Elastic Potential Energy Calculator
The energy stored in a stretched or compressed spring — ½kx² — and the speed it can launch a given mass to.
How much energy a spring holds.
How the elastic potential energy calculator works
A spring obeying Hooke's law stores ½kx² when displaced by x. The square matters: pulling twice as far stores four times the energy, because the force builds as you go.
Released onto a mass, all of it becomes kinetic energy, so the launch speed is √(kx²/m) — which is how a catapult, a crossbow and a pinball plunger are sized.
Formula: PE = ½ k x²
Worked examples
| Inputs | Stored energy | Note |
|---|---|---|
| 500 N/m compressed 0.2 m | 10 J | 10 J |
| Twice the compression | 40 J | four times the energy |
| A stiffer spring | 40 J | four times the energy again |
FAQFrequently asked questions
Why is it ½kx² rather than kx?
Because the force builds from zero as you stretch. The energy is the area under the force–displacement line, which is a triangle — hence the half.
What is the spring constant?
Newtons of force per metre of displacement. A 500 N/m spring takes 500 N to stretch one metre, or 100 N for 20 cm.
Does the energy come back?
Almost all of it, for an ideal spring. Real springs lose a little to internal friction, which is called hysteresis.
Where does Hooke's law fail?
Beyond the elastic limit. Stretch a spring too far and it deforms permanently, and the formula no longer applies.
How do I size a launcher?
Set ½kx² equal to the kinetic energy you need. Launching 0.5 kg at 6 m/s takes 9 J, which is a 500 N/m spring compressed 19 cm.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Measurement Institute — Australia's measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.