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Physics formula

How to calculate gravitational potential energy

Gravitational potential energy estimates stored energy from lifting a mass to a height.

See the formulaOpen calculator
Direct answer
Formula
PE = m * g * h

Use the table below to match each symbol with the right input. Keep units consistent before you start.

Gravitational potential energy formula
Start here when you only need the equation and variable names.
Formula
PE = m * g * h

Gravitational potential energy estimates stored energy from lifting a mass to a height.

Variable meanings
Check each symbol, meaning, and unit before you calculate.
SymbolNameDescriptionUnit
PEPotential energyStored gravitational energy.J
mMassObject mass.kg
gGravityGravitational acceleration.m/s^2
hHeightHeight above the reference point.m
When to use this formula
Check that your situation matches the formula before you trust the result.
  • Works near Earth's surface when g can be treated as about 9.81 m/s^2.
Step-by-step method
Follow these steps when you are solving it by hand.
  1. 1Convert mass to kilograms.
  2. 2Convert height to meters.
  3. 3Use g = 9.81 m/s^2 unless a problem gives another value.
  4. 4Multiply mass, gravity, and height.
Examples
These sample numbers show the order of operations and units.
Lifted box
m
5 kg
g
9.81 m/s^2
h
2 m
  1. 1.PE = 5 * 9.81 * 2
  2. 2.PE = 98.1 J
Result
The potential energy is 98.1 J.
Raised load
m
20 kg
g
9.81 m/s^2
h
10 m
  1. 1.PE = 20 * 9.81 * 10
  2. 2.PE = 1962 J
Result
The potential energy is 1,962 J.
Mistakes to avoid
Small input or unit errors can change the answer a lot.
  • Mixing metric and imperial units before solving the gravitational potential energy formula.
  • Forgetting squared units such as m^2, m/s^2, or velocity squared.
  • Dropping negative signs when direction matters.
  • Rounding measured values too early in the calculation.
Open the Potential Energy Calculator
Open the calculator for the answer without rewriting the formula.

Enter your values in the related calculator, then compare the output with the hand method above.

Open Potential Energy Calculator
FAQs
Short answers for common formula questions.
Can I calculate Gravitational potential energy by hand?

Yes. Write the units next to each value, convert rates or measurements first, and round only the final answer.

Why does my Gravitational potential energy result differ from another calculator?

Most differences come from rounding, unit conversions, rate timing, or a slightly different version of the formula.

When is the Potential Energy Calculator better than hand math?

Open the Potential Energy Calculator to check several scenarios or skip the hand arithmetic.