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Hooke's law says the force needed to stretch or compress a spring is proportional to the extension: F = kx. The constant k, the spring constant, measures how stiff the spring is.
Use this calculator to find the force, the spring constant or the extension. It also gives the elastic potential energy stored in the spring, ½kx².
| Find | Force (F) |
| Spring constant (k) | 200 N/m |
| Extension or compression (x) | 0.05 m |
| Force (N) | 10 |
| Spring constant (N/m) | 200 |
| Extension (m) | 0.05 |
| Elastic potential energy (J) | 0.25 |
A 200 N/m spring stretched by 5 cm needs 10 N and stores 0.25 J.
Try this example →| Find | Spring constant (k) |
| Extension or compression (x) | 0.07 m |
| Force (F) | 4.9 N |
| Force (N) | 4.9 |
| Spring constant (N/m) | 70 |
| Extension (m) | 0.07 |
| Elastic potential energy (J) | 0.1715 |
A 500 g mass (4.9 N) stretching a spring by 7 cm gives k = 70 N/m.
Try this example →Within the elastic limit, the extension of a spring is proportional to the force applied: F = kx.
Newtons per metre (N/m).
Hang known weights on the spring, measure each extension, and divide force by extension (or take the slope of the force–extension graph).
E = ½kx², the area under the force–extension graph.