Hooke's Law Calculator
Fill in any two of spring force, spring constant, and displacement, and it works out the third.
Fill in any two of restoring force, spring constant, and displacement — leave the third blank — and the calculator solves it from F = k·x. The result is the magnitude of the spring force; the real force points back toward the resting position.
Force
20N
Spring constant
200N/m
Displacement
0.1m
How it works
Hooke's law says the force a spring pushes back with is proportional to how far you've stretched or squeezed it: F = k·x. The spring constant k measures stiffness — a stiff car suspension might be thousands of newtons per meter, while a soft pen spring is only a few. Pull a 200 N/m spring 0.1 m and it resists with 20 N.
Because the relationship is a simple product, it rearranges three ways. Divide force by displacement to find the stiffness, or divide force by the spring constant to find how far it moved. Leave one box blank and the calculator picks the right form automatically.
The result here is the magnitude of the force. The actual spring force is a restoring force — it always points back toward the resting position, opposing whatever you did to it. And the law only holds up to the spring's elastic limit; stretch it too far and it deforms permanently, at which point the neat proportional relationship breaks down.
Frequently asked questions
What does the spring constant tell me?
It's the stiffness of the spring — how much force it takes to stretch it by one unit of length. A high k means a stiff spring that resists strongly; a low k means a soft, easily stretched one. Units are newtons per meter.
Why is there sometimes a minus sign in Hooke's law?
Physics textbooks often write F = −kx to show the force opposes the displacement — it's a restoring force pointing back toward rest. This calculator reports the magnitude, so it drops the sign and just gives you the size of the force.
Does Hooke's law always work?
Only within the elastic limit. As long as the spring springs back to its original shape, force stays proportional to stretch. Push past that limit and the material deforms permanently, so the linear F = k·x relationship no longer applies.