# Electric Potential Calculator

Our electric potential calculator can obtain the electric potential at any distance from a single point charge or a number of point charges (up to ten).

If you don't know what the electric potential is, don't worry. Within this short article, we will cover:

- Electric potential definition;
- Electric potential formula/equation;
- Electric potential due to a point charge; and
- Electric potential due to a system of point charges.

Let's start!

## What is the electric potential? Electric potential formula

We define the electric potential of a point charge at a point in space as the **work required to bring a $1\ \text{C}$ charge from infinity to that location**.

Sounds confusing? *Let's do some math first* so you can start working with the electric potential calculator.

💡 Alternatively, check our electric field calculator to get a proper introduction to this topic.

Assume we had **two positive point charges**, $q$ and $Q$, separated by a distance of $r$.

If you remember, Coulomb's law describes the force $F$ between these particles:

where $k_{e}$ is **Coulomb's constant**.

Now, assume we tried to bring the charges *closer* by moving $q$ from $r_{1}$ to $r_{2}$ ($r_{1} > r_{2}$). For that, we would need to do **work** against this repulsive force:

by integrating between $r_{1}$ and $r_{2}$ we get:

Lastly, if we replace one of the charges with a **unit test charge** (a $1\ \text{C}$ positive charge) and set our initial point at **infinity**, we obtain the **electric potential equation** for a point charge:

This potential depends only on $r$ and $Q$, and its unit is the volt (V).

🔎 **Electromagnetism** is an interesting topic with some counterintuitive repercussions, such as the force between current-carrying wires. **Read more about it in this calculator!**

## Electric potential due to a system of point charges

We can extend this definition to a system of multiple point charges easily.

The electric potential of multiple point charges $q_{i}$ at a point in space is simply the vector sum of each individual electric potential:

With our electric potential calculator, you can input up to ten point charges and it will output the resulting electric potential at any point. **Give it a try!**

🙋 Our electric potential calculator is straightforward: input the **charge** and the **distance**, and it will automatically output the electric potential at that position.