretch doubles the force until the spring yields.
Spring force is one type of applied force. Use the [[work]] calculator if you need energy to compress or stretch (often W = ½kx² in textbooks). The [[force]] calculator covers F = ma for attached masses in SHM setups. The [[kinetic-energy]] calculator helps when a mass on a spring oscillates. For pressure in fluids, switch to the [[pressure]] calculator.
Common uses
- Mass–spring simple harmonic motion problems
- Finding spring constant from force and extension in labs
- Engineering estimates for suspension and shock absorbers
- Class 11 oscillations chapter homework
- Checking whether a spring stays within its elastic limit
Frequently asked questions
What force does a 200 N/m spring exert at 5 cm stretch?
x = 0.05 m. F = −200 × 0.05 = −10 N. The negative sign means the force pulls toward equilibrium. Magnitude is 10 N.
What is the spring constant if 15 N stretches a spring 0.03 m?
k = |F|/|x| = 15 / 0.03 = 500 N/m. This calculator solves for F given k and x; rearrange for k in your notebook.
Does Hooke's law work for compression?
Yes, within the elastic limit. Compression uses negative x or positive x depending on your sign convention; force always opposes displacement.
How is spring potential energy related to Hooke's law?
Elastic PE stored is ½kx². Force is the derivative of that energy with respect to x. Use this calculator for force at a given stretch.