mgh Formula – How to Calculate Potential Energy (Practice)
PE = mgh — Gravitational potential energy near Earth
Near Earth’s surface, gravitational potential energy depends on mass, gravitational field strength g, and height above a chosen zero. Double the height at fixed mass and g, and PE doubles.
Guide — how to use this formula
- 1. Choose PE = 0 (floor, table, or ground) and stick to it.
- 2. Convert mass to kilograms and height to metres.
- 3. Use the g value from the question (9.8, 9.81, or 10).
- 4. Compute PE = m g h in joules, or rearrange for m or h.
Derivation
Near Earth, PE = mgh comes from the work needed to lift a mass against gravity at constant speed:
- The weight (downward force) of mass m is
F = mg - To raise it a vertical height h at constant speed, you apply an equal upward force through distance h. Work done is
W = F \, h = (mg)\, h - That work is stored as gravitational potential energy relative to the lower level:
PE = W = mgh
So PE = mgh when g is treated as constant (near Earth’s surface). Units: kg · m/s² · m = J.
Examples
Example: 2 kg lifted 1.5 m
With g = 9.8: PE = (2)(9.8)(1.5) = 29.4 J. Rough check with g = 10: about 30 J.
Example: find height from 25 J
m = 0.50 kg, PE = 25 J, g = 10 → h = 25 / (0.50 × 10) = 5.0 m.