Utilnaro

Work, energy and power

Gravitational potential energy

Calculate gravitational potential energy, mass, gravitational acceleration, or height near a planet surface.

Formula

Ep=mgh Ep = m × g × h

In a uniform gravitational field, the change in potential energy equals mass times gravitational acceleration times the vertical height change.

Gravitational potential energy calculator

What do you want to calculate?

Known values

The result updates automatically.

Energy relative to a reference level
hmgEp ?
  • Potential energy: value being calculated (?)
  • Mass: known value
  • Gravitational acceleration: known value
  • Height: known value

Result

981 J

Substitution and calculation

Ep = m × g × h = 10 kg × 9.81 m/s² × 10 m = 981 J

Symbols and units

SymbolQuantitySISupported units
Epgravitational potential energyEnergy relative to the chosen zero-height reference.JJ, kJ
mmassMass of the object.kgkg, g
ggravitational accelerationLocal magnitude of gravitational acceleration entered explicitly for the calculation.m/s²m/s²
hheight differenceVertical distance from the selected zero level.mm, cm, km

Formula rearrangements

Calculate energy

Ep = m × g × h

Calculate mass

m = Ep / (g × h)

Calculate gravitational acceleration

g = Ep / (m × h)

Calculate height

h = Ep / (m × g)

Worked examples

Energy of a box on a platform

A 12 kg box is lifted 5 m. Use g = 9.81 m/s² and calculate the energy increase.

  1. 1Step 1: Use Ep = m × g × h.
  2. 2Step 2: Substitute m = 12 kg, g = 9.81 m/s², and h = 5 m.
  3. 3Step 3: Multiply to obtain 588.6 J.

Result: 588.6 J

Height from potential energy

A 50 kg object gains 4.905 kJ of energy near Earth. Use g = 9.81 m/s² and find the height change.

  1. 1Step 1: Convert 4.905 kJ to 4905 J.
  2. 2Step 2: Use h = Ep / (m × g).
  3. 3Step 3: Divide by 50 × 9.81 to obtain 10 m.

Result: 10 m

Sources and review