Coulomb's Law Calculator

Coulomb's law is the electric equivalent of Newton's law of gravity. It says the force between two point charges is proportional to both charges and falls off with the square of the distance between them.

First chargeThe first charge, in microcoulombs. Negative for the opposite sign.Second chargeThe second charge, in microcoulombs. Negative for the opposite sign.DistanceHow far apart the charges are, in the unit chosen below.Distance unitThe conversion factor from the chosen unit to metres.

Electrostatic force

21.57

Force in micronewtons: 21,570,000
Separation in metres: 0.05
Force at twice the distance: 5.3925
Force at half the distance: 86.28

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

The formula this calculator uses

F = k x q1 x q2 / r^2, with k = 8.9875 x 10^9 N m^2 / C^2

F: The electrostatic force, in newtons
q1, q2: The two charges, in coulombs
r: The separation between them, in metres
k: Coulomb's constant, 8.9875 x 10^9 in SI units

How to check the result by hand

1
Convert the charges to coulombs
Multiply microcoulombs by one millionth. Two microcoulombs is 0.000002 coulombs and three microcoulombs is 0.000003.
2
Convert the separation to metres
Five centimetres is 0.05 metres. The formula needs metres because the constant is quoted in SI units.
3
Multiply the charges and the constant
8.9875 billion times 0.000002 times 0.000003 gives 0.053925, which is the numerator.
4
Divide by the square of the distance
0.05 squared is 0.0025, and 0.053925 divided by 0.0025 is 21.57 newtons.
5
Check the direction
The product of the two charges is positive, so the force is repulsive. The magnitude does not depend on the sign, only the direction does.

For worked examples, common mistakes and the limits of this formula, read the full How To Calculate Coulomb's Law page.