Potential Energy Calculator
Gravitational potential energy PE = mgh, solved for any of the four quantities.
What is Potential Energy?
Gravitational potential energy is the energy stored in lifting something: PE = mgh. It is what a roller coaster has at the top of its first hill, and what converts into kinetic energy on the way down. It is always measured relative to a height you choose, since only changes in potential energy are physically meaningful.
How it works
The formula is rearranged for whichever field is blank, so the tool can also answer 'how high does this mass have to be raised' or 'what g must this be'. Heights may be in metres, centimetres, kilometres or feet, and g can be set for anywhere from the Moon to Jupiter — or to 9.8, the rounding most textbooks use.
- Enter what you know. Every field recalculates as you type — there is no submit button. Leave the quantity you want blank and the page solves for it.
- Read the answer and the working. The result appears above the fold; underneath it is the formula with your numbers substituted, so the arithmetic can be checked rather than trusted.
- Check the units and the size. Units are shown on every value and selectable per field, so a result in kJ, kPa or km/h is converted rather than assumed. Sanity-check the magnitude against a known landmark such as 1 g/cm³ for water.
Examples
A textbook problem with a known answer
Every tool here is checked against standard example problems — the molar mass of C6H12O6 is 180.16 g/mol, and free fall from 20 m takes about 2.02 s at g = 9.8 m/s².
A result you want to reason backwards from
Leave the quantity you already know blank instead: given the final answer, most tools recover the starting value — the mass needed for a target concentration, or the height a fall must have had.
Common mistakes
Forgetting that a formula is only as good as its subscripts
H2O and H2O2 are different compounds. The formula field shows its parse — element by element — so a mis-typed subscript is visible before it reaches the arithmetic.
Mixing units in the middle of a calculation
The most common source of a wrong answer is a value in grams next to a formula expecting kilograms, or Celsius next to a gas constant expecting kelvin. This category converts on the way in and labels what it used.
Frequently asked questions
What is the potential energy of 2 kg raised 3 m?
58.8 J at g = 9.8 m/s². PE = mgh = 2 × 9.8 × 3 — the example on this page loads exactly those values.
Why do textbooks use 9.8 rather than 9.80665?
Rounding to 9.8 keeps the working clean and rarely changes the answer beyond the significant figures given in a problem. This calculator offers both so a check against a textbook answer is exact.
Does it matter where I measure height from?
No, as long as you are consistent, because only the change in height enters any calculation. A datum of the floor, the tabletop or sea level all give the same answer for the same fall.