Quick answer
Gravitational potential energy is PE = m g h. A 10 kg mass raised 5 m with g = 9.80665 m/s² stores 490.33 J.
Enter mass, height and gravitational acceleration. The calculator returns the potential energy.
Related tools: Energy Converter: Convert joules, calories, kWh, BTU and more. Power Calculator: Mechanical power from work and time, or force and velocity. Solar Panel Output Calculator: Daily, monthly and yearly energy from a solar array.
How to use the Potential Energy Calculator
- Enter mass (kg) (above 0).
- Enter height (m).
- Enter gravitational acceleration (m/s²) (above 0). It starts at 9.80665.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Mass | A number, in kg | > 0 |
| Height | A number, in m | — |
| Gravitational acceleration | A number, in m/s² | > 0, starts at 9.80665 |
Formula and method
Formula
PE = m g h
IEEE-754 double precision; shown to the decimals indicated.
Standard gravity by default; use 1.62 for the Moon or 3.71 for Mars.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Mass = 10; Height = 5; Gravitational acceleration = 9.80665.
| Result | Value |
|---|---|
| Potential energy | 490.3325 J |
Example 2
Inputs: Mass = 70; Height = 100; Gravitational acceleration = 9.80665.
| Result | Value |
|---|---|
| Potential energy | 68,646.55 J |
Example 3
Inputs: Mass = 2; Height = 3; Gravitational acceleration = 1.62.
| Result | Value |
|---|---|
| Potential energy | 9.72 J |
The first line is the headline result (potential energy). IEEE-754 double precision; shown to the decimals indicated.
Reference level
Height is relative to your chosen zero level, so only changes in PE matter. Letting the 10 kg mass fall 5 m converts the 490.33 J to kinetic energy: v = √(2gh) = 9.9 m/s.
Other gravity
On the Moon (g = 1.62 m/s²) the same lift stores 81 J. For large heights use the full inverse-square form. A 1 kg book lifted 1 m stores 9.8 J.
How the result changes with mass
Holding every other input at the first worked example, this table changes only mass. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Mass | Potential energy |
|---|---|
| 5 | 245.16625 J |
| 10 | 490.3325 J |
| 20 | 980.665 J |
| 40 | 1,961.33 J |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Mass: entering "0" shows "Mass must be greater than 0." beside that field and no result.
- Gravitational acceleration: entering "0" shows "Gravitational acceleration must be greater than 0." beside that field and no result.
Choosing between the Potential Energy Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Energy Converter](/converters/energy-converter/) | value, from and to | Megawatt-hour (MWh) → Kilowatt-hour (kWh) |
| [Power Calculator](/science/power-calculator/) | use | Power |
| [Solar Panel Output Calculator](/science/solar-panel-output-calculator/) | panel rating, number of panels and peak sun hours per day | Energy |
| [Solar Payback Calculator](/science/solar-payback-calculator/) | system cost and annual savings | Payback period |
| [Wind Power Estimate Calculator](/science/wind-power-estimate-calculator/) | rotor diameter, wind speed and power coefficient | Power |
Background: motion and mechanics
For constant acceleration the standard relations are v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t. Pick the equation that contains your three known quantities and the one you want. Use SI units (metres, seconds, kilograms, newtons, joules) throughout or the answer will be off by a factor.
These equations stop applying when acceleration changes during the motion, as with a rocket burning fuel; that needs calculus or numerical methods.
Assumptions and limitations
- Height is relative to your chosen zero level
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for mass and gravitational acceleration to confirm this.
Frequently asked questions
What is the unit of PE?
Potential energy is in joules; a 10 kg mass lifted 5 m stores 490.33 J.
Does PE depend on the path?
No. Gravitational potential energy depends only on the height difference, not the route taken.
How much PE does a 70 kg climber gain going up 100 m?
A 70 kg climber gains 70 × 9.80665 × 100 ≈ 68,647 J, about 68.6 kJ.
What does the Potential Energy Calculator calculate?
Gravitational potential energy from mass, height and gravity. It returns Potential energy.
What formula does the Potential Energy Calculator use?
PE = m g h. Standard gravity by default; use 1.62 for the Moon or 3.71 for Mars.
What do I need to enter in the potential Energy Calculator?
You enter Mass (kg), Height (m) and Gravitational acceleration (m/s²).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Height is relative to your chosen zero level.
What is an example of a potential Energy result?
With mass 10, height 5 and gravitational acceleration 9.80665, the potential energy is 490.3325 J.
Related calculators
- Energy Converter — Convert joules, calories, kWh, BTU and more.
- Power Calculator — Mechanical power from work and time, or force and velocity.
- Solar Panel Output Calculator — Daily, monthly and yearly energy from a solar array.
- Solar Payback Calculator — Simple payback period of an installation after incentives.
- Wind Power Estimate Calculator — Power from a wind turbine rotor at a wind speed.
- Work Calculator — Work done by a force over a distance at an angle.
Sources
- CODATA 2018 / SI exact constants: g₀ = 9.80665 m/s², c = 299,792,458 m/s, h = 6.62607015×10⁻³⁴ J·s, e = 1.602176634×10⁻¹⁹ C, G = 6.67430×10⁻¹¹ m³/(kg·s²)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.