Potential Energy Calculator
Calculate gravitational potential energy, mass, or height using the fundamental physics formula PE = mgh. Enter your values and select the gravitational environment to get instant, accurate results in joules.
Potential Energy Calculator
Inputs
Enter parameters to calculate Gravitational Potential Energy, Mass, or Height.
Understanding Potential Energy
Potential energy is the energy stored in an object due to its position, configuration, or state within a force field. It represents the capacity to perform work when the object is released or allowed to change its position. Unlike kinetic energy, which is the energy of motion, potential energy is latent -- it exists as stored energy waiting to be converted into other forms.
The PE = mgh Formula
The gravitational potential energy of an object near the surface of a planet is calculated using the formula PE = mgh. This equation tells us that potential energy increases linearly with mass, gravitational acceleration, and height. Doubling any one of these variables will double the potential energy. The result is expressed in joules (J), the standard SI unit of energy. One joule is equal to the energy required to lift a 102-gram object by one meter on Earth.
PE = m × g × h
- PE = Potential Energy in joules (J)
- m = Mass in kilograms (kg)
- g = Gravitational acceleration in m/s² (9.8 m/s² on Earth)
- h = Height above the reference point in meters (m)
Types of Potential Energy
While this calculator focuses on gravitational potential energy, there are several important types of potential energy encountered in physics and engineering:
- Gravitational Potential Energy: Energy stored due to an object's elevation in a gravitational field. A ball held at shoulder height, water behind a dam, and a skydiver in an aircraft all possess gravitational PE.
- Elastic Potential Energy: Energy stored in objects that are stretched or compressed. Springs, rubber bands, trampolines, and archery bows store elastic PE described by the formula PE = ½kx².
- Chemical Potential Energy: Energy stored in the bonds between atoms and molecules. Food, fossil fuels, batteries, and explosives all contain chemical PE that is released during chemical reactions.
Energy Conservation and the PE-KE Relationship
The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. When an object falls, its gravitational potential energy is progressively converted into kinetic energy. At the top of its path, the object has maximum PE and zero KE. At the bottom, just before impact, the object has maximum KE and minimum PE. The total mechanical energy (PE + KE) remains constant throughout the fall, assuming no energy is lost to air resistance or friction.
How Height Affects Potential Energy
Height is one of the most intuitive factors in the PE = mgh equation. The higher an object is positioned above the reference point, the greater its gravitational potential energy. This is why hydroelectric dams are built in mountainous terrain where water can fall from great heights, and why roller coasters start with a tall initial hill. A 1 kg object at 10 meters has 98 J of PE on Earth, but the same object at 100 meters stores 980 J -- ten times the energy for ten times the height. This linear relationship makes height a powerful lever for engineering applications that harness gravitational energy.
Potential Energy of Common Scenarios
The following table provides approximate gravitational potential energy values for everyday objects and situations on Earth (g = 9.8 m/s²). These values illustrate how mass and height combine to determine stored energy.
| Scenario | Mass (kg) | Height (m) | PE (Joules) |
|---|---|---|---|
| Book on a shelf | 1.5 | 1.8 | 26.5 J |
| Person on stairs (2nd floor) | 70 | 3.5 | 2,401 J |
| Roller coaster at peak | 3,000 | 65 | 1,911,000 J |
| Skydiver at jump altitude | 85 | 4,000 | 3,332,000 J |
| Hydroelectric dam reservoir | 1,000,000 | 150 | 1,470,000,000 J |
Note: Values are calculated using g = 9.8 m/s² and rounded for clarity. Actual values may vary slightly depending on geographic location and altitude.
How to Calculate Potential Energy
The following step-by-step examples demonstrate how to apply the PE = mgh formula to solve for potential energy, mass, and height in real-world situations.
Example 1: Finding Potential Energy
A 5 kg bowling ball sits on a shelf that is 2 meters above the floor. What is the gravitational potential energy of the bowling ball relative to the floor?
Given:
Mass (m) = 5 kg
Height (h) = 2 m
Gravity (g) = 9.8 m/s²
Solution:
PE = m × g × h
PE = 5 × 9.8 × 2
PE = 98 Joules
The bowling ball stores 98 joules of gravitational potential energy. If it falls off the shelf, all 98 J will convert into kinetic energy just before hitting the floor.
Example 2: Finding Mass from Known PE and Height
An object resting on a platform 12 meters above the ground has 3,528 joules of gravitational potential energy. What is the mass of the object?
Given:
Potential Energy (PE) = 3,528 J
Height (h) = 12 m
Gravity (g) = 9.8 m/s²
Solution (rearranged: m = PE / (g × h)):
m = 3528 / (9.8 × 12)
m = 3528 / 117.6
m = 30 kg
The object has a mass of 30 kilograms. By rearranging the PE formula, you can determine any unknown variable when the other two are known.
Example 3: Finding Height on the Moon
A 50 kg lunar rover module has 4,050 joules of gravitational potential energy on the Moon (g = 1.62 m/s²). At what height above the lunar surface is the module positioned?
Given:
Potential Energy (PE) = 4,050 J
Mass (m) = 50 kg
Gravity (g) = 1.62 m/s² (Moon)
Solution (rearranged: h = PE / (m × g)):
h = 4050 / (50 × 1.62)
h = 4050 / 81
h = 50 meters
The lunar rover module is 50 meters above the Moon's surface. Notice that on the Moon, where gravity is only about 16.5% of Earth's, the same amount of energy corresponds to a much greater height than it would on Earth.
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