# Elastic Potential Energy Calculator

Calculate elastic potential energy stored in a spring with PE = ½kx² and restoring force with F = kx. Free online Hooke's law calculator for physics.

## What this calculates

Elastic potential energy is the energy stored in a spring or elastic material when it is stretched or compressed from its natural (equilibrium) position. Governed by Hooke's law, the energy stored is PE = ½kx², where k is the spring constant and x is the displacement. This calculator computes both the stored energy and the restoring force.

## Inputs

- **Spring Constant (k)** (N/m) — min 0 — Stiffness of the spring in Newtons per meter.
- **Displacement (x)** (m) — How far the spring is stretched or compressed from its natural length.

## Outputs

- **Elastic Potential Energy** (J) — PE = ½kx²
- **Restoring Force** (N) — F = kx (Hooke's law)

## Details

Hooke's law states that the restoring force of a spring is proportional to its displacement: F = kx. The spring constant k (in N/m) measures stiffness — a stiffer spring has a higher k value. The force always acts to return the spring to its equilibrium length.

The elastic potential energy PE = ½kx² is derived by integrating the force over the displacement. Because energy depends on x², doubling the displacement quadruples the stored energy. This quadratic relationship is why compressed springs and drawn bows can release energy explosively.

This principle applies far beyond mechanical springs. Chemical bonds behave like springs at small displacements, elastic bands store energy, and even the vibrations of atoms in a crystal lattice follow Hooke's law. The concept is fundamental to understanding oscillations, simple harmonic motion, and energy storage in elastic systems.

## Frequently Asked Questions

**Q: What is elastic potential energy?**

A: Elastic potential energy is energy stored in an elastic object (like a spring) when it is deformed. It equals ½kx², where k is the spring constant and x is the displacement from equilibrium. This energy is released when the spring returns to its natural length.

**Q: What is Hooke's law?**

A: Hooke's law states that the force exerted by a spring is proportional to its displacement: F = kx (or F = -kx to show the restoring direction). It holds for small deformations where the material behaves elastically. Beyond the elastic limit, the material deforms permanently.

**Q: Does it matter if the spring is stretched or compressed?**

A: No. Since energy depends on x², both stretching and compressing by the same amount store the same energy. The sign of x only affects the direction of the restoring force, not the magnitude of the stored energy.

**Q: What is the spring constant?**

A: The spring constant k (in N/m) measures a spring's stiffness. A higher k means the spring is stiffer and requires more force to stretch or compress by a given amount. It depends on the material, wire diameter, coil diameter, and number of coils.

**Q: When does Hooke's law break down?**

A: Hooke's law is only valid within the elastic limit of the material. If a spring is stretched too far, it undergoes plastic (permanent) deformation and the force-displacement relationship becomes nonlinear. The spring will not return to its original length.

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Source: https://vastcalc.com/calculators/physics/elastic-potential-energy
Category: Physics
Last updated: 2026-04-21