Gravitational Potential Energy Calculator – PE = mgh

Gravitational potential energy (GPE) is the energy an object possesses due to its position in a gravitational field. It represents the work done against gravity to move an object to a certain height. The higher the object and the greater its mass, the more gravitational potential energy it stores. When the object falls, this stored energy converts into kinetic energy.

The formula PE = mgh is an approximation valid when the gravitational field strength (g) is approximately uniform — typically near the surface of a planet where height changes are small relative to the planet's radius. For large distances (e.g., satellites in orbit), you must use the more general formula: PE = -GMm/r, where G is the universal gravitational constant, M is the planet's mass, and r is the distance from the center.

The SI unit of gravitational potential energy is the Joule (J). One Joule equals 1 kg·m²/s². In everyday terms, lifting a medium-sized apple (~100g) vertically by 1 meter on Earth requires approximately 1 Joule of energy. Other common units include kilojoules (kJ, 1 kJ = 1,000 J) and calories (1 cal ≈ 4.184 J).

Surface gravity varies significantly across the solar system. Earth's gravity is 9.81 m/s². The Moon has only 1.62 m/s² (about 1/6 of Earth's). Mars has 3.71 m/s² (~38% of Earth's). Jupiter, the most massive planet, has 24.79 m/s² (~2.5× Earth's). The Sun's surface gravity is a staggering 274 m/s² (~28× Earth's). This means an object on Jupiter would have about 2.5 times more gravitational potential energy at the same height compared to Earth.

In the simplified PE = mgh formula, potential energy is typically considered zero at the reference height (h=0) and positive above it. However, in the more general Newtonian formula (PE = -GMm/r), gravitational potential energy is always negative and approaches zero only at infinite distance. The sign convention depends on where you set your reference point. In most introductory physics problems using PE = mgh, we only deal with positive values.

As an object falls, its gravitational potential energy decreases and converts into kinetic energy (energy of motion). In the absence of air resistance, the total mechanical energy (GPE + kinetic energy) remains constant — this is the principle of conservation of mechanical energy. At the moment just before impact, almost all the initial GPE has been converted to kinetic energy.

The gravitational potential energy gained by an object equals the work done against gravity to lift it. Work = Force × Distance. Since the force needed to lift an object at constant speed equals its weight (mg), the work done to lift it by height h is W = mg × h, which is exactly the formula for GPE. This is why PE = mgh represents stored energy — it's the energy "invested" in lifting the object.

GPE has numerous practical applications: Hydroelectric dams convert the GPE of elevated water into electricity. Pumped-storage hydroelectricity uses excess energy to pump water uphill, storing it as GPE for later use. Roller coasters rely on GPE at the top of hills to power the ride. Pile drivers use the GPE of a heavy weight to drive foundations into the ground. Even clocks historically used weights (GPE) to power their mechanisms.