Hooke's Law Spring Force Calculator

Reviewed by the CalculatorHub team, edited by James Graham. Based on Hooke's law, F = k * x. Last verified 19 June 2026.

Hooke's law describes how an ideal spring resists being stretched or compressed: the restoring force grows in direct proportion to the displacement. Enter the spring constant and the displacement to find the spring force and the elastic potential energy stored. The spring constant measures stiffness in newtons per metre, and the energy term shows the work stored in the deformed spring. The relationship holds within the spring's elastic limit.

Spring constant k (N/m)

Displacement x (m)

Spring force F (N)

0.00

Stored energy (J)

0.00

Hooke's law formula

F = k * x
Stored energy E = (1/2) * k * x2
where k = spring constant (N/m), x = displacement (m)

The force is the magnitude of the spring's restoring force. The stored energy is the work done deforming the spring, recoverable when it returns to its natural length.

Worked example

A spring with k = 200 N/m is stretched by x = 0.1 m. The spring force is F = 200 * 0.1 = 20.00 N. The stored elastic potential energy is E = 0.5 * 200 * 0.1 * 0.1 = 1.00 J.

Hooke's law: 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 displacement: F = k * x. Here k is the spring constant (stiffness) and x is the displacement from the spring's natural length.

What are the units?

Force is in newtons, the spring constant k is in newtons per metre (N/m), and displacement x is in metres. Stored energy is in joules.

How much energy does a stretched spring store?

The elastic potential energy is E = (1/2) k x2. This calculator returns it alongside the force so you can see both the restoring force and the work stored in the spring.

When does Hooke's law stop being accurate?

Hooke's law holds only within the spring's elastic limit. If a spring is stretched too far it deforms permanently and the linear F = k * x relationship no longer applies.

Sources

NIST: SI units (newton, joule, metre).
Hooke's law and the elastic potential energy formula are standard results of classical mechanics.

Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.