Elastic Potential Energy Calculator

What Is Elastic Potential Energy?

Elastic potential energy is the energy stored in an elastic material — such as a spring, rubber band, or bow — when it is deformed. This stored energy can be converted into kinetic energy when the material returns to its original shape.

Unlike gravitational potential energy, which depends on height, elastic PE depends on how far the material has been stretched or compressed from its equilibrium position and how stiff the material is.

How to Calculate Elastic Potential Energy

Elastic Potential Energy Formula

Where:

• PE = elastic potential energy (J)
• k = spring constant (N/m)
• x = displacement from equilibrium (m)

Because energy depends on x², doubling the stretch quadruples the stored energy. Compressing a spring by 10 cm stores 4 times as much energy as compressing it by 5 cm.

Worked Example

A spring with a spring constant of 500 N/m is compressed by 0.1 meters (10 cm). How much elastic potential energy is stored?

PE = ½ × 500 × 0.1² = ½ × 500 × 0.01 = 2.5 J

Hooke's Law and the Spring Constant

Elastic PE is derived from Hooke's Law (F = kx), which states that the restoring force of a spring is proportional to its displacement. The spring constant k measures stiffness — a higher k means a stiffer spring that stores more energy for the same displacement.