Coulomb's law calculator

Choose what to solve for and fill in the rest. Charges use one shared unit from coulombs down to nanocoulombs, and a negative sign marks a negative charge. The box for the quantity you solve for is ignored.

Use a minus sign for a negative charge. When you solve for a force, opposite signs attract and equal signs repel.
Force (magnitude)0.00898755 N
Direction
Repulsive (same signs)

Runs in your browser: nothing you enter is sent anywhere.

How to use it

  1. Choose to solve for force, distance or the size of charge 1.
  2. Enter the other values with their units. For charges, use one shared unit.
  3. Read the result. For a force, the tool also says whether it is attractive or repulsive.

How it works

F = k|q₁q₂|/r². The distance is r = √(k|q₁q₂|/F) and charge 1 is |q₁| = F·r²/(k·|q₂|). When solving for a charge or distance, signs are not needed because only the magnitude is determined.

Worked example

Two charges of +1 µC at 10 cm: F = 8.9875517923e9 × (1e-6)² ÷ 0.1² = 0.8988 N, repulsive. If one is −1 µC the force has the same size but is attractive.

Tips

  • Convert the distance carefully: 10 cm is 0.1 m, and an error there is squared in the result.
  • The force on each charge has the same size, by Newton’s third law.

Frequently asked questions

What is Coulomb's law?

The electric force between two point charges is F = k × |q₁ × q₂| ÷ r². It grows with the product of the charges and falls with the square of the distance. Like charges repel and opposite charges attract.

What constant does it use?

k = 8.9875517923e9 N·m²/C², which is 1 ÷ (4π ε₀) for a vacuum (air is very close). In another material the force is smaller by the relative permittivity, which this tool does not include.

Why does a coulomb sound so large?

One coulomb is an enormous charge: two of them one metre apart would repel with about 9 billion newtons. Everyday static charges are in microcoulombs or nanocoulombs, which is why the unit selector goes that small.

Does it work for charged spheres?

For uniformly charged spheres, measure the distance between their centres and the formula holds outside them. For other shapes or very short distances it does not.

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