Hooke's Law Calculator
Calculate the force a spring exerts, the energy it stores and how far a hanging mass stretches it, from the spring constant.
How hard a spring pushes back, and the energy it stores.
How the hooke's law calculator works
Within its elastic limit a spring pushes back in proportion to how far it is stretched or compressed: F = kx, where k is the spring constant in newtons per meter. The energy stored is the area under that line, ½kx². Hang a mass on it and it settles where kx equals the weight, x = mg ÷ k.
Stiffer springs have larger k. Car suspension springs run around 20–60 kN/m; a ballpoint-pen spring a few hundred N/m.
Formula: F = k x · E = ½ k x²
Worked examples
| Inputs | Spring force | Note |
|---|---|---|
| 200 N/m stretched 0.1 m | 20 N | 20 N, 1 J stored |
| 200 N/m stretched 0.2 m | 40 N | double the stretch, four times the energy |
| 30 kN/m car spring compressed 0.05 m | 1,500 N | 1.5 kN |
FAQFrequently asked questions
What is the spring constant?
The force needed per meter of stretch, in N/m. It depends on the wire, coil diameter and number of turns; stiffer springs have larger k.
When does Hooke's law stop working?
Past the elastic limit, where the spring deforms permanently. Up to that point force and extension are proportional.
How do I find k experimentally?
Hang known masses and measure the extension; k is the slope of force against extension, mg ÷ x.
Why is the energy ½kx² and not kx²?
Because the force grows from zero to kx as you stretch it, so the average force is ½kx and the work is that times x.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.