How to use it
- Type the First charge with its unit and sign, for example 2 µC, and the Second charge, for example -3 µC.
- Type the Distance between the charges, centre to centre, for example 50 cm.
- Read the Electric force and whether it is attractive or repulsive.
- Read the table of the force at other distances, and the steps that show the working.
Coulomb's law
Coulomb's law gives the electric force between two point charges. The force is proportional to the product of the two charges and falls off with the square of the distance between them (OpenStax, University Physics Volume 2, section 5.3).
F = k |q1 q2| ÷ r²
k = 1 ÷ (4π ε0) = 8.987 551 79 × 10⁹ N·m²/C²
ε0 = 8.854 187 8188 × 10⁻¹² F/m, the permittivity of vacuum
q1, q2 = the charges, C
r = the distance between their centres, m
F = the force, N- Charges of opposite sign attract each other; charges of the same sign repel each other. The formula gives the size of the force, and the sign tells the direction.
- Doubling the distance makes the force a quarter as large.
- The prefixes are powers of ten: 1 µC is 10⁻⁶ C, 1 nC is 10⁻⁹ C and 1 mC is 10⁻³ C.
Where the law applies
The law is exact for point charges, and for spheres whose charge is spread evenly, when the distance is measured from their centres. It is for charges at rest in vacuum. In air the result is almost the same, and the calculator says so in its note.
What this calculator does not include
- Forces from three or more charges. Add the force of each pair as a vector, with its direction.
- Charges in motion, which also make magnetic forces.
- Charges inside a material with a different permittivity, such as water or glass.
Worked example: +2 µC and −3 µC, 50 cm apart
The size of the force is F = k × 2 × 10⁻⁶ × 3 × 10⁻⁶ ÷ 0.5² = 8.988 × 10⁹ × 6 × 10⁻¹² ÷ 0.25 = 0.2157 N, which is 215.7 mN. The signs are opposite, so the charges attract. At 1 m the force is a quarter of that, 53.93 mN.
| Distance | Force |
|---|---|
| 0.25 m | 862.8 mN |
| 0.5 m | 215.7 mN |
| 1 m | 53.93 mN |
| 2 m | 13.48 mN |
Frequently asked questions
Which unit should I type for a charge?
Coulombs, with a prefix. µC is a millionth of a coulomb, nC a billionth and mC a thousandth. A number alone is read as coulombs, so 2 means 2 C.
Why does the result have no minus sign?
The formula gives the size of the force, which is never negative. The result says whether the force is attractive or repulsive, and that is the direction that matters.
Why is the force so small for everyday objects?
The constant k is very large, but the charges of everyday objects are tiny fractions of a coulomb. A coulomb is a very large charge, so the forces between small charges are small.
Can I use the calculator for charges in air?
Yes. The permittivity of air is almost that of vacuum, so the result is practically the same. The calculator uses the vacuum value.
Is my data sent to a server?
No. The calculation runs in your browser, and nothing you type is sent to us or stored.
Sources
- OpenStax University Physics Volume 2, section 5.3: Coulomb's Law (F = k|q1 q2|/r²)
- NIST: vacuum electric permittivity ε0, CODATA 2022 (8.854 187 8188 × 10⁻¹² F/m)
- OpenStax University Physics Volume 2, Appendix C: Fundamental Constants (Coulomb constant k_e)
Figures and text last checked on Tuesday, November 10, 2026.