# Hooke’s Law Calculator

> Find a spring’s constant from a load and its stretch, or the force or extension from the other two, with the elastic energy stored in the spring.

Category: Science & engineering · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/hookes-law-calculator

Within its elastic range a spring stretches in proportion to the force on it: F = k x. Any two of force, spring constant and extension give the third.

Also called: Spring constant calculator, Spring rate calculator, F = kx calculator.

## Inputs
- Solve for (options: Spring constant, Force, Extension; default stiffness)
- Force on the spring (default 50)
- Force unit (options: newtons (N), kilonewtons (kN), pounds-force (lbf), kilograms-force (kgf); default n)
- Extension or compression (default 25)
- Extension unit (options: metres (m), centimetres (cm), millimetres (mm), kilometres (km), feet (ft), inches (in), miles (mi); default mm)
- Spring constant (k) (default 2000)
- Spring constant unit (options: N/m, N/mm, lbf/in; default nm)

## Results
- Result
- Spring constant
- Spring rate
- Force
- Extension
- Elastic energy stored (½ k x²)

## Formula

```
F = k x;  k = F ÷ x;  x = F ÷ k;  E = ½ k x²
```

Where:
- F: force in N
- k: spring constant in N/m (1 lbf/in = 175.127 N/m)
- x: extension or compression from the free length in m
- E: elastic potential energy in J

## Worked example
1. x = 25 mm = 0.025 m.
2. k = 50 ÷ 0.025 = 2,000 N/m.
3. E = ½ × 2,000 × 0.025² = 0.625 J.

**Result:** A spring that stretches 25 mm under 50 N has a constant of 2,000 N/m (about 11.4 lbf/in) and stores 0.625 J.

## What the result means

Measure k by hanging known weights and recording the stretch; the slope of force against extension is k. If the points stop lying on a straight line, the spring has passed its elastic limit.

## Assumptions and limits
- Linear elastic behaviour, measured from the spring’s free (unloaded) length.
- Not valid beyond the elastic limit, for progressive-rate springs or for coils that touch (coil bind).

## Questions

### What happens to k for springs in series or parallel?

In parallel the constants add (k = k₁ + k₂). In series the reciprocals add (1/k = 1/k₁ + 1/k₂), so the combination is softer.

### Why is the stored energy ½ k x² and not k x²?

The force rises from zero to k x as the spring stretches, so the average force is half the final force.

## Sources
- [BIPM: The International System of Units (SI)](https://www.bipm.org/)

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- [Potential Energy Calculator](https://calculators.geekmidst.com/calculators/potential-energy-calculator)
- [Force Calculator (F = ma)](https://calculators.geekmidst.com/calculators/force-mass-acceleration-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/hookes-law-calculator