Potential Energy Calculator

Gravitational potential energy (PE) is the energy stored in an object due to its position in a gravitational field. The formula PE = mgh shows that potential energy depends on mass (m), gravitational acceleration (g), and height (h) above a reference point. When an object is lifted, work is done against gravity, and this work is stored as potential energy.

The reference point (zero height) is arbitrary and chosen for convenience. Common choices include ground level, floor level, or the bottom of a trajectory. Potential energy is always relative to this reference point. What matters for calculations is the height difference, not the absolute height.

Through the conservation of mechanical energy, PE + KE = constant (in absence of friction). When an object falls, its PE decreases while KE increases. At the highest point, PE is maximum and KE is zero. At the lowest point, PE is zero and KE is maximum. A dropped object converts all its PE to KE: mgh = (1/2)mv², giving v = √(2gh).

Gravitational acceleration varies by celestial body: Earth (9.81 m/s²), Moon (1.62 m/s²), Mars (3.72 m/s²), Jupiter (24.79 m/s²). Since PE = mgh, the same object at the same height has different potential energy on different planets. On the Moon, PE would be about 1/6 of Earth, while on Jupiter it would be about 2.5x Earth.

It is called "potential" because it represents stored energy that has the potential to do work or convert to other forms of energy. Unlike kinetic energy (energy of motion), potential energy is energy of position or configuration. When released, this potential converts to kinetic energy or other forms.

Yes, if the object is below the chosen reference point. For example, if you choose ground level as zero, an object in a basement has negative PE. However, only changes in PE (ΔPE) have physical meaning. The absolute value depends on the arbitrary choice of reference point.

The work done against gravity equals the change in potential energy: W = ΔPE = mgΔh. To lift an object, you must do positive work against gravity. When an object falls, gravity does positive work on the object (and potential energy decreases). The work done against gravity is independent of the path taken.

Using energy conservation, when PE converts to KE: mgh = (1/2)mv². Solving for velocity: v = √(2gh). This gives the velocity of an object dropped from height h (assuming no air resistance). For example, dropping from 10m: v = √(2 × 9.81 × 10) = 14 m/s.