Coulomb's Law Calculator

Coulomb's Law describes the electrostatic force between two point charges. It states that the force is proportional to the product of the two charges and inversely proportional to the square of the distance between them. The formula is F = kₑ × |q₁ × q₂| / r², where kₑ ≈ 8.9876 × 10⁹ N·m²/C².

Multiply the two charge values together (in Coulombs), multiply by the Coulomb constant (kₑ = 8.9876 × 10⁹ N·m²/C²), then divide by the square of the distance between the charges (in meters). The result is the electrostatic force in Newtons.

The force is repulsive when both charges have the same sign (both positive or both negative), and attractive when the charges have opposite signs (one positive and one negative). The direction of the force always acts along the line joining the two charges.

Yes. Coulomb's Law is an inverse square law because the electrostatic force decreases with the square of the distance between the charges. If you double the distance, the force becomes four times weaker.

In a hydrogen atom, a proton and electron are separated by approximately 5.29 × 10⁻¹¹ m (the Bohr radius). Each has a charge of magnitude 1.602 × 10⁻¹⁹ C. Using Coulomb's Law, the attractive force between them is approximately 8.2 × 10⁻⁸ N.

This calculator accepts charges in nanocoulombs (nC), where 1 nC = 10⁻⁹ C. This is a convenient unit for everyday electrostatics problems. The distance is entered in meters and the resulting force is displayed in Newtons.

Coulomb's Law is valid for point charges (or spherically symmetric charge distributions) that are stationary or moving slowly compared to the speed of light, in a vacuum or specified medium. It does not directly apply to extended charge distributions or relativistic speeds without modification.

The electric field E created by a point charge q at a distance r is defined as E = kₑ × q / r². Coulomb's Law can be seen as the force a charge q₁ experiences when placed in the electric field E created by q₂, i.e., F = q₁ × E.