Spring Potential Energy Calculator
Storing Energy in Springs
Springs and other elastic devices play a central role in classical mechanics. When a spring is stretched or compressed from its equilibrium position, it stores energy that can later be released to do work. The amount of stored energy is governed by Hooke's law and is quantified by the expression .
In this formula, denotes elastic potential energy in joules, represents the spring constant in newtons per meter, and is the displacement in meters from the equilibrium position. Because the force grows linearly with displacement, the work done—and thus the energy stored—scales with the square of the extension.
How the Calculator Works
Enter any two of the three variables and the script rearranges Hooke's law. When k and x are supplied, energy is computed directly. If you provide U and x, the calculator solves for the spring constant using , while U and k yield the displacement from .
Example Spring Constants
| System | Typical k (N/m) |
|---|---|
| Soft pen spring | 5 |
| Archery bow limb | 200 |
| Precision balance spring | 0.5 |
| Industrial scale spring | 1,000 |
| Automotive suspension spring | 30,000 |
Energy Comparisons
Elastic potential energy can convert into kinetic energy when the spring releases. Equating with kinetic energy shows how a compressed spring can launch a mass with speed . This relation explains the behavior of pinball plungers, toy darts, and vibration energy harvesters.
Continue exploring oscillatory systems with the Damped Harmonic Oscillator Calculator, Kinetic Energy Calculator, and the Simple Pendulum Period Calculator.
Spring Launcher Arcade
Compress the spring and launch payloads into floating target zones. Feel how displacement affects stored energy—the quadratic relationship comes alive as you dial in the perfect compression for each shot. Chase combos, hit bullseyes, and master the physics before time runs out.