Coulomb's Law Calculator

Coulomb's Law Explained

Coulomb's Law describes the electrostatic force between two point charges — how strongly they push apart or pull together depends on how large the charges are and how far apart they sit.

$$F = \frac{k_eq_1q_2}{r^2}$$

The sign of the result tells you the direction: a positive result (same-sign charges) means repulsion, a negative result (opposite-sign charges) means attraction.

Worked Example: Opposite Charges Attracting

Using the calculator's own defaults — a +1 microcoulomb charge and a -2 microcoulomb charge, separated by 0.5 meters — the force works out to about -0.072 N, or roughly 0.072 N of attraction (the negative sign reflects that the charges have opposite signs and pull toward each other). Doubling the distance to 1 meter would cut that force to a quarter of its original strength, since Coulomb's Law follows the same inverse-square relationship as gravity.

Coulomb's Law vs. Gravity

Both Coulomb's Law and Newton's Law of Universal Gravitation share the same inverse-square structure — force divided by the square of distance — but they differ enormously in scale and behavior. Electrostatic force is vastly stronger than gravity for charged particles (roughly 10⁴² times stronger between two electrons) and can either attract or repel depending on charge signs, while gravity is always attractive and comparatively weak. Gravity dominates at planetary scales mainly because most matter is electrically neutral overall, so opposing charges cancel out, while mass always adds up in the same direction.

A Brief History of Coulomb's Law

French physicist Charles-Augustin de Coulomb published the law bearing his name in 1785, using a delicate torsion balance of his own design to measure the tiny forces between charged spheres — a similar experimental technique to the one Henry Cavendish would later use for measuring gravity. Coulomb's careful measurements confirmed the inverse-square relationship experimentally, cementing electrostatics as a quantitative science and laying groundwork that later fed into James Clerk Maxwell's unification of electricity and magnetism in the 1860s.

Common Coulomb's Law Mistakes

Forgetting to account for the sign of each charge is the most common error — plugging in only the magnitude of a negative charge loses the information about whether the pair attracts or repels. Confusing Coulomb's constant with the vacuum permittivity constant (they're related but different values, and mixing them up gives answers off by a factor of $4\pi$) is another frequent slip when working from a less common form of the formula. Forgetting the inverse-square relationship — assuming force is simply proportional to 1/r rather than 1/r² — is a third common mistake, same as with gravity.

Electrostatics Terms You Should Know

Coulomb (C) — the SI unit of electric charge; one electron carries about -1.602 × 10⁻¹⁹ C.

Coulomb's Constant — a proportionality constant setting the strength of electrostatic force, about 8.99 × 10⁹ N·m²/C².

Point Charge — an idealized charge treated as concentrated at a single point in space, simplifying the force calculation.

Electrostatic Induction — a temporary charge separation induced in a neutral conductor by a nearby charged object, causing a weaker secondary attraction.

This calculator assumes point charges in a vacuum. Consult a physics reference for charges in other media, where the surrounding material affects the force.