Elastic Potential Energy Calculator
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.
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.