Like charges repel and unlike charges attract with a force that falls off with the square of the distance. Coulomb’s law holds atoms together and is about 10³⁶ times stronger than gravity between two protons.
How to use the Coulomb’s Law Calculator
- Charge q₁
- Charge q₂
- Distance r
- Relative permittivity ε_r
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter both charges with their signs, the distance and the relative permittivity of the medium (1 for vacuum or air).
Inputs explained
| Field | What to enter |
|---|---|
| Charge q₁ | Units: nC, µC, C, pC, e |
| Charge q₂ | Units: nC, µC, C, pC, e |
| Distance r | Units: cm, mm, m, in, ft |
| Relative permittivity ε_r | A number |
Example values
How the main result changes when Charge q₁ changes and everything else stays at the example values above:
| Charge q₁ (nC) | Force magnitude (N) |
|---|---|
| 1 | 1.0785e-5 |
| 1.5 | 1.6178e-5 |
| 2 | 2.1570e-5 |
| 2.5 | 2.6963e-5 |
| 3 | 3.2355e-5 |
| 4 | 4.3140e-5 |
Formula
F = k·q₁·q₂ / (ε_r·r²), k = 8.988 × 10⁹ N·m²/C²
Worked example
Inputs — Charge q₁: 2 nC; Charge q₂: -3 nC; Distance r: 5 cm; Relative permittivity ε_r: 1.
Results — Force magnitude = 0.000022 N; Force type = Attractive.
Key terms
- Point charge
- A charge with negligible size.
Frequently asked questions
What is Coulomb's constant?
k = 1/(4πε₀) ≈ 8.988 × 10⁹ N·m²/C².
Why does a medium reduce the force?
Its molecules polarise and partly screen the charges.
How does force change with distance?
Doubling the distance quarters the force.
Is Coulomb's law valid for spheres?
Yes, for uniformly charged spheres measured from their centres.