Key takeaways
- Potential energy is PE = m × g × h, measured in joules.
- On Earth, g is about 9.8 m/s²; on the Moon it's only about 1.6 m/s².
- Height must be measured in metres from the point where the object would land.
- As an object falls, potential energy converts into kinetic energy.
In this guide
What is gravitational potential energy?
Potential energy is stored energy based on position. A book on a high shelf has more of it than the same book on the floor, because gravity is ready to pull it down and do work along the way.
Why does gravitational potential energy matter?
Every roller coaster, dam, and pendulum runs on the same idea: lift something up, and it stores energy you can release later. The higher you lift it, the more energy is waiting.
A hydroelectric dam is really just a giant potential-energy battery. Water held high behind the wall stores energy that turns into electricity the moment it's allowed to fall.
The formula
| Symbol | What it means | Example |
|---|---|---|
| PE | The potential energy, in joules (J) | 29.4 J |
| m | The mass of the object, in kilograms (kg) | 2 kg |
| g | Gravity's pull, about 9.8 m/s² on Earth | 9.8 m/s² |
| h | The height above the reference point, in metres (m) | 1.5 m |
How to calculate potential energy step by step
- 1Find the mass. Weigh the object in kilograms.
- 2Use g = 9.8 m/s². This is Earth's gravity — no need to measure it yourself.
- 3Measure the height. Use metres, counted from where the object would land.
- 4Multiply all three together.
m × g × hgives the energy in joules.
Try the calculator below with your own mass and height to see the full working.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Forgetting units. Height must be in metres — 150 cm needs to become 1.5 m first.
- Using the wrong g. On the Moon, g is about 1.6 m/s², so the same object stores much less potential energy there than on Earth.
- Treating PE as a fixed property. Potential energy always depends on your chosen reference height, so the same object can have different PE values depending on what you measure from.
Tips and tricks
- To estimate quickly, round g to 10 m/s². It's close enough for a rough answer and much easier to multiply.
- Working backwards from energy to height? Divide by mass, then by gravity:
h = PE ÷ (m × g). - Potential energy is the natural partner of kinetic energy — together they track an object's energy as it falls, as in the free fall distance calculator.
Where you'll use it in real life
- Energy: hydroelectric dams store water at height and release it to generate power.
- Entertainment: roller coasters convert stored height into speed at the bottom of every drop.
- Construction: cranes do work lifting materials, storing potential energy that must be controlled carefully as loads come back down.
- Sport: a diver standing on a high board carries more potential energy than one on a low board, before either of them jumps.
Quick summary
To find gravitational potential energy, multiply mass by gravity (9.8 m/s² on Earth) by height in metres. The higher or heavier the object, the more energy it has stored, ready to convert into motion the moment it falls. Use the calculator above to work through your own example.
Worked example
You lift a 2 kg book from the floor onto a shelf 1.5 m high. How much gravitational potential energy does the book gain?
- 01PE = mgh
- 02PE = 2 × 9.8 × 1.5
- 03PE = 29.4 J
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I calculate gravitational potential energy?
Multiply the object's mass in kilograms by gravity (9.8 m/s² on Earth) by its height above the ground in metres. The result is in joules.
What value of gravity should I use?
Use 9.8 m/s² for Earth. Some textbooks round it to 9.81 m/s², which changes the answer only slightly.
What happens to potential energy when an object falls?
It converts into kinetic energy. As height decreases, speed increases, so the total energy, ignoring air resistance, stays the same.
Can potential energy be negative?
Yes, if you measure height below your chosen reference point, such as an object at the bottom of a well relative to ground level.
