Calculators/Physics/Hooke's law

Hooke's law

F = k·x · elastic potential energy

Hooke's law — illustration

Leave one field empty — I'll compute it.

F
10 N
Elastic potential energy
0.25 J

Hooke's law: F = k·x (for small deformations, within the elastic range). Energy stored in the spring: Eₚ = ½·k·x².

Hooke's law describes the elastic force under a small deformation:

F=k⋅xF=k\cdot x

where kk is the spring constant (stiffness) in N/m, and xx — the extension (or compression) in metres. The larger kk, the stiffer the spring.

The energy stored in a deformed spring is:

Ep=12 k x2E_p=\tfrac12\,k\,x^2

Enter two of the three quantities (FF, kk, xx) and the calculator works out the third as well as the elastic potential energy. The law holds within the elastic range (for too large an extension it stops being linear).

Examples

k = 200 N/m, x = 0.05 m
→ F = 10 N, Eₚ = ½·200·0.05² = 0.25 J
F = 20 N, x = 0.1 m
→ k = 200 N/m

Frequently asked questions

What does the spring constant k mean?+

The stiffness of the spring — how many newtons of force are needed per 1 metre of extension. A large k is a stiff spring (hard to stretch), a small k — a soft one.

When does Hooke's law stop working?+

Once the elastic limit is exceeded — the spring no longer returns to its original shape, and the dependence of force on extension stops being linear.

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