Coulomb's Law Calculator
The Electric Force Behind Every Charge Interaction
Coulomb's law is the electric analogue of Newton's law of gravitation: two charged particles pull or push on each other with a force that depends on how large the charges are and how far apart they sit. Charles-Augustin de Coulomb worked out the relationship using a torsion balance in 1785, and it remains the starting point for essentially all of classical electrostatics, from chemical bonding to capacitor design.
The Formula
k is Coulomb's constant, 8.99×10&sup9; N·m²/C². Like charges (both positive or both negative) produce a positive force value, meaning repulsion; opposite charges produce a negative value, meaning attraction. Because the distance term is squared, force falls off steeply as separation increases.
Why the Inverse-Square Term Matters
- Atomic and molecular structure — the attraction between electrons and nuclei, and the repulsion between electron clouds, is fundamentally a Coulomb force problem.
- Electrostatic discharge and safety — static buildup and spark risk in industrial settings depend on charge magnitude and proximity, both Coulomb's law inputs.
- Capacitor and sensor design — components that store or detect charge are engineered around the forces those charges exert on nearby conductors.
- Particle physics — Coulomb repulsion between protons is one of the forces that nuclear binding energy has to overcome.
How Fast Force Drops With Distance
For two fixed 1-microcoulomb charges, moving them apart shows just how quickly the inverse-square relationship weakens the force:
| Distance | Force |
|---|---|
| 0.01 m | 89.9 N |
| 0.1 m | 0.899 N |
| 1.0 m | 0.00899 N |
A tenfold increase in distance reduces the force to 1/100th of its original value — the signature of an inverse-square law.
How to Use This Calculator
- Enter Charge q1 and Charge q2, in coulombs (use negative values for negative charges).
- Enter Distance r, the separation between the two charges, in meters.
- Select Calculate to get the force in newtons, along with whether it is attractive or repulsive.
Related Calculations
For the broader family of electric and magnetic forces on a moving charge, see the Electromagnetic Force Calculator, or compare this to the analogous mass-based force with the Gravitational Force Calculator.