# Coulomb's Law Calculator

Created by Gabriela Diaz
Last updated: Jul 05, 2022

Use Coulomb's law calculator to quickly determine the electrostatic force between two charges separated by a given distance.

• What is Coulomb's law?;
• The particularities of the electrostatic force formula; and
• The variables present in Coulomb's law equation.

## What is Coulomb's law?

The interaction between two electrically charged particles is in the form of a non-contact force, known as electrostatic force. This force is exerted by one particle on another and vice versa, both having the same magnitude and direction but opposing sense.

The magnitude of this electrostatic force may be calculated using Coulomb's law equation. This law states that:

"The magnitude that each of the electrical forces with which two point charges interact is directly proportional to the product of charges' magnitudes and inversely proportional to the square of the distance between them."

Like any other force, the electrostatic force is a vector described by its magnitude, direction, and sense. Each of them is determined by the following factors:

• Magnitude — Determined by the charges' scalar values and distance.
• Direction — Provided by the line connecting the two charges.
• Sense — Given by the charges' sign, repulsion, or attraction.

If you'd like to learn about vector addition, why not take a look at our vector addition calculator?

Coulomb's law is analogous to Newton's law of universal gravitation. However, electrical interactions and gravitational interactions are two different types of phenomena. Electrical interactions depend on the magnitude of the charges and can be either of repulsion or attraction, whereas the gravitational interactions depend on the masses and are always of attraction.

## Coulomb's law equation — Electrostatic force formula

Let's see how to find the electrostatic force using the mathematical expression for Coulomb's law:

$\small F = k_e \cfrac{q_1 \, q_2}{r^2}$

where:

• $F$ — Electrostatic force between two charges in Newtons units;
• $k_e$ — Coulomb's constant, and it's equal to 8.98755 × 10⁹ N·m²/C²;
• $q_1$ — Magnitude of the first charge in Coulombs;
• $q_2$ — Magnitude of the second charge in Coulombs; and
• $r$ — Shortest distance between the charges in meters.

The typical order of magnitude of an electric charge is $10^{-6} \ \text C$ microcoulombs or even $10^{-9} \ \text C$ nanocoulombs.

Because $q_1$ and $q_2$ are directly proportional to force's magnitude, the greater their values, the greater the value of the electrostatic force $F$.

However, since force is inversely proportional to the squared distance between the charges, the greater the distance between them, the lower the magnitude of the force. For example, if two charges are initially separated by a distance "r" and later separated by "2r," the magnitude of the force decreases by 1/4 of its initial value.

The electrostatic force formula above is used to obtain the magnitude of the force. If you like to determine whether this force is of attraction or repulsion keep in mind that when:

• The charges are of the same sign, both "+" or "-", the force is of repulsion; and
• The charges are of opposite signs, one is "+" and the other one is "-", the force is of attraction.

You could also include the signs of the charges in the formula to calculate $F$. If the result is negative, the force is of attraction; if the result is positive, the force is repulsive.

## How to use Coulomb's law calculator

To use the Coulomb's law calculator, simply enter three values to obtain the fourth as a result. For example, if you'd like to determine the magnitude of an electrostatic force, enter the magnitudes of the charges and the distance between them.

When using this calculator, please take into account that Coulomb's law has some conditions that must be met for it to be valid. These are:

1. Charges must be point charges or charged bodies that are sufficiently separated that can be considered as points or particles;
2. Charges must be stationary; and
3. Charges cannot overlap.

🙋 Click on the Advanced mode of the Coulomb's law calculator to show Coulomb's constant $k_e$ and relative permittivity.

Gabriela Diaz
Charges are...
not equal
Charge 1 (q₁)
nC
Charge 2 (q₂)
nC
Distance (r)
mm
Force (F)
lbf
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