Last updated: 2026-06-14

Coulomb's Law

Coulomb's law describes the electrostatic force between two stationary electric charges. The force is proportional to the product of the charges and inversely proportional to the square of the distance between them: $F = k \cdot \frac{q_1 q_2}{r^2}$. Here $q_1$ and $q_2$ are the charges, $r$ is their separation, and $k \approx 8.99 \times 10^9\ \text{N·m}^2/\text{C}^2$ is Coulomb's constant. Charles-Augustin de Coulomb established the relationship experimentally in 1785, and it is the foundation of electrostatics.

This calculator returns the magnitude of the force between two point charges and states whether it is attractive or repulsive based on the signs of the charges.

Same signs repel, opposite signs attract

The direction of the force depends only on the signs of the two charges. Two charges of the same sign — both positive or both negative — push each other apart, so the force is repulsive. A positive and a negative charge pull toward each other, so the force is attractive. The force always acts along the straight line joining the two charges, and by Newton's third law each charge feels an equal and opposite pull or push.

Formula

Because the force falls off as $1/r^2$, doubling the distance reduces the force to one-quarter, and tripling it to one-ninth — the same inverse-square behaviour as gravity and light intensity.

Worked example

Two small spheres each carry a charge of +1 µC ($1 \times 10^{-6}$ C) and sit 1 cm (0.01 m) apart. The force between them is:

Both charges are positive, so the force is repulsive. Entering 1 µC for each charge and 0.01 m for the distance reproduces this result. Note how a charge of just one microcoulomb produces a force of nearly 90 newtons at centimetre range — electrostatic forces are enormous compared with gravity.

Coulomb's law and gravity

Coulomb's law has the same inverse-square form as Newton's law of gravitation, $F = G \cdot \frac{m_1 m_2}{r^2}$. The differences are instructive. Gravity depends on mass and is always attractive, while the electrostatic force depends on charge and can attract or repel. The electrostatic force is also far stronger: between two protons it exceeds their gravitational attraction by a factor of roughly $10^{36}$, which is why everyday matter is held together by electric forces rather than gravity.

Limitations

The formula applies to point charges — objects small compared with the distance between them — at rest in a vacuum or, to good approximation, in air. Inside another medium the force is reduced by the material's relative permittivity. Moving charges also produce magnetic effects that Coulomb's law alone does not capture; those require the full framework of electromagnetism.