# Coulomb’s Law Calculator

URL: https://speedycalculator.com/calculators/physics/coulombs-law/
Last updated: 2026-10-30

> The Coulomb's law calculator finds the electrostatic force between two point charges from their magnitudes and signs, the distance between them and the medium.

## Inputs

- Charge q₁ (nC, µC, C, pC, e)
- Charge q₂ (nC, µC, C, pC, e)
- Distance r (cm, mm, m, in, ft)
- Relative permittivity ε_r

## Results

- Force magnitude
- Force type

## Formula

```
F = k·q₁·q₂ / (ε_r·r²),  k = 8.988 × 10⁹ N·m²/C²
```

## Explanation

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

FieldWhat to enterCharge q₁Units: nC, µC, C, pC, eCharge q₂Units: nC, µC, C, pC, eDistance rUnits: cm, mm, m, in, ftRelative permittivity ε_rA 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)11.0785e-51.51.6178e-522.1570e-52.52.6963e-533.2355e-544.3140e-5

## 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.

## FAQ

**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.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)