Spring Energy Calculator
Calculate elastic potential energy, spring constant, or displacement using E = ½kx².
Related: | | |
What is Spring Energy?
Spring energy, also called elastic potential energy, is the energy stored in a deformed elastic object. For a spring following Hooke's Law, this energy is proportional to the square of the displacement:
E = ½kx²
Where E is elastic potential energy in joules (J), k is the spring constant in N/m, and x is displacement from equilibrium in meters (m). The energy is always positive (since x² is always positive) and reaches maximum at maximum compression or extension.
Common Spring Energy Reference Values
| Application | Energy (J) |
|---|---|
| Car suspension spring (compressed 0.1 m) | 175 |
| Trampoline spring (stretched 0.3 m) | 180 |
| Pen click spring (compressed 5 mm) | 0.006 |
| Slingshot (stretched 0.5 m) | 25 |
| Watch mainspring (fully wound) | 0.001 |
| Garage door spring (extended) | 500 |
| Pogo stick (compressed at bounce) | 300 |
| Crossbow (drawn) | 200 |
Related Calculators
Authoritative References
Frequently Asked Questions
What is spring energy?
Spring energy (elastic potential energy) is the energy stored in a spring when it is stretched or compressed. It is defined by the formula E = ½kx², where k is the spring constant and x is displacement from equilibrium. This energy is released when the spring returns to its natural length.
How do I calculate spring energy?
Spring energy is calculated using E = ½ × k × x². For example, a spring with k = 500 N/m compressed by 0.1 m stores E = 0.5 × 500 × 0.01 = 2.5 J. Doubling the displacement quadruples the stored energy.
How is spring energy related to spring force?
The relationship comes from integrating Hooke's Law (F = kx) over displacement. Since work = ∫F dx = ∫kx dx = ½kx², the energy stored equals the work done to deform the spring. Graphically, it's the area under the force-displacement curve.
What are practical applications of spring energy?
Spring energy is used in: mechanical watches (mainspring stores energy to power the watch), vehicle suspensions (absorb bumps), pogo sticks and trampolines (store and release energy for bouncing), crossbows and slingshots (projectile propulsion), retractable tape measures, and garage door openers.
How does spring energy convert to other forms?
When a compressed spring is released, its elastic potential energy converts to kinetic energy of the attached mass. In a mass-spring system, energy continuously converts between kinetic and potential as the spring oscillates. Friction eventually dissipates the energy as heat.
Can a spring store infinite energy?
No, every spring has an elastic limit beyond which it deforms permanently. The maximum energy storage is limited by the spring's material properties. A typical steel spring can store about 10³ J/kg, while carbon fiber springs can store up to 10⁴ J/kg. Beyond the elastic limit, Hooke's Law no longer applies.