Calculates the restoring force an ideal spring exerts when stretched or compressed from its rest position.
How it works
The spring constant is multiplied by the displacement from rest to give the restoring force.
What this does not include
This only applies within a spring’s elastic limit — stretch or compress a spring too far and it permanently deforms, at which point this formula no longer holds.
How to use this calculator
- Enter the spring constant and the displacement from the spring’s rest position.
A worked example
A spring with constant 200 N/m stretched 0.05 m: force = k × x = 200 × 0.05 = 10 N.
A stiffer spring, constant 500 N/m, stretched only 0.02 m: force is also 10 N — a stiffer spring needs less displacement to produce the same force.
What the variables mean
| Variable | Meaning |
|---|---|
| Spring constant (k) | Stiffness of the spring, in newtons per meter |
| Displacement (x) | Distance the spring is stretched or compressed from its rest length |
Edge cases worth knowing
The same force can come from very different spring/displacement combinations — the two examples above both produce 10 N, showing force depends on the product, not either value alone.
Hooke’s law only holds within a spring’s elastic limit. Stretch a spring too far and it permanently deforms, and the force no longer scales linearly with displacement — a limit this simple formula doesn’t capture.
Frequently asked questions
What does a higher spring constant mean?
A stiffer spring — it takes more force to stretch or compress it the same distance compared to a spring with a lower constant.
Why is it called a “restoring” force?
Because the spring always pushes or pulls back toward its rest position, opposing whatever displaced it — that’s what makes springs useful for oscillation and shock absorption.
What’s the elastic limit?
The point beyond which a spring stops returning to its original shape — stretch it past this limit and it permanently deforms, and Hooke’s law no longer predicts its behavior accurately.
