Case 1
- Spring constant k (N/m)
- 200N/m
- Displacement x (m)
- 0.1m
1.0000J
Open with these valuesSpring Potential Energy Calculator
1.0000J
Result: 1.0000 JHalf the spring constant times the displacement squared: 200 N/m stretched 0.1 m stores 1 J. The half is easy to drop and doubles every answer if you do. Enter metres, not centimetres — 10 cm is 0.1 m, and a compression stores the same energy as the equal stretch.
The numbers at a glance
Held fixed: Spring constant k (N/m) 200.000 N/m.
| Displacement x (m) (m) | Result (J) |
|---|---|
| 0.0000 | 0.0000 |
| 0.0250 | 0.0625 |
| 0.0500 | 0.2500 |
| 0.0750 | 0.5625 |
| 0.1000Your value | 1.0000 |
| 0.1250 | 1.5625 |
| 0.1500 | 2.2500 |
| 0.1750 | 3.0625 |
| 0.2000 | 4.0000 |
Worked examples
Case 2
- Spring constant k (N/m)
- 500N/m
- Displacement x (m)
- 0.05m
0.6250J
Open with these valuesCase 3
- Spring constant k (N/m)
- 50N/m
- Displacement x (m)
- 1m
25.0000J
Open with these valuesHow it's calculated
E = ½ × k × x²
- StepEnter the spring constant in newtons per metre — how stiff the spring is.
- StepEnter how far it is stretched or compressed, in metres.
- ResultRead the stored energy in joules; one joule is one newton-metre.
Reference table
| k (N/m), x (m) | What it describes | Energy (J) |
|---|---|---|
| 500, 0.05 | Stiff spring, 5 cm of travel | 0.625 |
| 200, 0.1 | Firm spring, 10 cm of travel | 1 |
| 200, -0.1 | The same spring compressed instead | 1 |
| 100, 0.2 | Door spring, 20 cm of travel | 2 |
| 10, 2 | Soft spring pulled a long way | 20 |
| 50, 1 | Medium spring, a full metre | 25 |
Questions
How do I calculate spring potential energy?
Multiply half the spring constant by the displacement squared: E = ½ × k × x². Use newtons per metre for the constant and metres for the displacement to get joules. A spring with k = 200 N/m stretched 0.1 m stores ½ × 200 × 0.1² = 1 J.
What is elastic potential energy?
It is the energy stored in a spring when it is stretched or compressed away from its rest position. The spring holds that energy and releases it as motion when it springs back. It is measured in joules, the same unit used for every other form of energy.
Why does doubling the stretch quadruple the energy?
Because the displacement is squared in the formula. Doubling the stretch multiplies the stored energy by four and tripling it by nine. That is why a spring pulled twice as far snaps back far more forcefully.
What does the spring constant k mean?
It measures how stiff a spring is, in newtons per metre — the force needed to stretch or compress it by one metre. A larger k means a stiffer spring that stores more energy for the same displacement, because the energy is directly proportional to k. A firm car suspension spring is roughly 20000 N/m.
Does a compression store the same energy as a stretch?
Yes, because the displacement is squared, so its sign disappears. Compressing that 200 N/m spring by 0.1 m stores the same 1 J as stretching it by 0.1 m. Enter the displacement with whichever sign you like.
Sources and last check
Information, not professional advice.