Hooke's Law Calculator
Enter spring constant and displacement to compute the spring force F = −k·x and its elastic potential energy.
Input Data
Results
At a glance:Hooke's law (Hooke, 1676) says the restoring force of an ideal spring is proportional to its displacement from equilibrium: F = −k·x, where k (N/m) is the spring constant (stiffness) and x the displacement. The minus sign shows the force opposes the stretch. The elastic potential energy stored is U = ½·k·x². The law holds for small deformations; beyond the elastic limit materials deform permanently. It underlies simple harmonic motion with ω = √(k/m).
Formula
Hooke's law: F = −k·x
Potential energy: U = ½·k·x²
$$F = k x$$$$PE = \tfrac{1}{2} k x^2$$How to Use
- Enter the spring constant k (N/m).
- Enter the displacement x (m).
- The calculator returns F and U.
Case Studies
Stretching a spring
k = 200 N/m, x = 0.1 m.
F = 200×0.1 = 20 N (restoring).
U = ½×200×0.01 = 1 J stored.
FAQ
What does the spring constant mean?
k measures stiffness: a larger k needs more force per unit stretch. Units N/m. Stiffer springs (thicker wire, more coils) have larger k.
Why the negative sign?
The spring pulls/pushes back toward equilibrium, opposite to the displacement direction — a restoring force.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.