Gravitational Potential Energy Calculator
Calculate Gravitational Potential Energy, Mass, Height, or Gravity with different units. Select the calculation type and units for each input.
Choose Calculation Type
Gravitational potential energy (GPE) is the stored energy an object has due to its position in a gravitational field. Whether you’re a physics student, engineer, or researcher, calculating GPE manually can be time-consuming.
This is where you will need the Gravitational Potential Energy Calculator! It allows you to instantly find the GPE of an object by entering mass, height, and gravitational acceleration—eliminating the need for manual calculations.
What is Gravitational Potential Energy?
Gravitational potential energy is the energy stored in an object due to its height above the ground. It depends on three key factors:
- Mass (m) – The object’s mass in kilograms (kg).
- Height (h) – The vertical distance from a reference point in meters (m).
- Gravitational Acceleration (g) – The acceleration due to gravity (9.81 m/s² on Earth).
The higher the object is above the ground, the greater its gravitational potential energy. This concept is crucial in physics, engineering, space exploration, and energy conservation.
For example:
- A book on a shelf has GPE due to its height.
- A roller coaster at its peak stores maximum GPE before descending.
- A dam stores potential energy in the form of water at a higher elevation.
Find Elastic Potential Energy for any elastic material using our Elastic Potential Energy Calculator.
Gravitational Potential Energy Formula
The standard formula to calculate gravitational potential energy is:
GPE Formula:
U = m × g × h
Where:
- U = Gravitational Potential Energy (Joules, J)
- m = Mass of the object (kg)
- g = Gravitational acceleration (9.81 m/s² on Earth)
- h = Height above reference point (m)
This equation shows that gravitational potential energy increases with greater mass and height.
Example Calculation
If a 5 kg object is lifted to a height of 10 meters, its gravitational potential energy will be:
Using the formula:
U = m × g × h
Substituting the values:
U = 5 × 9.81 × 10
Result:
U = 490.5 J
Thus, the object stores 490.5 Joules of energy.
You can also calculate Electric Potential Energy using our Electric Potential Energy Calculator.
How to Calculate Gravitational Potential Energy Using the Above Calculator?
Our Gravitational Potential Energy Calculator simplifies the process of calculating GPE, mass, height, or gravity with just a few inputs. Here’s how you can use it:
Steps to Use the Calculator
- Select Calculation Type:
- Choose what you want to calculate (GPE, mass, height, or gravity).
- Enter Known Values:
- If calculating GPE, enter mass, height, and gravity.
- If solving for mass, input GPE, height, and gravity.
- If finding height, provide GPE, mass, and gravity.
- If determining gravity, enter GPE, mass, and height.
- Choose Units:
- The calculator supports multiple units for mass, height, gravity, and energy to match your needs.
- Click ‘Calculate’:
- The tool will instantly compute the result and display it in multiple units.
- View and Convert Results:
- The results are shown in Joules (J), kilojoules (kJ), foot-pounds (ft-lb), and calories (cal) for easy reference.
Example Usage
Let’s say you want to find the gravitational potential energy of a 2 kg object lifted 5 meters above the ground.
- Select “Gravitational Potential Energy” as the calculation type.
- Enter mass = 2 kg, height = 5 m, and gravity = 9.81 m/s².
- Click “Calculate”, and the result will show:
Using the formula:
U = m × g × h
Substituting the values:
U = 2 × 9.81 × 5
Result:
U = 98.1 J
Calculate Potential Energy using our Potential Energy Calculator.
How Does the Gravitational Potential Energy Calculator Work?
The calculator follows three main steps to compute the result accurately:
1. Converts All Inputs to SI Units
Any input given in grams, centimeters, feet, or inches is first converted to standard units:
- Mass → kilograms (kg)
- Height → meters (m)
- Gravity → meters per second squared (m/s²)
These conversions ensure accuracy in gravitational potential energy calculations.
2. Uses the Standard GPE Formula
After converting units, the calculator applies the gravitational potential energy (GPE) equation:
Formula:
U = m × g × h
If solving for mass, height, or gravity, the formula is rearranged as follows:
Mass:
m = U / (g × h)
Height:
h = U / (m × g)
Gravity:
g = U / (m × h)
3. Converts Results into Multiple Units
Once the calculations are complete, the computed values are converted into various units for better usability:
- Energy → Joules (J), kilojoules (kJ), foot-pounds (ft-lb), calories (cal)
- Mass → kilograms (kg), grams (g), pounds (lb), ounces (oz)
- Height → meters (m), centimeters (cm), millimeters (mm), feet (ft), inches (in)
This allows flexibility in calculations for different measurement systems.
This makes the Gravitational Potential Energy Calculator extremely versatile and suitable for students, engineers, and researchers.
Gravitational Potential Energy of Different Objects
Different objects have varying gravitational potential energy based on their mass and height. The table below gives an idea of how GPE varies for real-world objects:
| Object | Mass (kg) | Height (m) | GPE (Joules) |
|---|---|---|---|
| Apple | 0.2 | 1 | 1.96 |
| Basketball | 0.6 | 2 | 11.77 |
| Brick | 2.5 | 3 | 73.58 |
| Bowling Ball | 5 | 4 | 196.2 |
| Human (Avg) | 70 | 1.5 | 1030.35 |
| Car | 1500 | 1 | 14715 |
- Higher mass and height = Higher GPE
- Lighter objects have lower stored energy
Gravitational Potential Energy Units
Gravitational potential energy can be expressed in different units, depending on the system of measurement used. Here’s a quick conversion table for common units:
| Unit | Symbol | Equivalent to 1 Joule (J) |
|---|---|---|
| Joule | J | 1 |
| Kilojoule | kJ | 0.001 |
| Foot-pound | ft-lb | 0.73756 |
| Calorie | cal | 0.239 |
- SI Unit: The Joule (J) is the standard unit for GPE.
- Other Common Units: kJ (kilojoules) and ft-lb (foot-pounds) are used in engineering.
- Calorie (cal) is often used in food energy calculations but is also applicable for energy comparisons.
Examples of Gravitational Potential Energy
To understand gravitational potential energy better, here are some real-life examples:
- Pendulum at its Peak
- When a pendulum reaches its highest point, it has maximum gravitational potential energy before swinging down.
- Hydroelectric Dams
- Water stored behind a dam at a height has gravitational potential energy, which is later converted into electricity.
- Roller Coasters
- A roller coaster at its highest point before descending has maximum GPE and converts it into kinetic energy as it moves downward.
- Lifting Weights
- A weightlifter holding a barbell overhead is storing gravitational potential energy in the weight.
Solved Problems of Gravitational Potential Energy
Here are some numerical problems with step-by-step solutions, written in HTML for better formatting and SEO optimization.
Problem 1: Finding Gravitational Potential Energy
Problem: A 10 kg object is lifted to a height of 8 meters. Calculate its gravitational potential energy.
Solution:
Given:
- Mass (m) = 10 kg
- Height (h) = 8 m
- Gravity (g) = 9.81 m/s²
Using the formula:
U = m × g × h
U = 10 × 9.81 × 8
U = 784.8 J
Answer: The gravitational potential energy is 784.8 Joules.
Problem 2: Finding Mass Using G.P.E. Formula
Problem: An object has 500 Joules of gravitational potential energy and is 5 meters above the ground. Find its mass.
Solution:
Given:
- GPE (U) = 500 J
- Height (h) = 5 m
- Gravity (g) = 9.81 m/s²
Using the formula:
m = U / (g × h)
m = 500 / (9.81 × 5)
m = 10.19 kg
Answer: The object’s mass is 10.19 kg.
About the Creator
Dr. Evren Frost | PhD in Physics
I am a physicist with a passion for creating educational tools that simplify physics concepts for students. With years of experience in research and teaching, I have designed this platform to help learners understand and solve complicated scientific problems effortlessly using different types of tools.
Conclusion
The Gravitational Potential Energy Calculator is an essential tool for students, engineers, and researchers who need quick and accurate GPE calculations.
Gravitational potential energy is a fundamental concept in physics and engineering, playing a key role in mechanical systems, power generation, and energy conservation.
FAQs
Gravitational potential energy (G.P.E.) is the energy stored in an object due to its height in a gravitational field. It depends on the object’s mass, height, and gravity.
The SI unit of GPE is the Joule (J).
You can use the formula: U=mghU = mghU=mgh
Where:
m = mass in kg
g = gravity (9.81 m/s² on Earth)
h = height in meters
Yes, GPE is directly proportional to mass. A heavier object has more gravitational potential energy than a lighter one at the same height.
Yes, if the reference point is chosen above the object, G.P.E. can be negative. However, in most physics problems, height is taken as positive from a reference point (ground level).
When an object falls, its GPE converts into kinetic energy (KE). At the lowest point, all energy is kinetic.
In zero gravity (space), gravitational potential energy is minimal or negligible since there is no significant gravitational force acting on objects.
Some common applications include:
1. Dams and hydroelectric power plants
2. Roller coasters and amusement park rides
3. Satellite and space station calculations
4. Elevators and mechanical pulleys
The G.P.E. calculator was designed by Dr. Evren Frost, a physicist with a PhD in Physics, who is passionate about creating tools to help students master physics concepts easily.