Spring Potential Energy Calculator
Find the elastic potential energy stored in a spring from its spring constant and how far it is stretched or compressed.
N/m
m
J
Energy stored in the spring
- 1
Displacement squared (x²)
0.1² = 0.01 - 2
k × x²
200 × 0.01 = 2 - 3
Elastic PE = ½ × k × x²
½ × 2 = 1
How does this calculator work?
Elastic potential energy stored in a spring is PE = ½·k·x², where k is the spring constant (N/m) and x is the displacement from rest (m). Enter any two of k, x, and PE to solve for the third. Energy is in joules and always non-negative because displacement is squared.
Formula
How this is calculated
A spring that obeys Hooke's law stores elastic potential energy equal to PE = ½·k·x², where k is the spring constant in newtons per metre (N/m) and x is the displacement in metres (m) measured from the natural, unstretched length. The energy grows with the square of the displacement, so doubling the stretch quadruples the stored energy.
Enter any two of the three quantities and leave the third blank to solve for it. With k and x the calculator returns PE directly. Given PE and k it solves x = √(2·PE / k); given PE and x it solves k = 2·PE / x². The restoring force at the entered displacement, F = k·x, is also reported.
Assumptions: the spring is ideal and linear (constant k) and is not stretched past its elastic limit. Displacement may be positive (stretch) or negative (compression); because x is squared, energy is always non-negative. Negative spring constants or negative energies are physically invalid and are rejected, as is solving for k when x = 0.
Frequently asked questions
Because PE depends on x², the square of the displacement. Stretching or compressing by the same distance stores the same elastic potential energy.
Use the spring constant in newtons per metre (N/m) and displacement in metres (m). The result is then in joules (J). Convert centimetres to metres before entering.
Rearrange the formula to k = 2·PE / x². Enter the energy and displacement, leave k blank, and the calculator returns the stiffness.
Also known as
TG we-Calculate Editorial Team. (2026). Spring Potential Energy Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/spring-potential-energy-calculator
TG we-Calculate Editorial Team. "Spring Potential Energy Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/spring-potential-energy-calculator.
TG we-Calculate Editorial Team, "Spring Potential Energy Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/spring-potential-energy-calculator
@misc{wecalculate_spring_potential_energy_calculator, title = {Spring Potential Energy Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/spring-potential-energy-calculator}}, year = {2026}, note = {TG we-Calculate} }
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