Potential Energy Calculator

Common Examples

Input	Result
m = 10 kg, g = 9.81 m/s^2, h = 5 m	PE = 490.50 J
m = 75 kg, g = 9.81 m/s^2, h = 10 m	PE = 7,357.50 J
PE = 1,000 J, g = 9.81 m/s^2, h = 20 m	m = 5.10 kg
PE = 500 J, m = 25 kg, g = 9.81 m/s^2	h = 2.04 m
m = 50 kg, g = 1.62 m/s^2 (Moon), h = 10 m	PE = 810.00 J

How It Works

This calculator uses the gravitational potential energy formula:

PE = m x g x h

Where:

PE = gravitational potential energy in Joules (J)
m = mass of the object in kilograms (kg)
g = gravitational acceleration in meters per second squared (m/s^2)
h = height above the reference point in meters (m)

The formula can be rearranged to solve for any variable:

Potential Energy: PE = m x g x h
Mass: m = PE / (g x h)
Height: h = PE / (m x g)

Gravitational Acceleration Values

On Earth, g is approximately 9.81 m/s^2. This value varies slightly by location and altitude. For other celestial bodies: the Moon has g = 1.62 m/s^2, Mars has g = 3.72 m/s^2, and Jupiter has g = 24.79 m/s^2. The calculator allows you to change the gravity value for calculations on different planets or at different altitudes.

Potential vs. Kinetic Energy

Potential energy is stored energy based on an object’s position in a gravitational field. When an object falls, its potential energy converts to kinetic energy (KE = 0.5 x m x v^2). At the highest point, all energy is potential. At the lowest point (just before impact), all energy is kinetic. The total mechanical energy remains constant in the absence of friction and air resistance.

Reference Point

Potential energy is always measured relative to a chosen reference point (typically the ground or the lowest point in the system). The absolute value of PE depends on where you set h = 0. Only changes in potential energy have physical significance, so the choice of reference point does not affect the physics of the problem.

Worked Example

A 10 kg object sits on a shelf 5 meters above the ground. Using Earth’s gravity (g = 9.81 m/s^2): PE = 10 x 9.81 x 5 = 490.5 Joules. If the same object were on the Moon (g = 1.62 m/s^2) at the same height: PE = 10 x 1.62 x 5 = 81.0 Joules. To find what mass would store 1,000 Joules at 20 meters on Earth: m = 1,000 / (9.81 x 20) = 1,000 / 196.2 = 5.10 kg. To find the height needed to store 500 Joules with a 25 kg object on Earth: h = 500 / (25 x 9.81) = 500 / 245.25 = 2.04 meters.

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Frequently Asked Questions

What is gravitational potential energy?

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. The higher an object is above a reference point, the more potential energy it has. This energy can be converted into kinetic energy when the object falls. It is measured in Joules (J).

What units does this calculator use?

The calculator uses SI units: kilograms (kg) for mass, meters per second squared (m/s^2) for gravitational acceleration, meters (m) for height, and Joules (J) for energy. One Joule equals one kilogram-meter squared per second squared (kg x m^2/s^2).

Why is the default gravity 9.81 m/s^2?

The value 9.81 m/s^2 is the standard acceleration due to gravity near Earth's surface. It varies slightly depending on latitude and altitude, ranging from about 9.78 m/s^2 at the equator to 9.83 m/s^2 at the poles. For most calculations, 9.81 m/s^2 provides sufficient accuracy.

Can potential energy be negative?

Yes. If the height is negative (meaning the object is below the chosen reference point), the potential energy will be negative. This is common in problems involving wells, valleys, or underground structures. The sign of PE depends on the reference point, but energy differences remain physically meaningful regardless.

How does potential energy relate to kinetic energy?

In a closed system without friction, the total mechanical energy (PE + KE) is conserved. As an object falls, its height decreases and its speed increases, converting potential energy into kinetic energy. At the top of a trajectory, PE is at its maximum and KE is zero. At the bottom, KE is at its maximum and PE is zero (relative to that point).