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Science

Coulomb's Law Calculator

Coulomb's law is the foundation of electrostatics: the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the separation. Like charges repel, unlike charges attract.

Magnitude |F|

Other units

Millinewtons (mN)
Micronewtons (μN)
Kilonewtons (kN)

Formula

F = kₑ · q₁ · q₂ / r², kₑ ≈ 8.9876 × 10⁹ N·m²/C²

Uses the CODATA vacuum Coulomb constant; a dielectric medium (water, air) reduces the actual force by a factor of εᵣ.

Formula

F = kₑ · q₁ · q₂ / r², kₑ ≈ 8.9876 × 10⁹ N·m²/C²

Frequently asked

What does the sign of the result mean?

A positive result means the charges repel (both positive or both negative). A negative result means they attract (opposite signs). The tool labels this directly as "Repulsive" or "Attractive".

Why is the force for 1 C so enormous?

1 coulomb corresponds to the charge of about 6.24 × 10¹⁸ electrons — an enormous quantity on everyday scales. Two 1-C charges at 1 m apart experience ~9 GN of force, dozens of orders of magnitude more than the gravity between two 1-kg masses. Realistic everyday problems use µC or nC.

Can I use this for more than two charges?

This tool only computes the pairwise force between two charges. For a multi-charge system, apply the superposition principle: compute each pairwise force separately as a vector and sum them — direction matters.

Can I use it to analyse ions in water?

You can use it for an order-of-magnitude estimate, but water has a relative permittivity εᵣ ≈ 80, which reduces the actual force by that factor. In a dielectric medium, divide the result by εᵣ — i.e. F = kₑ · q₁ · q₂ / (εᵣ · r²).

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