Potential Energy Calculator

Created by Mateusz Mucha
Reviewed by Jack Bowater
Last updated: Feb 27, 2023

This potential energy calculator enables you to calculate the stored energy of an elevated object. The full name of this effect is gravitational potential energy because it relates to the energy which is stored by an object as a result of its vertical position or height.

Prefer watching rather than reading? Check out our video lesson on gravitational potential energy here:

Keep reading to find out:

• How to calculate potential energy
• What the gravitational potential energy formula is

How to calculate potential energy

The easiest way to calculate gravitational potential energy is to use our potential energy calculator. This tool estimates the potential energy on the basis of three values. These are:

1. The mass of the object;
2. Gravitational acceleration, which on Earth amounts to $9.81 \ \mathrm{m/s^2}$ or $1 \ \mathrm g$ (the acceleration due to gravity calculator explains why it has such a value); and
3. The height of the object.

Then the calculator will give you the result in joules which you can convert to other units using, e.g., the energy conversion calculator. As with all of our calculators, this potential energy calculator does not have to be exclusively used to calculate potential energy. Just input any three of the four variables to find the fourth with ease.

If you want to calculate the energy of an object which is in motion, our kinetic energy calculator is highly recommended.

The potential energy formula

Let's look under the hood of the potential energy calculator. To help you picture it, our example will be the massive wrecking ball on a crane. The gravitational potential energy of this ball depends on two factors - the mass of the ball and the height it's raised to. The relationship between gravitational potential energy and the mass and height of an object is described by the following equation:

$\mathrm{PE \ grav.} = m \times h \times g$

Where:

• $\mathrm{PE \ grav.}$ - Gravitational potential energy of an object;
• $m$ - Mass of the object in question;
• $h$ - Height of the object; and
• $g$ - Gravitational field strength acting upon the object (1 g or 9.81 m/s2 on Earth).

The formula is relatively simple. An object which is not raised above the ground will have a height of zero and, therefore, zero potential energy. When you double the mass or the height of an object, its potential energy will also double.

Analyzing potential energy is handy in certain physics problems. We discussed them in the below tools:

1. The inclined plane calculator - an object sliding down the ramp loses its potential energy that converts to kinetic energy and heat due to friction.
2. The free fall calculator - similarly, an object is falling in the gravitational force, gaining speed and, thus, kinetic energy.

FAQ

What is potential energy?

Potential energy measures how much energy is stored in a system. There are multiple types of potential energy: gravitational, elastic, chemical, and so on. Potential energy can be converted into other types of energy, thus "releasing" what was accumulated. In the case of gravitational potential energy, an elevated object standing still has a specific potential, because when it eventually falls, it will gain speed due to the conversion of potential energy in kinetic energy.

How do I calculate the gravitational potential energy?

To calculate the gravitational potential energy, follow these easy steps:

1. Find the value of the gravitational acceleration at the reference point. On Earth's surface, you can use g = 9.81 m/s².
2. Multiply the mass of the object (m) and the height above the reference level (h) by the acceleration g to find the potential energy:
E = m · g · h.
3. The result will be in joules if you used SI units.

What is the potential energy of an apple on a tree?

For an apple with mass m = 0.1 kg hanging at a height h = 2.5 m, the gravitational potential energy is E = 2.4525 J, or roughly half a calorie. To find this result, multiply m by h and by g, with g = 9.81 m\s²:

E = 0.1 kg · 2.5 m · 0.81 m/s² = 2.4525 J.

Is potential energy the same as kinetic energy?

Not exactly. Kinetic and potential energy are both forms of energy, but they are not the same.

• Potential energy is a static quantity that describes the energy stored by an object at a given height.
• Kinetic energy is associated with motion and describes the energy of an object as a function of its speed.

Kinetic energy can transform into potential energy and vice-versa by vertical movement.

Mateusz Mucha
Mass
kg
Grav. acceleration
g
Height
m
Potential energy
J
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