Coulomb's Law Calculator
Enter two charges and the distance between them to get the electrostatic force in newtons — and see why the force falls off with the square of the separation.
Use SI units
Charges in coulombs (C) and distance in metres (m) give the force in newtons — a microcoulomb is 0.000001 C, so enter 1 µC as 0.000001.
What is Coulomb's law?
The force between electric charges
Coulomb's law describes the electrostatic force between two stationary point charges. The force is proportional to the product of the two charges and inversely proportional to the square of the distance between them. The Coulomb's law calculator turns three measurements — the first charge in coulombs, the second charge in coulombs, and the separation in metres — into the magnitude of the force in newtons. It is the number behind why like charges repel and opposite charges attract, and it sets the scale for everything from static cling to the binding of electrons to atoms.
Enter two charges in coulombs and a distance in metres to get the electrostatic force in newtons instantly.
The force is the Coulomb constant multiplied by the absolute value of the product of the charges, divided by the square of the distance between them.
F = kₑ × |q₁ × q₂| ÷ r²The Coulomb constant kₑ is 8.98755179 × 10⁹ N·m²/C². The distance is squared in the denominator, so it dominates the result: move the charges twice as far apart and the force drops to a quarter. Taking the absolute value of the charge product gives the magnitude of the force; the sign of the charges then tells you the direction — like charges repel, opposite charges attract.
Suppose two charges of 1 microcoulomb each (0.000001 C) sit 0.1 m apart.
Multiply the charges
0.000001 × 0.000001 = 1×10⁻¹² — the product of the two charges in C².
Square the distance
0.1² = 0.01 — the squared separation in m².
Apply the constant
8.98755179×10⁹ × 1×10⁻¹² ÷ 0.01 = 0.899 N — the electrostatic force. Because both charges are positive, it is a repulsion.
The result is the magnitude of the force each charge exerts on the other, in newtons. The two 1 µC charges above push apart with about 0.899 N — roughly the weight of a 90-gram object, which is a surprisingly strong push for charges that small, and shows just how powerful the electrostatic interaction is. The crucial insight is the inverse-square distance term: the force scales with 1/r². Halve the separation from 0.1 m to 0.05 m and the force jumps fourfold; double it to 0.2 m and the force falls to a quarter. The charge product matters too, but only in direct proportion — multiply one charge by ten and the force grows tenfold. The sign of the charges sets the direction: two charges of the same sign repel, while charges of opposite sign attract with the same magnitude. That single relationship explains static electricity, why electrons stay bound to nuclei, and the forces inside every capacitor.
The formula is exact for point charges, but a couple of practical points are worth keeping in mind.
Point charges in a vacuum and consistent units
Coulomb's law as used here applies to point charges (or uniformly charged spheres treated from their centres) in a vacuum or air. A surrounding medium with a different permittivity reduces the force, and the formula breaks down inside extended or moving charge distributions. Keep your units consistent — coulombs for charge and metres for distance — or the newtons will be wrong: remember that 1 microcoulomb is 0.000001 C and 1 nanocoulomb is 0.000000001 C.