Gravitational Potential EnergyFree online science calculator — instant results, no sign-up
Calculate potential energy from mass, height and gravity (PE = mgh).
About the Gravitational Potential Energy
The Gravitational Potential Energy calculator computes PE = mgh from mass in kilograms and height in meters using a fixed gravity of 9.80665 m/s². It estimates energy relative to a chosen reference height in a uniform gravitational field. With the default mass of 10 kg and height of 5 m, the calculator displays a potential energy of 490.332 J.
- Mass (kg)
- The object's mass in kilograms, with a default value of 10 kg.
- Height (m)
- The object's vertical height in meters above your chosen zero-energy reference level, with a default value of 5 m.
Formula and method
PE = m × g × h, with g = 9.80665 m/s²; for the default inputs, PE = 10 × 9.80665 × 5 = 490.3325 J, displayed as 490.332 J.
- PEGravitational potential energy relative to the reference level, measured in joules (J).
- mThe object's mass, measured in kilograms (kg).
- gGravitational acceleration, fixed by this calculator at the standard value of 9.80665 m/s².
- hVertical height above the chosen reference level, measured in meters (m).
The calculator multiplies the entered mass by the fixed gravitational acceleration and the entered height. The resulting units, kg·m²/s², are equivalent to joules. For 10 kg and 5 m, the unformatted product is 490.3325 J; the supplied example displays 490.332 J and reports the gravity used separately.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Mass10 kg
- Height5 m
Results
- Potential energy490.332 J
- Gravity used9.80665 m/s²
How to use the Gravitational Potential Energy
- 1Choose a reference level where gravitational potential energy is defined as zero.
- 2Enter the object's mass in Mass (kg), or keep the default of 10.
- 3Enter its vertical height above that reference in Height (m), or keep the default of 5.
- 4Run the calculation using the fixed gravity of 9.80665 m/s².
- 5Read the Potential energy and Gravity used rows; the defaults display 490.332 J and 9.80665 m/s².
Reading your result
Potential energy reports the energy associated with the object's height relative to your chosen reference level. The default result of 490.332 J represents the ideal work needed to raise a 10 kg object through 5 m at constant speed, ignoring losses. Gravity used reports 9.80665 m/s², the fixed acceleration used in the calculation, not a measurement of local gravity.
Limitations
The formula assumes gravity is uniform over the height interval, making it appropriate for ordinary height changes near Earth's surface. Actual gravity varies with location and altitude, and this tool does not accept a custom gravity value. Large altitude changes or calculations for other celestial bodies require a different treatment. Results depend on the selected zero-height reference and do not include friction, air resistance, or lifting-system efficiency. Display precision does not establish physical measurement accuracy.
Common questions
Can I use this calculator for the Moon or another planet?+
Not directly. This tool fixes gravity at 9.80665 m/s², so its output does not represent lunar or planetary potential energy unless that gravity value is appropriate.
Should height be measured from the ground or from sea level?+
Use the reference level relevant to your problem, such as the ground or the starting position of a lift. Height is the vertical separation from that reference, not necessarily elevation above sea level.
Why is the default result shown as 490.332 J rather than 490.3325 J?+
Multiplying 10 × 9.80665 × 5 gives 490.3325 J exactly for the stated inputs. The supplied output displays 490.332 J; that is a display-formatting difference, not a different gravity value.
Is the reported potential energy the electricity a hoist would consume?+
No. It is the ideal increase in gravitational potential energy. A real hoist generally consumes more energy because its motor and mechanical components are not perfectly efficient.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.