MihsabaShare this free calculator
Send this tool to someone who needs the calculation.
How to use
This gravitational potential energy (GPE) calculator uses U=mgh near a surface where gravitational acceleration can be treated as constant. It can solve for energy, mass, height or local g, and it keeps g (acceleration due to gravity) distinct from the universal gravitational constant G. Height may be negative below the chosen reference level.
- Choose the unknown: energy, mass, height or g.
- Choose SI or imperial units and enter the known values.
- Calculate to display all quantities after internal unit normalization.
How it is calculated
Example
GPE example: for m=2 kg, h=5 m and g=9.80665 m/s², U=2×9.80665×5≈98.0665 J. A second example, m=10 kg at h=3 m, gives U≈294.1995 J relative to the same chosen zero level.
Important notes
The value of U depends on the chosen zero level. mgh is a local constant-g approximation; large planetary distances or orbital problems require the general gravitational form U=-GMm/r.
Worked examples and interpreting results
A mass of 2 kg at height 5 m above a reference level has potential energy 98 J when g=9.8 m/s² is assumed. Doubling height doubles energy in the constant-gravity model.
| Case | Calculation | Result |
|---|---|---|
| Energy at height 5 m | 2 × 9.8 × 5 | 98 J |
| Energy at height 10 m | 2 × 9.8 × 10 | 196 J |
How to check the result
Choose the zero-height reference and set g to 9.8 to reproduce the example. This relation is a local approximation with constant gravity, not a universal formula at every distance from a planet. Energy differences use height differences relative to the same reference.
Frequently asked questions
Can potential energy be negative?
Yes in the mgh reference-level model if the object is below the chosen zero; energy differences are often what matter.
What is standard g in imperial units?
Standard gravity g₀=9.80665 m/s², which is approximately 32.1740486 ft/s². You can enter a different local value when needed.
Is g the same as the gravitational constant G?
No. g is local gravitational acceleration measured in m/s² or ft/s²; G is the universal gravitational constant used in Newton’s law of gravitation.
Why is default g 9.80665?
It is standard gravity used as a reference and for unit conversion; you can enter another local value.
Does the energy change depend on the chosen zero level?
No. Moving the zero level adds a constant to potential-energy values but does not change the difference between two positions when the same reference is used throughout.