Coulomb's Law Calculator

Coulomb's law gives the electrostatic force as F = kqq/r², where k ≈ 8.988×10 N·m²/C², charges are in coulombs, and distance is in metres. The result comes out in newtons. Two charges of 1 µC separated by 0.1 m exert F = 8.988×10 × (10^-6)² / 0.01 ≈ 0.9 N on each other. Same-sign charges push apart, opposite signs pull together. The inverse-square dependence means moving them twice as far apart cuts the force by a factor of four — small distance changes matter a lot.

Enter the two charges and the distance between them, and the calculator returns the force using F = kqq/r². Charges in coulombs (or microcoulombs if the tool accepts them), distance in metres, and force comes out in newtons. The sign tells you direction: positive means repulsion, negative means attraction. Most exam problems give charges in microcoulombs or nanocoulombs, so the calculator's unit handling saves real headaches. It's especially handy when you're juggling powers of ten and don't want to slip up converting 5 nC to 5×10^-6 C in the middle of a multi-step problem.

Start with F = kqq/r² and solve for r: r = √(k|qq|/F). Take absolute values to keep r positive, then plug in. If two charges of 2 µC each repel with 1 N of force, then r = √(8.988×10 × 4×10¹² / 1) ≈ 0.19 m. This reverse calculation crops up when you know the force two charges produce on each other (often from equilibrium conditions like a hanging charge) and want to know how far apart they sit. Watch for the square root — students sometimes forget it.

Coulomb's constant k equals approximately 8.988 × 10 N·m²/C², usually rounded to 9 × 10 for quick estimation. It also relates to the permittivity of free space through k = 1/(4πε), where ε ≈ 8.854 × 10¹² F/m. Some textbooks and exam papers prefer the 1/(4πε) form because it falls out cleanly in higher-level electromagnetism. For solving numerical problems, 9 × 10 is close enough unless the question demands precision. Keep this number on the formula sheet — it shows up everywhere from electrostatics to atomic physics.

Two positive charges or two negative charges push each other apart, while a positive and a negative charge pull together. The mathematics handles this automatically: if you put both charges in with their proper signs, F = kqq/r² gives a positive value for repulsion and a negative value for attraction. So +2 µC and +3 µC give a positive force, while +2 µC and −3 µC give a negative one. Direction-wise, the force on each charge always lies along the line joining them. The sign tells you whether they head toward or away from each other.

Coulomb's law works in coulombs, but most realistic charges in problems live in microcoulombs (µC) or nanocoulombs (nC). So before plugging into F = kqq/r², convert: 1 µC = 10^-6 C and 1 nC = 10^-6 C. Two 5 µC charges become 5×10^-6 C each, and forgetting that conversion gives forces a trillion times too big. Most online calculators let you pick the unit from a dropdown, which removes the guesswork. Still, learn to do it by hand — exam papers won't have a dropdown menu.

The electrostatic force follows an inverse-square law, meaning it weakens with the square of distance. Move charges twice as far apart and the force drops to a quarter. Three times further, and it's only one-ninth. Halve the distance and force quadruples. This is exactly the same shape as Newton's gravity formula, which isn't a coincidence — both are central forces from point sources. The inverse-square nature is why electric forces between distant objects fade so fast, but get extreme when charges sit very close together, like in atomic-scale physics.