Coulomb’s Law Calculator
Coulomb’s law calculator: force between two point charges from the charges and the distance, with attractive or repulsive result and a distance table.
Formula
Worked example
- q1 = 1 µC = 1 × 10⁻⁶ C and q2 = 2 µC = 2 × 10⁻⁶ C, r = 0.1 m
- F = 8.9875517923 × 10⁹ × (1 × 10⁻⁶) × (2 × 10⁻⁶) / 0.1² = 1.79751 N
- Both charges are positive, so the force is repulsive.
Force against distance
For the same two charges, 1 µC and 2 µC:
| Distance | Force |
|---|---|
| 0.05 m | 7.19004 N |
| 0.1 m | 1.79751 N |
| 0.2 m | 0.449378 N |
| 0.4 m | 0.112344 N |
| 0.8 m | 0.0280861 N |
An electron and a proton
At the Bohr radius, 5.29177 × 10⁻¹¹ m, the pull between one proton and one electron is 8.23873 × 10⁻⁸ N. The charge of one electron is 1.602176634 × 10⁻¹⁹ C (the unit e in the calculator).
Limits
The law is for point charges (or spheres, measured centre to centre) at rest, in a vacuum. In air it is almost the same. Moving charges also produce magnetic forces, which are not included.
Frequently asked questions
What is Coulomb’s law?
The force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance: F = k × q1 × q2 / r², with k = 8.9875517923 × 10⁹ N·m²/C².
Is the force attractive or repulsive?
Like charges (both positive or both negative) repel. Unlike charges attract. The calculator gives the size of the force and says which it is.
What happens if the distance doubles?
The force falls to a quarter, because of the r² in the formula. Halving the distance makes it four times larger. The table above shows this.
How does k relate to the permittivity of free space?
k = 1 / (4πε0), where ε0 = 8.8541878128 × 10⁻¹² F/m. In a material with relative permittivity εr the force is divided by εr.
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