Free Potential Energy Calculator

Mass (m)

Gravitational Acceleration (g)

Height (h)

Formula

PE = m × g × h

Enter mass, gravity, and height to see potential energy

Understanding Gravitational Potential Energy

The Potential Energy Calculator is a free online tool for computing gravitational potential energy based on the object's mass, height, and the local gravitational acceleration. Gravitational potential energy itself is the energy stored in an object due to its position above a reference level. With this calculator, you simply enter three values—the mass, the gravitational acceleration (typically $9.81\ \text{m/s}^{2}$ on Earth), and the height—and it instantly returns the stored energy in joules. If you have only three of the four related variables (mass, height, gravity, or potential energy), the tool can also solve for the missing one.

For studying moving objects, the companion Kinetic Energy Calculator is often used alongside this Gravitational Potential Energy Calculator to analyze conversions between potential and kinetic energy.

The Core Formula

The foundation of the calculation is the gravitational potential energy formula:

E_{\text{grav}} = m \cdot g \cdot h

where:

$E_{\text{grav}}$ — gravitational potential energy (joules),
$m$ — mass of the object (kilograms),
$h$ — height above the reference level (meters),
$g$ — gravitational field strength (approximately $9.81\ \text{m/s}^{2}$ at Earth's surface).

A key property is that potential energy is directly proportional to both mass and height. Therefore, if the mass or height is doubled, the potential energy doubles; if either is halved, the energy is halved. An object resting on the ground (height = 0) has zero potential energy.

Worked Example: Apple on a Branch

A practical illustration involves an apple with a mass of $0.1\ \text{kg}$ hanging from a branch $2.5\ \text{m}$ above the ground. Applying the formula:

E = 0.1\ \text{kg} \times 2.5\ \text{m} \times 9.81\ \text{m/s}^{2} = 2.4525\ \text{J}

This amount of energy is roughly half a calorie. When the apple detaches and falls, the gravitational potential energy converts into kinetic energy, demonstrating the conservation of mechanical energy. Similar conversions occur in physics problems involving inclined planes, free fall, and roller coasters.

Using the Formula in Real-World Scenarios

The Potential Energy Formula $E = mgh$ is widely used in physics and engineering. It helps calculate the potential energy stored in a raised weight, water behind a dam, or any object subject to gravity. Whether you are a student solving textbook problems or a professional estimating energy in a system, this tool makes the computation quick and accurate.

FAQ

1. How do I calculate gravitational potential energy with the calculator?

Input the mass (kg), height (m), and gravitational acceleration (default 9.81 m/s²). The calculator multiplies them using the formula E = m·g·h and displays the result in joules. You can also rearrange the inputs to find mass, height, or gravity if you know the other three.

2. What is the gravitational potential energy formula?

The formula is E = m·g·h, where E is potential energy, m is mass, g is gravitational acceleration (about 9.81 m/s² on Earth), and h is height above the reference level. It assumes a constant gravitational field.

3. What units does the calculator use?

It expects mass in kilograms, height in meters, and gravitational acceleration in meters per second squared, and outputs potential energy in joules. Some versions also allow alternative unit selections.

4. If I double the height of an object, what happens to its potential energy?

Since potential energy is directly proportional to height, doubling the height exactly doubles the stored energy. For example, raising the apple from 2.5 m to 5 m would increase its energy from 2.4525 J to 4.905 J.

5. How is gravitational potential energy different from kinetic energy?

Gravitational potential energy depends only on the object's position (height) and mass, while kinetic energy depends on its speed. They are different forms of mechanical energy that can convert into each other, such as during free fall where potential energy transforms into kinetic energy.

How to Use

Enter the mass of the object and select the appropriate mass unit (kg, g, lb, oz, etc.).
Enter the gravitational acceleration (default to Earth's 9.81 m/s²) and the height above the reference level.
The gravitational potential energy is calculated instantly. Switch the energy display unit to view the result in joules, kWh, calories, or other units.