Potential Energy Calculator
Use this calculator to find gravitational potential energy using the equation PE = m × g × h.
m = mass (kilograms), g = gravitational acceleration (m/s²), h = height (meters)
What is potential energy?
Potential energy is stored energy. In mechanics, it often refers to the energy an object has due to its position in a force field. The most common classroom example is gravitational potential energy: when an object is raised above the ground, it stores energy that can later convert into motion (kinetic energy) when the object falls.
If you lift a backpack onto a shelf, you do work against gravity. That work is now stored as potential energy in the backpack-Earth system. The higher you lift it (or the heavier the backpack), the more potential energy is stored.
The gravitational potential energy formula
Near Earth’s surface, gravitational potential energy is calculated with:
PE = m × g × h
- PE is potential energy in joules (J)
- m is mass in kilograms (kg)
- g is gravitational acceleration in meters per second squared (m/s²)
- h is vertical height in meters (m)
On Earth, g ≈ 9.81 m/s² is often used. In simpler exercises, you may see g = 9.8 or even 10 to make mental math easier.
Unit check (dimensional consistency)
A good habit in physics is to check units:
kg × (m/s²) × m = kg·m²/s² = joule (J)
So the formula is unit-consistent.
Step-by-step: how to calculate potential energy
- Measure or identify the object’s mass in kilograms.
- Find the vertical height above a reference level.
- Choose an appropriate value for gravitational acceleration.
- Multiply: mass × gravity × height.
- Report your answer in joules (J).
Worked example
Suppose a 5 kg object is lifted 2 meters on Earth:
PE = 5 × 9.81 × 2 = 98.1 J
The object has about 98.1 joules of gravitational potential energy relative to the original height.
Common gravity values
| Location | Approximate g (m/s²) |
|---|---|
| Earth | 9.81 |
| Moon | 1.62 |
| Mars | 3.71 |
| Jupiter | 24.79 |
Common mistakes when calculating potential energy
- Using weight instead of mass: The formula requires mass in kg, not force in newtons.
- Using the wrong height: Use vertical height difference, not path length.
- Mixing units: Convert centimeters to meters and grams to kilograms first.
- Using the wrong gravity: If the problem is on the Moon or Mars, change g accordingly.
Why this matters in real life
Potential energy calculations show up in engineering, sports science, construction, and energy systems:
- Hydropower: Water stored at height has potential energy that turbines convert into electricity.
- Roller coasters: Initial climb stores energy that drives the ride’s motion.
- Safety analysis: Estimating fall energy helps design safer equipment and structures.
- Robotics and lifting systems: Engineers estimate motor requirements using energy changes.
Beyond gravity: other forms of potential energy
Elastic potential energy
Springs and elastic materials store energy when stretched or compressed: PE = ½kx², where k is spring constant and x is displacement.
Electric potential energy
Charged particles in electric fields also store potential energy, which is central to circuits, batteries, and electromagnetism.
Final takeaways
Calculating potential energy is straightforward once you remember the three key inputs: mass, gravity, and height. Use consistent SI units, keep track of your reference level, and interpret the result in joules. The calculator above gives you a quick way to compute values for Earth or other celestial bodies.