Spring Potential Energy Calculator
Enter a spring constant and a displacement to get the elastic potential energy in joules — and see why the energy climbs with the square of the stretch.
Elastic energy in one step
Enter the spring constant and the displacement and the calculator returns the stored elastic potential energy (½kx²) in joules.
Use SI units
Spring constant in newtons per metre and displacement in metres give the energy in joules — keep both in SI units before you start.
What is spring potential energy?
The energy stored in a stretched spring
Elastic potential energy is the energy stored in a spring when it is stretched or compressed away from its rest position. The further you pull or push the spring, the more energy it holds, ready to be released as motion the moment it springs back. The spring potential energy calculator turns two measurements, the spring constant in newtons per metre and the displacement in metres, into the stored energy in joules. It is the number behind a drawn bow, a wound clock spring, a compressed shock absorber, and a trampoline ready to launch.
Enter a spring constant in N/m and a displacement in metres to get the elastic potential energy in joules instantly.
Elastic potential energy is half the spring constant multiplied by the displacement squared.
PE = ½ × k × x²The displacement is squared, so it dominates the result: a small change in stretch produces a large change in energy. The spring constant k enters to the first power, so a stiffer spring stores more energy for the same stretch in direct proportion. Use newtons per metre and metres and the energy comes back in joules.
Suppose a spring with a spring constant of 200 N/m is stretched 0.1 m (10 cm) from its rest position.
Square the displacement
0.1² = 0.01 — the squared stretch that drives the energy.
Multiply by the spring constant
200 × 0.01 = 2 — the spring constant times the displacement squared.
Take half
½ × 2 = 1 J — the elastic potential energy stored in the spring.
The result tells you how much energy the spring is holding and how much work it took to deform it that far. The 1 J stored by the spring above is exactly the energy it will return when it springs back to its rest position — enough to fling a small object into motion. The crucial insight is that energy scales with the square of displacement: double the stretch from 0.1 to 0.2 m and the stored energy jumps fourfold, from 1 to 4 J, while the spring constant only matters in direct proportion. That is why a bow drawn twice as far delivers four times the energy to an arrow, why over-compressing a spring stores energy so quickly, and why a stiffer spring (a bigger k) stores more energy for the very same stretch. Pulling further is the lever that moves the result the most.
The formula is exact for an ideal spring, but a couple of practical points are worth keeping in mind.
Ideal springs and the elastic limit
This calculator assumes an ideal spring that obeys Hooke's law, meaning the restoring force stays proportional to the displacement. That holds only within the spring's elastic limit — stretch it too far and it deforms permanently and the formula no longer applies. Keep your units consistent — newtons per metre for the spring constant and metres for the displacement — or the joules will be wrong.