Elastic Potential Energy Calculator
This calculator helps you determine the elastic potential energy stored in a spring or elastic object, based on Hooke's Law. You can calculate the energy given the spring constant and displacement, or find either the spring constant or displacement when the other two values are known.
Elastic Potential Energy Calculator
Elastic Potential Energy Formula
Where:
- $$PE$$ = Elastic potential energy (Joules, J)
- $$k$$ = Spring constant (Newtons per meter, N/m)
- $$x$$ = Displacement from equilibrium position (meters, m)
This formula calculates the energy stored in a spring when it is compressed or stretched from its equilibrium position.
Elastic Potential Energy – Worked Example
A spring with a spring constant of $$k = 200\ N/m$$ is compressed by $$x = 0.1\ m$$ from its equilibrium position. How much elastic potential energy is stored?
- $$k$$ = 200 N/m
- $$x$$ = 0.1 m
- $$PE = \frac{1}{2} \times 200 \times (0.1)^2$$
- $$PE = 100 \times 0.01$$
- $$PE = 1\ J$$
The spring stores 1 Joule of elastic potential energy.
Elastic potential energy is the energy stored in an object when it is stretched or compressed, following Hooke’s Law. This type of energy is common in springs, rubber bands, and other elastic materials. The amount of energy depends on both the stiffness of the material (spring constant) and how far it is displaced from its natural position. Understanding elastic potential energy is essential in physics, engineering, and mechanics for analyzing systems involving springs and elastic deformation.