What Is Coulomb's Law and How Is It Calculated?
Coulomb's law describes the electrostatic force between two stationary electric charges: the force is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them. It applies to point charges and is one of the foundational equations of electromagnetism.
The Coulomb's law formula — named after French physicist Charles-Augustin de Coulomb, who published it in 1785 — is: F = k × |q₁ × q₂| ÷ r², where F is the electrostatic force in newtons (N), q₁ and q₂ are the two charges in coulombs (C), r is the distance between their centers in meters (m), and k is Coulomb's constant.
According to the National Institute of Standards and Technology (NIST), Coulomb's constant k equals 8.9875517873681764 × 10⁹ N·m²/C² in a vacuum — a value derived from the permittivity of free space (k = 1 / 4πε₀).
How to Use This Coulomb's Law Calculator
Enter both charges and the distance between them, choose your preferred units, and the force updates instantly. Here's what each field means:
- Charge 1 & Charge 2: The magnitude and sign of each point charge, in nanocoulombs (nC), microcoulombs (μC), millicoulombs (mC), or coulombs (C). Most everyday static charges fall in the nanocoulomb-to-microcoulomb range.
- Distance: The straight-line separation between the two charges, in millimeters, centimeters, or meters.
- Show Force In: Displays the result in newtons, millinewtons, micronewtons, or pound-force, whichever suits your problem.
This calculator works entirely in SI-derived units with an imperial force option (pound-force), so it applies equally to physics coursework anywhere in the world and to engineering problems that use either metric or imperial conventions.
What the Coulomb's Law Result Means
The sign of the product q₁ × q₂ determines whether the charges attract or repel — the table below summarizes the three possible cases.
| Charge Signs | Force Nature | Effect |
|---|---|---|
| Both positive or both negative | Repulsive | Charges push apart along the line connecting them |
| One positive, one negative | Attractive | Charges pull toward each other |
| Either charge is zero | None | No electrostatic force acts between them |
For example, two charges of +1 μC each, separated by 1 cm, experience a repulsive force of about 89.88 N — roughly the weight of a 9 kg object — which illustrates why even small static charges produce noticeable forces at short range.
Frequently Asked Questions
What is Coulomb's law used for?
Coulomb's law calculates the electrostatic force between any two point charges, and it underlies electric field theory, capacitor design, and the behavior of charged particles in physics, chemistry, and electrical engineering.
How accurate is this Coulomb's law calculator?
This calculator applies the exact Coulomb's law formula for point charges in a vacuum or air, using the standard constant k = 8.9875517873681764 × 10⁹ N·m²/C². Charges spread over a larger surface, or separated by a medium other than air with a different dielectric constant, will experience a different force in practice.
What is the difference between Coulomb's law and the law of gravitation?
Both are inverse-square laws with a similar mathematical form, but Coulomb's law describes the force between electric charges and can be attractive or repulsive, while Newton's law of gravitation describes the force between masses and is always attractive.
How do I increase or decrease the electrostatic force between two charges?
Because force is proportional to the product of the charges and inversely proportional to the square of the distance, increasing either charge increases the force proportionally, while doubling the distance reduces the force to one quarter. Halving the distance instead quadruples it.