How to calculate gravitational potential energy
Lifting an object raises its gravitational potential energy relative to a reference height. The height reference must be stated because a height is never meaningful by itself.
What the formula is saying
Near Earth’s surface with constant g, weight is mg. Multiplying by height h gives PE = mgh. For an energy change, use the height change instead.
Read the symbols in plain language
- m
- Masskg
- g
- Gravitym/s²
- h
- Heightm
Sort out the units first
Use kg, m/s² and vertical metres to obtain joules. The example uses 2 m above the chosen zero level.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- m · Mass
- 50 kg
- g · Gravity
- 9.81 m/s²
- h · Height
- 2 m
Find the weight
Mass times g gives the downward gravitational force magnitude.
(50) × (9.81) = 490.5 NMultiply by vertical height
Use vertical rise, not distance travelled along a ramp.
(490.5) × (2) = 981 J
Does this worked answer make sense?
Doubling mass or height doubles the energy relative to the same reference. The worked result is 981 J.
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Use these new values. Work it out first, then check your answer.
- m · Mass
- 20 kg
- g · Gravity
- 9.81 m/s²
- h · Height
- 3 m
Find: gravitational potential energy
A hint, not the answer
Near Earth’s surface with constant g, weight is mg. Multiplying by height h gives PE = mgh. For an energy change, use the height change instead.
Use kg, m/s² and vertical metres to obtain joules. The example uses 2 m above the chosen zero level.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Find the weight
Mass times g gives the downward gravitational force magnitude.
(20) × (9.81) = 196.2 NMultiply by vertical height
Use vertical rise, not distance travelled along a ramp.
(196.2) × (3) = 588.6 J
Avoid the common trap
Ramp length is not h. A negative potential energy can simply mean the point is below the chosen zero, not that the calculation is broken.
When this method applies — and when it does not
Uniform gravitational field approximation. This is not the general gravitational potential formula for large changes in distance from Earth.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.