Coulomb's Law Calculator

Coulomb's law

Two electric charges at rest exert a force on each other. Its magnitude is proportional to the product of the charges and inversely proportional to the square of the distance between them:

F = k × |q₁| × |q₂| / r²

k is the Coulomb constant, k = 1 / (4 × π × ε₀) = 8.9876 × 10⁹ N·m²/C². Charges are in coulombs (C), distance in metres and force in newtons.

Attraction or repulsion?

Charges with the same sign (two positive or two negative) repel each other. Charges with opposite signs attract. The formula gives the size of the force, and the direction is read from the signs. The force acts along the line joining the charges and, by Newton's third law, is equal in size on both.

Example

For charges of 3 µC and −5 µC that are 20 cm apart, F = 8.9876 × 10⁹ × 3 × 10⁻⁶ × 5 × 10⁻⁶ / 0.2² = 3.37 N. The signs are opposite, so the force is attractive. Halving the distance makes the force four times larger.

Watch the units

Problems usually give charges in microcoulombs (1 µC = 10⁻⁶ C) or nanocoulombs (1 nC = 10⁻⁹ C) and distances in centimetres. They must be converted to coulombs and metres before going into the formula. The calculator does that for you. For atomic scale problems you can pick the elementary charge (e = 1.602 × 10⁻¹⁹ C) as the unit.

Limits

The law is for point charges at rest. If the medium is not vacuum or air, the force is divided by the relative permittivity of the medium. With more than two charges the forces have to be added as vectors, while this tool handles a single pair.