The Coulomb's law calculator computes the electrostatic force between two point charges using F = k × |q₁ × q₂| / r². Enter charge magnitudes and separation distance to find the attractive or repulsive force in Newtons.
Coulomb's Law Calculator (F = kq₁q₂/r²)
How to Use the Coulomb's Law Calculator
Coulomb's law quantifies the electrostatic force between charged particles. It's the foundation of electrostatics and explains chemical bonding, atomic structure, and electrical phenomena.
The Formula
F = k × |q₁| × |q₂| / r², where k = 8.9875 × 10⁹ N·m²/C² (Coulomb's constant, also written as 1/(4πε₀)). Like charges repel; opposite charges attract. The force follows an inverse square law — doubling the distance reduces the force by a factor of 4.
Example: Proton and Electron in Hydrogen
q₁ = +1.602 × 10⁻¹⁹ C (proton), q₂ = −1.602 × 10⁻¹⁹ C (electron), r = 5.29 × 10⁻¹¹ m (Bohr radius). F = 8.9875×10⁹ × (1.602×10⁻¹⁹)² / (5.29×10⁻¹¹)² ≈ 8.24 × 10⁻⁸ N. This attractive force keeps the electron in orbit.
Common Charge Values
Enter charges in μC (microcoulombs) for typical lab experiments. A microcoulomb is 10⁻⁶ C. Van de Graaff generators hold ~1–10 μC. Lightning transfers ~1–5 C. Elementary charge (proton/electron) = 1.602 × 10⁻¹⁹ C — select "e" from the unit dropdown for atomic-scale problems.
FAQ
What is Coulomb's law?
Coulomb's law gives the electrostatic force between two point charges: F = k × |q₁ × q₂| / r², where k = 8.9875 × 10⁹ N·m²/C² (Coulomb's constant), q₁ and q₂ are the charges in Coulombs, and r is the distance between them in meters. Like charges repel (F positive), opposite charges attract (F negative).
How does Coulomb's law compare to gravity?
Both forces follow an inverse square law (F ∝ 1/r²). But electrostatic forces are enormously stronger. The electromagnetic force between an electron and proton is 10³⁹ times stronger than their gravitational attraction. This is why chemistry (electron interactions) is dominated by electrostatics, not gravity.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
What are typical charge values in physics problems?
Elementary charge (proton or electron): 1.602 × 10⁻¹⁹ C. Typical electrostatics lab charges: 1-100 μC (microcoulombs). Lightning strike: 1-5 C transferred. A Van de Graaff generator holds up to ~10 μC. Entering charges in μC is most practical for most textbook problems.