Calculate gravitational potential energy near a planet's surface with PE = m g h — or solve for mass or height. Gravity defaults to Earth's 9.81 m/s².
Gravitational potential energy is the energy stored by lifting a mass against gravity. Near a planet's surface, where g is roughly constant, it is PE = m g h, with mass in kg, gravity in m/s² and height in metres, giving joules.
Only changes in height matter, so you choose a reference level (often the ground) where PE = 0. For large astronomical distances, where g is not constant, the more general form U = −GMm/r is used instead.
Near a surface it is PE = m g h — mass times gravitational acceleration times height. On Earth g = 9.81 m/s², so a 1 kg object 1 m up has about 9.81 J.
Rearrange to h = PE / (m g). Set 'Solve for' to Height, enter the energy, mass and gravity, and the calculator returns the height.
PE = mgh is the near-surface approximation where gravity is nearly constant. U = −GMm/r is the exact form for any separation and is used for orbits and escape-velocity problems.
The joule (J), the same unit as all energy. One joule equals one kg·m²/s².