# Electric Field Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Jun 05, 2023

With our electric field calculator, you can compute the magnitude of an electric field created at a specific distance from a single charge point.

In the text below, we will first try to answer the simple question: what is an electric field? Then, we will present the electric field equation for a point charge and describe other possible sources of an electric field.

To compute the electric potential at a point either due to a single point charge or a system of point charges, check out our electric potential calculator.

## What is an electric field?

An electric field is a field that exerts a force on charges – attracting or repelling them. Moreover, every single charge generates its own electric field. That's why, for example, two electrons with the elementary charge $e = 1.6 \times 10^{-19}\ \text{C}$ repel each other. You can check our Coulomb's law calculator if you want to quantify the amount of electric force between two charged particles.

You probably know that everything in nature is made of atoms, which consist of a nucleus (positive charge) and electrons orbiting around the nucleus (negative charge). The nucleus generates an electric field that attracts and holds electrons in their orbits, just like the sun and the planets around it.

## Electric field equation

You can estimate the electric field created by a point charge with the following electric field equation:

$\small E = \frac{kQ}{r^2},$

where:

• $E$ – Magnitude of the electric field;
• $Q$ – Charge point;
• $r$ – Distance from the point; and
• $k$ – Coulomb's constant:
\small \qquad \quad \begin{align*} k &= \frac{1}{4\pi\varepsilon_0} \\[1em] &= 8.9876 \times 10^9\ \text{N}\cdot\text{m}^2 / \text{C}^2 \end{align*}

where $\varepsilon_0$ is vacuum permittivity.

You can check with our electric field calculator that the magnitude of the electric field decreases rapidly as the distance from the charge point increases.

An interesting fact is how extremely fast electrons accelerate in the electric field. You can learn more about it from the acceleration in the electric field calculator.

## Electric and magnetic fields

Did you know that electricity is always strictly linked to magnetism? Two of four well-known Maxwell's equations state that:

• Charges are a source of an electric field (this is the case of our electric field calculator); and
• A magnetic field that varies in time produces an electric field (and thus electricity – check our Faraday's law calculator).

Both electric and magnetic fields store energy. We have written more about it in our energy density of fields calculator. You should check it out too!

## FAQ

### How do I find the electric field of a point charge?

To find the electric field at a point due to a point charge, proceed as follows:

1. Divide the magnitude of the charge by the square of the distance of the charge from the point.

2. Multiply the value from step 1 with Coulomb's constant, i.e., 8.9876 × 10⁹ N·m²/C².

3. You will get the electric field at a point due to a single-point charge.

### Is electric field intensity a scalar or a vector quantity?

Electric field intensity is a vector quantity as it requires both the magnitude and direction for its complete description. The direction of the electric field is the same as that of the electric force on a unit-positive test charge.

### What is the SI unit of electric field?

The SI unit of the electric field is newton per coulomb, i.e., N/C. We can define the electric field as the force per unit charge. Since the SI unit of force is newton and that of charge is the coulomb, the electric field unit is newton per coulomb.

### How does the electric field vary with distance for a point charge?

The electric field varies as the inverse of the square of the distance from the point charge that generates it, i.e., E ∝ 1/r². Hence, the strength of the electric field decreases as we move away from the charge and increases as we move toward it.

Dominik Czernia, PhD
Electric field of a
single point charge
Charge
e
Distance
μm
Electric field
×10³
N/C
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