Spring Potential Energy Calculator
Calculate elastic potential energy stored in a compressed or stretched spring using PE = 1/2 * k * x^2. Enter spring constant in N/m and displacement in metres. Essential for SHM, mechanical design, and energy storage analysis.
Did this tool answer your question?
Thanks — this helps us improve the tool.
How to use this tool
- Enter spring constant (k) and displacement (x) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your spring potential energy and the full breakdown beneath it.
Formula
PE = 0.5 * k * x^2
How it works
The elastic potential energy stored in a spring deformed by x metres from its rest length is PE = ½kx². This energy is recovered when the spring returns to equilibrium.
Worked examples
Compressed spring
Stiffer spring stretched further
Common mistakes to avoid
- Forgetting the 1/2 factor and computing k*x^2 instead of (1/2)*k*x^2, giving twice the correct elastic potential energy.
- Entering displacement in centimetres while k is in N/m — x must be in metres for the result to come out in joules.
- Using the total length of the spring as x instead of the displacement from equilibrium (compression or extension distance).
Key terms
Frequently asked questions
- Why is there a 1/2 factor in the elastic potential energy formula?
- Because the force increases linearly with displacement (F = kx), the average force over the displacement from 0 to x is kx/2. Work = average force * distance = (kx/2)*x = (1/2)kx^2.
- How is spring potential energy related to kinetic energy in simple harmonic motion?
- In an ideal spring-mass system with no friction, energy converts between elastic PE and kinetic energy. At maximum compression or extension, all energy is PE = (1/2)kx^2; at the equilibrium position, all energy is KE = (1/2)mv^2.
- Does it matter whether the spring is compressed or stretched?
- No. Because x is squared in (1/2)kx^2, the sign of x (extension vs. compression) does not affect the magnitude of stored energy. The same displacement stores the same energy whether the spring is pushed or pulled.