Hooke's Law Calculator
Find spring force and stored energy from displacement.
Results update as you type.
How it works
Hooke's law describes how springs and elastic materials respond to being stretched or compressed, and this calculator finds both the restoring force and the energy stored. You enter the spring constant, which measures the spring's stiffness, and the displacement from its natural length, and it returns the force the spring pushes back with and the elastic potential energy it holds. The law states that force is directly proportional to displacement, so doubling how far you stretch a spring doubles the force it resists with, at least until the material reaches its elastic limit and the relationship breaks down. The stored energy grows with the square of displacement, so stretching twice as far stores four times the energy. Hooke's law underlies the design of everything from car suspensions and mattresses to scales, clock mechanisms, and the atomic bonds modelled as tiny springs in physics and chemistry. Students meet it early in mechanics, and engineers use it constantly to size springs and predict deflection. The spring constant is negative in the strict vector form because the force opposes displacement, but the magnitude is what matters here. Enter the spring constant and displacement to compute the force and energy.
F = k · x; PE = ½ · k · x²
Hooke's law states that the force a spring exerts is proportional to how far it is stretched or compressed, so the force equals the spring constant multiplied by the displacement. The elastic potential energy stored in the spring is half the spring constant times the displacement squared, which is the area under the force-versus-displacement line, representing the work done to deform the spring.
Source:Classical mechanics (Hooke's law)
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Worked example
How to use this calculator
- 1
Enter your values
Enter spring constant (k) and displacement (x).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Restoring force updates instantly as you type — no button to press.
Frequently asked questions
What is Hooke's law?
Hooke's law states that the force needed to extend or compress a spring is proportional to the distance it is displaced from its natural length. Written as force equals the spring constant times displacement, it holds as long as the spring is not stretched beyond its elastic limit. It is a foundational principle for understanding elastic behaviour in springs and materials.
What is the spring constant?
The spring constant, written k and measured in newtons per metre, quantifies a spring's stiffness. A high spring constant means a stiff spring that resists deformation strongly, while a low value means a soft, easily stretched spring. It is the proportionality factor in Hooke's law, so it directly sets how much force a given displacement produces.
How much energy does a stretched spring store?
A stretched or compressed spring stores elastic potential energy equal to half the spring constant times the square of the displacement. Because the displacement is squared, stretching a spring twice as far stores four times the energy. This energy is released when the spring returns to its natural length, which is how spring-powered mechanisms and shock absorbers work.
When does Hooke's law stop working?
Hooke's law holds only within a material's elastic region. If you stretch a spring or material beyond its elastic limit, it deforms permanently and no longer returns to its original shape, and the force is no longer proportional to displacement. Beyond that point the linear relationship fails, so the calculator's result applies only to elastic, reversible deformation.
Why is the force called a restoring force?
The force is called restoring because it always acts to return the spring to its natural, unstretched length, opposing whatever displacement you apply. Stretch the spring and it pulls back inward; compress it and it pushes back outward. This restoring nature is what drives oscillation in springs and is central to simple harmonic motion throughout physics.