Potential Energy⚠ unverified
Physics / Mechanics · Compute gravitational potential energy near a planetary surface
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| mass | mass | kg | 1.0 | Mass of the body |
| gravity | gravity | m/s^2 | 1.0 | Local gravitational acceleration |
| height | height | m | 1.0 | Height above the reference datum |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | PE | J | Gravitational potential energy, in joules (J) |
The science & history
Understanding the Parameters
- $m$ — heavier objects store more PE at the same height.
- $g$ — use local $g$; not the same as Newton’s $G$. Registry default
1.0is a placeholder. - $h$ — vertical height relative to your datum (floor, table, sea level, …).
- $PE$ — convertible to Kinetic Energy in free fall (ideal: $mgh = \tfrac12 mv^{2}$).
Derivation (Approaching a Proof)
Weight force is $F = mg$ downward (constant $g$). Work to lift slowly through height $h$ is $W = mgh$. That work is stored as gravitational PE in the uniform-field approximation. For Newtonian point masses use $U = -GMm/r$ instead (see Escape Velocity energy balance).
History
Gravitational PE in the $mgh$ form is the engineering workhorse for lifting, hydropower head, and introductory mechanics; the $1/r$ form is required for orbital scales.
Related Concepts: Kinetic Energy, Work Constant Force, Gravitational Force, Elastic Potential Energy, Power
Notes: Registry calculator potential-energy (unverified). Uniform $g$ only. Set $g \approx 9.81$
for Earth-surface problems if the default is 1.