Springs follow a simple rule: F = kx. Plug in any two of force, spring constant, or displacement and we'll solve the third — handy for physics homework or a real mechanical design check.
A Hooke's Law calculator lets you instantly compute the relationship between force, spring constant, and displacement for any ideal spring, using the formula F = kx. Enter any two of the three values — spring constant, displacement, or force — and the calculator solves for the missing one, letting you analyze spring behavior for physics problems, mechanical design, or general curiosity.
Hooke's Law, formulated by English scientist Robert Hooke in 1676, is one of the foundational principles of classical mechanics and materials science. It describes how springs — and many other elastic materials — respond to applied forces: the extension or compression is directly proportional to the force applied, at least within the material's elastic limit. This simple linear relationship underlies everything from the suspension in your car to the tension in a mechanical watch spring to the springs inside a mattress.
This calculator is useful in many contexts: physics students use it to solve spring force and elastic potential energy problems, engineers use it to select springs with the correct stiffness for mechanical designs, and hobbyists use it to understand the springs in everyday devices like pens, trampolines, and suspension systems.
A spring with a spring constant of 250 N/m is compressed by 0.05 meters. Using F = kx: F = 250 × 0.05 = 12.5 N. This is the force the spring exerts as it resists compression, pushing back toward its equilibrium length.
The force value this calculator produces represents the magnitude of the spring's restoring force at a given displacement — the actual force direction always opposes the displacement, pulling or pushing the spring back toward equilibrium. When comparing your result to the reference table, remember that spring constant values span an enormous range — from soft springs in retractable pens (tens of N/m) to stiff automotive suspension springs (tens of thousands of N/m) — reflecting vastly different design purposes. If your calculated force seems unreasonably large for a given displacement, double-check that your spring constant is realistic for the type of spring you're modeling, and verify the spring is still operating within its elastic limit at that displacement.
Enter any two of spring constant, displacement, or force, and leave the third blank — the calculator solves for the missing value using F = kx.
| Spring | Spring Constant |
|---|---|
| Retractable pen click spring | 50 N/m |
| Trampoline spring | 5,000 N/m |
| Car suspension spring | 25,000 N/m |
| Garage door torsion spring | 8,000 N/m |
| Mattress coil spring | 3,000 N/m |