MotionLab

Spring Energy Calculator

Hooke's Law in action — how much energy a compressed or stretched spring stores.

Spring constant k (N/m)

Displacement x (m)

Potential energy (J)

0.25

PE = ½kx²

Restoring force (N): 10

What you entered

Spring constant k (N/m): 200Displacement x (m): 0.05

1
Spring force: F = k|x|
200 × 0.05= 10 N
2
Potential energy: PE = ½kx²
0.5 × 200 × 0.05²= 0.25 J

Result

Potential energy (J): 0.25

A spring (k = 200 N/m) compressed 0.05 m stores 0.25 J of potential energy with a restoring force of 10 N.

Energy stored in a compressed or stretched spring

Elastic potential energy is half the spring constant times the displacement squared. The force at that displacement is shown alongside.

Spring constant (N/m)	Displacement (m)	Stored energy (J)	Force (N)
50	0.3	2.2500	15.00
100	0.1	0.5000	10.00
200	0.15	2.2500	30.00
500	0.05	0.6250	25.00
1000	0.02	0.2000	20.00

Rows one and three store identical energy at 2.25 J despite one spring being four times stiffer, because the softer spring travels twice as far and displacement is squared. That is why energy storage favours long travel over stiffness. Doubling the displacement quadruples the stored energy while only doubling the force, which is the same squared relationship as kinetic energy. Release the spring and this energy converts to kinetic energy, which is how a catapult, a clock mainspring and a pogo stick all work.

Why energy is proportional to displacement squared

Force increases linearly with displacement (F = kx) per Hooke's Law, so the work done (and energy stored) is the area under that linear force curve — a triangle, which gives ½kx². Double the compression stores four times the energy, not two.

Springs everywhere

Springs aren't just metal coils — atomic bonds, guitar strings, diving boards, and even the suspension in your car all follow Hooke's Law (within their elastic limit). The same ½kx² formula applies to molecular vibrations in spectroscopy and to the oscillation of buildings during earthquakes.

Frequently asked questions

A spring with k = 500 N/m is compressed 0.1 m. How much energy is stored?

PE = ½kx² = ½ × 500 × 0.01 = 2.5 J. If released, this energy converts to kinetic energy of whatever the spring launches. A 0.05 kg ball would reach v = √(2E/m) = √(100) = 10 m/s.

How is spring energy related to Hooke's law?

Hooke's law gives the force at any displacement (F = kx). Spring energy is the integral of that force over displacement: PE = ∫kx dx = ½kx². Alternatively, it's the area under the force-vs-displacement line (a triangle). See the Hooke's law calculator for force problems.

Why does doubling the compression quadruple the energy?

Energy goes as x² (not x). Doubling compression doubles the force AND doubles the distance over which that force acts, so energy quadruples. This is why car suspension springs store much more energy in a pothole than in a small bump — nonlinear response to displacement.