Coulomb's Law formula
| Symbol | Quantity | SI unit | Meaning |
|---|---|---|---|
| F | Electrostatic force | N | Electrostatic force (positive = repulsive) |
| q₁ | Charge 1 | C | First point charge (with sign) |
| q₂ | Charge 2 | C | Second point charge (with sign) |
| r | Distance between charges | m | Separation between the charges |
What is Coulomb's Law?
Coulomb's Law: The electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. — Charles-Augustin de Coulomb, 1785
Coulomb's law is the inverse-square law of electrostatics. The constant ke = 1/(4πε₀) ≈ 8.988 × 10⁹ N·m²/C². Like charges repel and opposite charges attract. In this calculator a negative force means attraction.
Electrostatic forces are enormously stronger than gravity. Between two electrons, the electric force is about 4 × 10⁴² times the gravitational force. Coulomb interactions govern chemical bonding, ion migration in electrolytes and the stability of colloids.
How to use this calculator
- Choose the quantity you want to find in the Calculate menu. It is highlighted as the result field.
- Enter the known values. Scientific notation such as
1.6e-11is accepted. - Select a unit for each value. Units are converted to SI automatically.
- The answer updates as you type. Open Show calculation steps to see the working, or use Copy result to share a link with your inputs.
Worked example
Charges of +3 µC and −2 µC are 10 cm apart.
- F = 8.988 × 10⁹ × (3 × 10⁻⁶)(−2 × 10⁻⁶) / 0.1².
- F = −5.39 N: an attractive force of 5.39 N.
Frequently asked questions
What about charges in water or another medium?
Divide by the relative permittivity εᵣ of the medium. Water has εᵣ ≈ 80, so forces between ions in water are about 80 times weaker than in vacuum.
Does Coulomb's law work for charged spheres?
Yes, for uniformly charged spheres, measured from their centres, as long as they do not overlap.