Hooke’s Law Calculator: Force, Spring Constant & Extension
Solve F = kx in any direction. Pick what you want to find, enter the other two values in the units you have, and see the answer, the working and the energy stored in the spring.
Enter the spring constant and the extension.
Try a worked example
Illustration is not to scale — the spring stretches more as extension grows.
Step-by-step working
- Enter the two known values to see the working.
What is Hooke’s law?
Hooke’s law says that the force needed to stretch or compress a spring is directly proportional to how far the spring is stretched or compressed from its natural length, as long as the spring has not passed its elastic limit. Double the extension and you need double the force.
The spring constant k measures stiffness. A car suspension spring has a very large k; the spring inside a ball-point pen has a small one. Rearranging gives the two other forms this calculator uses:
x = F ÷ k
Why you will see F = −kx in textbooks
Many textbooks write F = −kx. That minus sign describes the restoring force the spring pulls back with: it always points opposite to the displacement. The force you apply has the same size but the opposite direction, so this calculator uses the magnitude form F = kx. If you enter a negative extension, the spring is treated as compressed.
Elastic potential energy stored in a spring
Stretching a spring does work, and that work is stored as elastic potential energy:
Because x is squared, stretching a spring twice as far stores four times the energy. The calculator shows U for every set of values you enter.
Units used in this calculator
| Quantity | SI unit | Also supported |
|---|---|---|
| Force (F) | newton (N) | kN, mN, kgf, lbf |
| Spring constant (k) | N/m | N/cm, N/mm, kN/m, lbf/in |
| Extension (x) | metre (m) | cm, mm, in, ft |
The calculator converts everything to SI first, does the sum, then converts the answer back to the unit you picked. Need other conversions? Try the unit converter, pressure converter or energy converter.
Worked examples
1. Find the force
A spring with k = 200 N/m is stretched by 5 cm. What force is needed?
Convert: x = 5 cm = 0.05 m. Then F = kx = 200 × 0.05 = 10 N. Energy stored: ½ × 200 × 0.05² = 0.25 J.
2. Find the spring constant
A force of 12 N stretches a spring by 3 cm. What is k?
x = 3 cm = 0.03 m, so k = F ÷ x = 12 ÷ 0.03 = 400 N/m.
3. Find the extension
A 25 N force acts on a spring with k = 500 N/m. How far does it stretch?
x = F ÷ k = 25 ÷ 500 = 0.05 m = 5 cm. Energy stored: ½ × 25 × 0.05 = 0.625 J.
Springs in series and parallel
If you have more than one spring, find the combined spring constant first, then use it in the calculator above.
Series: 1/k = 1/k₁ + 1/k₂ Springs side by side share the load and are stiffer; springs end to end are softer.
Where Hooke’s law stops working
Hooke’s law only holds within the elastic limit. Past that point the spring is permanently deformed and the force–extension graph is no longer a straight line. In a force–extension graph, the straight part through the origin has a gradient equal to k. Use the calculator for values inside that straight region.
Common mistakes to avoid
Mixing units. Using x in centimetres with k in N/m gives an answer 100 times too large. Pick the right unit from the drop-down and let the calculator convert.
Using total length instead of extension. x is the change from the natural length, not the length of the stretched spring.
Hooke’s law questions, answered
Hooke’s law states that the force needed to stretch or compress a spring is directly proportional to the extension, as long as the spring stays within its elastic limit. It is written F = kx, where k is the spring constant.
F = kx, where F is the force in newtons, k is the spring constant in newtons per metre and x is the extension or compression in metres. Rearranged, k = F / x and x = F / k.
The SI unit is newton per metre (N/m). A stiffer spring has a larger k. N/cm, N/mm and lbf/in are also common.
F = −kx describes the restoring force the spring exerts, which points opposite to the displacement. This calculator finds the magnitude of the force you apply, F = kx.
It is the largest extension for which the spring still returns to its original length once the force is removed. Beyond it the spring deforms permanently and Hooke’s law no longer applies.
Plot force on the y-axis against extension on the x-axis. In the elastic region the graph is a straight line through the origin, and its gradient is the spring constant k.
The elastic potential energy is U = ½kx², which equals ½Fx. The calculator shows it in joules for every calculation.
In parallel the spring constants add: k = k₁ + k₂. In series the reciprocals add: 1/k = 1/k₁ + 1/k₂, so the pair is softer than either spring alone.
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