Potential Energy Calculator

Gravitational potential energy stores work done against gravity when an object is raised to a height. Release that object and gravity converts stored energy back into kinetic energy — the principle behind hydroelectric dams, roller coasters, and falling weight clocks. Near Earth's surface the simple mgh model captures most everyday situations accurately.

Gravitational potential energy:

PE = m × g × h

Where PE is energy in joules, m is mass in kg, g is gravitational acceleration (9.81 m/s² on Earth), and h is vertical height in meters above a reference level. Only vertical displacement matters for uniform gravity; horizontal movement does not change gravitational PE. Reference height is arbitrary — energy differences between two levels are physically meaningful, not absolute values.

Enter mass, height, and optionally customize g for other planets. On the Moon g ≈ 1.62 m/s², so the same lifted mass stores less energy. Elastic potential energy in springs follows PE = ½kx² — a different mechanism handled conceptually alongside but not mixed into mgh without clear separation.

Worked example: A 50 kg rock on a 120 m cliff has PE = 50 × 9.81 × 120 = 58,860 J ≈ 58.9 kJ. If it falls freely (ignoring air drag), that converts to kinetic energy at impact. A 500 kg elevator car raised 40 m in a shaft stores PE = 500 × 9.81 × 40 = 196,200 J — the motor must supply at least that much work plus losses.

Pair with the kinetic energy calculator for energy conservation problems, the pendulum calculator where height trades with speed each swing, and the work calculator when forces move objects vertically. Convert joules to calories or kWh when comparing to electrical or thermal energy budgets.