Potential Energy Calculator

This calculator helps you compute variables related to gravitational potential energy—a form of stored energy possessed by an object due to its height in a gravitational field.

The formula for gravitational potential energy is:

PE=mgh

Where:

PE = Potential energy
m = Mass of the object
g = Gravitational acceleration
h = Height above the reference point

The SI unit of potential energy is joule (J), where 1 J = 1 kg·m²/s².

Potential energy can be symbolized as PE, E_p, U, or V.

How to Use This Calculator

Select the variable you want to solve for: potential energy, mass, height, or gravitational acceleration.
Enter the known values in the appropriate units. You can switch between unit systems as needed.
The result will update automatically based on the formula PE = mgh.

Understanding Gravitational Potential Energy

Gravitational potential energy represents the energy an object has due to its position in a gravitational field. It is directly proportional to the object's mass and its height relative to a reference point (typically ground level).

On Earth, g is generally approximated as 9.80665 m/s², but it can vary slightly depending on altitude and latitude.

Why It Matters

Potential energy is a key concept in mechanics and conservation of energy.
It's used in physics, engineering, structural design, and energy systems.
Real-world applications include roller coasters, cranes, and hydroelectric power.

Rearranged Forms

The following potential energy formula contains three variables that can each be expressed in terms of the others.

PE = mgh

1. Solving for Mass

m = \frac{PE}{gh}

2. Solving for Height

h = \frac{PE}{mg}

3. Solving for Gravitational Acceleration

g = \frac{PE}{mh}

Applications of Potential Energy

Potential energy is a fundamental concept in physics that plays a key role in understanding how energy is stored and transferred. Common applications include:

Designing roller coasters and theme park rides
Calculating the energy in lifted or suspended loads in cranes and elevators
Analyzing dam and hydroelectric power systems (water stored at height)
Studying gravitational fields and planetary motion
Understanding biomechanics, such as energy stored in raised limbs

Important Notes

Gravitational potential energy is relative—it depends on the chosen reference height (zero level).
It is also a scalar quantity, meaning it has magnitude but no direction.
If either the mass, height, or gravitational acceleration is zero, then the potential energy is zero.
In a closed system, potential energy can convert to kinetic energy and vice versa, illustrating the conservation of mechanical energy.

Tip: Increasing the height of an object has a linear effect on potential energy. For example, doubling the height will double the potential energy, assuming mass and gravity stay constant.

Try Different Scenarios

You can experiment with different mass and height values to see how energy changes in various conditions. For example:

Lifting a 10 kg object to 5 meters yields $PE = 10 \times 9.80665 \times 5 = 490.33\, \text{J}$
A feather with negligible mass has little potential energy even at high altitudes.