Coulomb's Force Calculator
Calculate the electrostatic force between two charged particles using Coulomb's Law.
Enter charge and distance to find the force.
Coulomb’s Law, formulated by French physicist Charles-Augustin de Coulomb in 1785, describes the force between two electrically charged particles. It is the foundation of electrostatics and one of the fundamental laws of physics.
The Formula
F = k × |q₁ × q₂| / r²
Where:
- F = Electrostatic force (Newtons)
- k = Coulomb’s constant = 8.9875 × 10⁹ N·m²/C²
- q₁ = Charge of first particle (Coulombs)
- q₂ = Charge of second particle (Coulombs)
- r = Distance between the particles (meters)
- |q₁ × q₂| = The absolute value of the product (force is always positive magnitude)
Nature of the Force
- If both charges are the same sign (both positive or both negative): the force is repulsive — the particles push each other away
- If the charges are opposite signs (one positive, one negative): the force is attractive — the particles pull toward each other
This is the basis of “opposites attract” in electricity and chemistry — protons attract electrons because of their opposite charges.
Common Charge Values
| Particle | Charge |
|---|---|
| Electron | −1.602 × 10⁻¹⁹ C |
| Proton | +1.602 × 10⁻¹⁹ C |
| 1 microcoulomb (μC) | 1 × 10⁻⁶ C |
| 1 nanocoulomb (nC) | 1 × 10⁻⁹ C |
| 1 picocoulomb (pC) | 1 × 10⁻¹² C |
Inverse Square Law
The r² denominator means the force falls off rapidly with distance. Double the distance and the force is reduced to 1/4. Triple the distance and it becomes 1/9. This is the same relationship as gravity (Newton’s Law of Gravitation) and light intensity.
Comparison to Gravity
The electrostatic force is vastly stronger than gravity at atomic scales. The Coulomb force between an electron and proton in a hydrogen atom (~0.53 Å apart) is about 10³⁹ times stronger than their gravitational attraction. This is why electrostatics, not gravity, governs atomic and molecular structure.
Practical Applications
Coulomb’s Law underlies the structure of atoms, chemical bonding, the design of capacitors, laser printers (which use electrostatic forces to apply toner), and the behaviour of particles in electric fields.