Potential Energy Calculator

Category: Physics

- March 19, 2025

| |

Potential energy is the energy stored in an object due to its position relative to some reference point. The most common types are gravitational potential energy and elastic potential energy.

This calculator helps you determine potential energy using different methods based on the physical situation.

Energy Type:

Gravitational

Elastic (Spring)

Electric

Mass (m):

Height (h):

Gravitational Acceleration (g):

Location:

Decimal Places:

About Potential Energy

Potential energy is the energy an object possesses due to its position or state, rather than its motion. It's energy that is stored in an object and has the potential to be converted into other forms of energy.

Gravitational Potential Energy:

The energy stored in an object due to its height above a reference point in a gravitational field.

Formula: PE = m × g × h
Where:
PE = Gravitational potential energy (joules, J)
m = Mass (kilograms, kg)
g = Gravitational acceleration (meters per second squared, m/s²)
h = Height above reference point (meters, m)

Elastic Potential Energy:

The energy stored in elastic materials when they are stretched or compressed.

Formula: PE = ½ × k × x²
Where:
PE = Elastic potential energy (joules, J)
k = Spring constant (newtons per meter, N/m)
x = Displacement from equilibrium position (meters, m)

Electric Potential Energy:

The energy stored in a system of charged particles due to their positions relative to each other.

Formula: PE = k × q₁ × q₂ / r
Where:
PE = Electric potential energy (joules, J)
k = Coulomb's constant (8.99 × 10⁹ N·m²/C²)
q₁, q₂ = Electric charges (coulombs, C)
r = Distance between charges (meters, m)
ε = Permittivity of medium (F/m)

Applications of Potential Energy:

Gravitational: Hydroelectric power, pendulums, roller coasters
Elastic: Springs, bungee cords, bow and arrow
Electric: Batteries, capacitors, atomic bonds

Energy Conversion:

Potential energy can be converted to kinetic energy (energy of motion) and vice versa. The Law of Conservation of Energy states that energy cannot be created or destroyed, only converted from one form to another.

What Is the Potential Energy Calculator?

The Potential Energy Calculator is a tool that helps you determine the stored energy in an object due to its position, elasticity, or electric charge interactions. It supports three types of potential energy calculations:

Gravitational Potential Energy: Energy stored in an object due to its height above a reference point.
Elastic Potential Energy: Energy stored in a stretched or compressed spring.
Electric Potential Energy: Energy between charged particles due to electrostatic forces.

Potential Energy Formulas

Different types of potential energy follow distinct formulas:

Gravitational Potential Energy

\( PE = m \times g \times h \)

PE = Gravitational potential energy (Joules, J)
m = Mass (kg)
g = Gravitational acceleration (m/s²)
h = Height above the reference point (m)

Elastic Potential Energy

\( PE = \frac{1}{2} k x^2 \)

PE = Elastic potential energy (Joules, J)
k = Spring constant (N/m)
x = Displacement from the equilibrium position (m)

Electric Potential Energy

\( PE = \frac{k q_1 q_2}{r} \)

PE = Electric potential energy (Joules, J)
k = Coulomb’s constant (8.99 × 10⁹ N·m²/C²)
q₁, q₂ = Electric charges (Coulombs, C)
r = Distance between charges (m)

How to Use the Calculator

The calculator is simple to use and provides instant results. Follow these steps:

Select the Energy Type: Choose between gravitational, elastic, or electric potential energy.
Enter Required Values:
- For gravitational energy: Enter mass, height, and gravitational acceleration.
- For elastic energy: Enter the spring constant and displacement.
- For electric energy: Enter two charges and their separation distance.
Choose Units: Select the appropriate unit for each input.
Click “Calculate”: The calculator will instantly compute the potential energy.
View Results: The calculated energy is displayed with conversions into other units.

Why Use This Calculator?

Potential energy is a fundamental concept in physics, affecting everything from mechanical systems to electrical fields. This calculator is useful for:

Students learning about energy principles in physics.
Engineers calculating energy storage in mechanical systems.
Researchers analyzing gravitational, elastic, or electric forces.
Anyone curious about how energy is stored and transferred.

Frequently Asked Questions

What is potential energy?

Potential energy is stored energy due to an object’s position, shape, or charge. It has the potential to be converted into kinetic energy (motion).

How does gravitational potential energy change with height?

Gravitational potential energy increases as height increases because it depends on mass, gravity, and height.

What happens if I change the spring constant in the elastic energy calculation?

A higher spring constant means the spring is stiffer, resulting in more stored energy when compressed or stretched.

Can I use this calculator for electric potential energy in different mediums?

Yes! The calculator allows you to input a dielectric constant, which affects the force between charges in different materials like air, water, or glass.

Final Thoughts

Understanding potential energy helps in various real-world applications, from designing roller coasters to engineering energy-efficient systems. This calculator simplifies the process, making energy calculations accessible to everyone.