Hookes Law Spring Calculator
Hookes law describes how an ideal spring responds to being stretched or compressed: the force it exerts grows in direct proportion to the displacement. From the spring constant and the displacement you can find the restoring force and the elastic potential energy stored. This calculator applies Hookes law and the elastic energy formula, taking the spring constant and the displacement, and returns the spring force, the stored energy, and the equivalent average force over the stretch. It is valid within the elastic limit.
Hookes law formula
Spring force F = k * x
Stored energy U = 0.5 * k * x^2
Average force over stretch = 0.5 * F = 0.5 * k * x
The force rises linearly with displacement, so the stored energy is the triangular area under the force-displacement line. The average force over the stretch is half the final force, which is why the energy is one half k x squared.
Spring facts
- Force is proportional to displacement within the elastic limit.
- Stored energy rises with the square of the displacement.
- The spring constant is the force per metre of stretch.
- Stretch and compression of equal size store equal energy.
- Beyond the elastic limit the material yields and the law fails.
Hookes law: frequently asked questions
What is Hookes law?
Hookes law states that the force a spring exerts is proportional to how far it is stretched or compressed: F = k x, where k is the spring constant (stiffness) and x is the displacement from the natural length. It holds while the spring stays within its elastic limit.
How is the energy stored in a spring calculated?
The elastic potential energy stored in a Hookean spring is one half the spring constant times the displacement squared: 0.5 k x squared. This is the area under the force-versus-displacement line, since force rises linearly with displacement.
What are the units of the spring constant?
The spring constant is in newtons per metre in SI units: it is the force needed to stretch the spring by one metre. A stiffer spring has a larger constant. Enter the constant and the displacement in metres for results in newtons and joules.
When does Hookes law stop being accurate?
Hookes law applies only within the elastic region. Beyond the spring's elastic limit the material yields and deforms permanently, and the force is no longer proportional to displacement. Very large displacements and coil binding also break the linear relationship.
Does it matter if the spring is stretched or compressed?
For an ideal spring the magnitude of the force and the stored energy are the same for a given displacement whether stretched or compressed; only the direction of the force reverses. This calculator uses the magnitude of the displacement you enter.
Official sources
- NIST: Physical Measurement Laboratory: force and energy units.
- NASA: NASA Glenn Research Center: elastic forces.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.