Gravitational potential energy
Energy for the stated reference and ideal model.
Physics · Mechanics · Motion & Energy
Gravitational potential energy calculator
Calculate gravitational potential energy relative to a chosen zero level, or the energy change between two signed heights.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Energy change
Final potential energy minus initial potential energy.
Relation and numerical substitution
U = m × g × h—
Uniform gravity; m,g > 0; heights measured upward from the same reference.
01Formulas and symbols
Formulas used
U
U = m × g × hEnergy for the stated reference and ideal model.ΔU
ΔU = m × g × (h − h₀)Final potential energy minus initial potential energy.02Assumptions and limits
Scope of validity
- Uniform gravity; m,g > 0; heights measured upward from the same reference.
03Validation example
Reference numerical case
- m = 10 kg, g = 9.80665 m/s², h = 2 m: U = 196.133 J. From h₀ = 4 m to h = 2 m: ΔU = 10 × 9.80665 × (2 − 4) = −196.133 J.
04References
Technical references
FAQ
Why can gravitational potential energy be negative?
In the near-Earth relation U = mgh, the zero level is chosen by the user. A position below that reference has h < 0 and therefore negative U; only energy differences are physically meaningful in this model.
Does changing the reference height change the physical result?
It changes the numerical value assigned to potential energy by adding a constant offset, but it does not change ΔU between two heights. Forces and energy changes are therefore unaffected by the chosen zero level.
05How it works
The reference level is arbitrary: changing it changes U but not ΔU for the same two positions. Raising a mass increases its potential energy; lowering it gives a negative change. Work by gravity is −ΔU, whereas quasistatic lifting against gravity requires +ΔU.
06Limits of the model
Constant mass and uniform positive g over a height small compared with Earth’s radius. For large altitude changes use the inverse-square gravitational model. Negative energy relative to the chosen zero is allowed.
07Common mistakes
Enter height above the reference, not altitude above sea level unless that is your zero. Do not confuse the energy change with gravitational work, whose sign is opposite.