Potential Energy Calculator

Potential energy: gravitational and elastic

Potential energy (Ep) is energy a system holds because of where its parts sit or how they're arranged. You'll meet two forms most often. There's gravitational, Ep = m·g·h, and elastic, Ep = (1/2)·k·x², where k is the spring constant and x the deformation away from equilibrium. At Earth's surface g ≈ 9.81 m/s², though it drifts a bit (9.78 at the equator, 9.83 at the poles). Lift a 2 kg body to 5 m and it stores about 98 J. The conservation of mechanical energy says Ec + Ep stays constant when nothing dissipates, which is what makes the simple pendulum period T = 2π√(L/g) work, with Ec and Ep trading back and forth.

Applications

Hydroelectric plants turn gravitational Ep into electricity (Itaipu runs 14 GW installed). Roller coasters, objects in free fall, ballistics, and pumped-storage batteries all lean on the Ep ↔ Ec swap. Over in chemistry, bond energy is a kind of potential energy; in electricity, electric Ep works out to qV.

FAQ

Does the reference level matter? What carries physical meaning is the difference in Ep, not its absolute value. Pick whatever reference you like, the floor, a tabletop, sea level. The work done depends on Δh, not on the height measured from zero.

Is elastic Ep always positive? Yes. Because x² can never go below zero, the spring stores energy either way, whether you stretch it or squeeze it.

Why does a pendulum slow down? Real systems bleed energy into air drag and friction at the pivot. As the mechanical energy drops, the swing gets smaller and smaller until the pendulum stops.