Hooke's Law Spring Force Calculator
Calculate the restoring force of a spring using Hooke's law F = kx. Enter the spring constant in N/m and the displacement from equilibrium in metres. Results in newtons. Used in physics, engineering, and vibration analysis.
How to use this tool
- Enter spring constant (k) and displacement (x) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your spring force and the full breakdown beneath it.
Formula
F = k * x
How it works
Hooke's law states that the restoring force F of an ideal spring equals the spring constant k multiplied by the displacement x from its natural length. A negative sign indicates the force opposes displacement.
Worked examples
Compressed spring
Extended spring
Common mistakes to avoid
- Using displacement in centimetres instead of metres — if x is entered in cm, the spring constant k must also be in N/cm to be consistent; mixing N/m with cm gives a force 100 times too small.
- Applying Hooke's law beyond the elastic limit — the formula F = kx is only valid while the spring deforms elastically; past the yield point, the relationship becomes nonlinear.
- Ignoring the sign convention — Hooke's law gives a restoring force (F = -kx in vector form), meaning the force opposes the displacement direction.
Key terms
Frequently asked questions
- What is the spring constant k and how is it determined?
- k (in N/m) describes the stiffness of a spring. A higher k means a stiffer spring requiring more force for the same displacement. It is found experimentally by plotting force vs. displacement and finding the slope, or from the manufacturer's specification.
- Does Hooke's law apply only to springs?
- No. Hooke's law applies to any elastic material within its elastic limit — rubber bands, metal beams in bending, tendons, and atomic bonds all follow it approximately in their linear range.
- What happens when a spring is compressed vs. stretched?
- The formula F = kx works for both. By convention, positive x is extension and negative x is compression. The restoring force always acts opposite to x: it pulls back when stretched and pushes back when compressed.