Coulomb's Law Calculator

Two one-microcoulomb charges ten centimetres apart push each other with about 0.9 newtons — roughly the weight of a small apple. That sounds modest until you consider that a microcoulomb is about 6 × 10¹² elementary charges, which is a vanishingly small fraction of the electrons in a gram of matter.

The standard comparison makes the point better. Between two protons, the electrostatic repulsion is around 10³⁶ times stronger than their gravitational attraction. Gravity dominates the universe at large scales only because matter is electrically neutral almost everywhere: positive and negative charges cancel so precisely that the residual force is negligible, while mass only ever adds.

It also explains why you do not fall through your chair. The contact forces of everyday life are electrostatic repulsion between electron clouds, and they are stiff enough to feel like solidity.

Coulomb's law in vacuum is the version usually taught, but most real electrostatics happens in a medium. A material with polar molecules reorients them around any embedded charge, and that polarisation partly cancels the field — screening the charge from its neighbours.

The effect is quantified by relative permittivity. Air is about 1.0006, so close to vacuum that the distinction rarely matters. Water is about 80, which weakens electrostatic forces by nearly two orders of magnitude.

That single number explains a great deal of chemistry. Salt crystals are held together by strong ionic attraction, yet water dissolves them readily, because in water that attraction drops eightyfold — weak enough for thermal jostling to break the lattice apart. In a non-polar solvent like oil, the attraction stays strong and the salt stays solid.

The law as written applies to point charges, or to spherically symmetric distributions, where the geometry lets you treat all the charge as concentrated at the centre. For charges that are close relative to their own size, the distribution matters and the simple inverse square is an approximation.

It is also a statics law. Charges in motion produce magnetic fields as well, and accelerating charges radiate. Coulomb's law is the electrostatic limit of the full electromagnetic description, and it is only exact when nothing is moving.

Within its domain, though, it is among the most precisely tested statements in physics. If the exponent were not exactly 2, a charged conducting shell would have a field inside it — and experiments looking for that field constrain the deviation to about one part in 10¹⁶.