Coulomb's law calculator

What is a Coulomb’s law calculator?

A Coulomb’s law calculator is a free online tool that works out the electrostatic force acting between two point charges. Enter the magnitude of each charge and the distance separating them, and the calculator returns the force in newtons. The result is signed: a positive value means the charges push each other apart (a repulsive force), while a negative value means they pull toward each other (an attractive force). The tool removes the arithmetic burden of handling very small charges and powers of ten, making it handy for students, teachers, and anyone exploring electrostatics.

The concept of electrostatic force

Electrostatic force is the interaction between electrically charged objects. Like charges (two positives or two negatives) repel, and unlike charges (one positive and one negative) attract. The force acts along the straight line joining the two charges and obeys an inverse-square relationship with distance, just as gravity does. The constant of proportionality, known as Coulomb’s constant, is far larger than the gravitational constant, which is why even tiny amounts of charge can produce forces that dwarf the gravitational attraction between everyday objects.

Applications of Coulomb’s law in daily life

Coulomb’s law underpins a wide range of technologies and natural phenomena. It explains why a balloon rubbed on hair sticks to a wall, how dust clings to a charged screen, and why lightning discharges between clouds and the ground. Engineers rely on it when designing capacitors, electrostatic precipitators that clean exhaust gases, photocopiers and laser printers that move toner with charged drums, and the insulation that keeps high-voltage equipment safe. At the atomic scale, the same law governs how electrons are held to nuclei and how ions bond into molecules.

Formula

The magnitude and direction of the electrostatic force $F$ between two point charges is given by:

$F = k\,\frac{q_1 q_2}{r^2}$

Where:

• $F$ is the electrostatic force between the charges (positive for repulsion, negative for attraction),
• $k$ is Coulomb’s constant ($8.9875517873681764 \times 10^{9} \, \text{N} \cdot \text{m}^2 \cdot \text{C}^{-2}$),
• $q_1$ and $q_2$ are the two charges in coulombs,
• $r$ is the distance between the charges.

Because the charges keep their signs in the product $q_1 q_2$, the sign of the result tells you the nature of the force, and the inverse-square term means the force falls off rapidly as the charges move apart.

Examples

Example 1: Two equal charges of $q_1 = q_2 = 1 \times 10^{-6}$ C sit $0.1$ m apart. Find the force between them.

1. Substitute the values into the formula: $F = 8.9875517873681764 \times 10^{9} \cdot \frac{(1 \times 10^{-6})(1 \times 10^{-6})}{(0.1)^2}$

2. Simplify the numerator and denominator: $F = 8.9875517873681764 \times 10^{9} \cdot \frac{1 \times 10^{-12}}{0.01}$

3. The result is $F \approx 0.898755$ N. Both charges are positive, so the force is repulsive.

Example 2: A charge of $q_1 = 2 \times 10^{-6}$ C and a charge of $q_2 = 3 \times 10^{-6}$ C are separated by $0.5$ m. Find the force.

1. Substitute the values: $F = 8.9875517873681764 \times 10^{9} \cdot \frac{(2 \times 10^{-6})(3 \times 10^{-6})}{(0.5)^2}$

2. Simplify: $F = 8.9875517873681764 \times 10^{9} \cdot \frac{6 \times 10^{-12}}{0.25}$

3. The result is $F \approx 0.215701$ N, again a repulsive force because both charges are positive.

Notes

• Enter a negative value for a charge to represent it being negative; the calculator then reports an attractive (negative) force when the two charges have opposite signs.
• Coulomb’s law applies to point charges or to spherically symmetric charge distributions, where $r$ is measured between their centers.
• The constant $k$ assumes the charges sit in a vacuum (or, to a good approximation, in air). In other media the effective force is reduced by the material’s relative permittivity.
• Like gravity, the electrostatic force follows an inverse-square law, but it can be either attractive or repulsive, whereas gravity is always attractive.

FAQs

What units should I use for charge and distance?

Enter charges in coulombs (or pick a smaller unit such as microcoulombs) and the distance in meters or another supported length unit. The force is reported in newtons.

Why is the force sometimes negative?

A negative result indicates an attractive force, which happens when the two charges have opposite signs. A positive result indicates a repulsive force between charges of the same sign.

How is Coulomb’s law related to gravitational force?

Both are inverse-square laws with the same mathematical shape. The key differences are that Coulomb’s constant is enormous compared with the gravitational constant, and that the electrostatic force can attract or repel, while gravity only attracts.

Does the medium between the charges matter?

Yes. This calculator assumes a vacuum or air. Inside a material, the surrounding molecules screen the charges and reduce the force by a factor equal to the relative permittivity of the medium.

Can I use this calculator for more than two charges?

It computes the force between a single pair of charges. For systems with several charges, calculate the pairwise forces separately and add them as vectors to find the net force on any one charge.

You can find this tool at https://www.mega-calculator.com/physics/coulombs-law/.