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.
Enter valid charge values; distance must be greater than 0.
Magnitude |F|
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Other units
- Millinewtons (mN)
- —
- Micronewtons (μN)
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- Kilonewtons (kN)
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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
- · Uses the CODATA recommended vacuum Coulomb constant kₑ = 8.9875517873681764 × 10⁹ N·m²/C² (exact since the 2019 SI redefinition).
- · The sign of F encodes direction: positive = repulsive (like charges), negative = attractive (unlike charges); the widget shows it as a colour-coded label.
- · Valid for point charges in vacuum / air. A dielectric medium (water, plastic, …) reduces the actual force by the relative permittivity εᵣ.
- · 1 C is a huge charge; everyday static-electricity problems use µC (10⁻⁶ C) or nC (10⁻⁹ C).
- · Like Newtonian gravity, Coulomb force follows an inverse-square law — but at atomic scales it is ~10³⁶ times stronger than gravity.
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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