Coulomb's Law Calculator
Calculate the electrostatic force between two point charges using Coulomb's law: F = kq₁q₂/r². Enter the two charges (C) and separation distance (m).
How to use this tool
- Enter charge q₁, charge q₂ and separation r in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your electrostatic force and the full breakdown beneath it.
Coulomb's law gives the electrostatic force between two point charges: F = kq₁q₂/r², where k = 8.9875×10⁹ N·m²/C². Like charges repel; opposite charges attract.
Formula
F = k |q1| |q2| ÷ r2
Where: k = 8.9875 × 109 N·m²/C² (Coulomb's constant), q1, q2 = charges (C), r = separation (m).
How it works
Coulomb's law gives the magnitude of the electrostatic force between two point charges. The calculator uses the absolute values of both charges to compute force magnitude, then determines whether the interaction is attractive (opposite signs) or repulsive (same signs) from the product q1q2.
The result is rounded to 6 decimal places. The formula applies strictly to point charges or uniformly charged spheres in a vacuum; the presence of a dielectric medium would require dividing k by the relative permittivity εr.
Worked example
Worked example
- Given: q₁ = 1 × 10⁻⁶ C (μC), q₂ = 1 × 10⁻⁶ C, separation r = 0.1 m.
- Apply: F = k × |q₁| × |q₂| / r² = 8.9875×10⁹ × 10⁻⁶ × 10⁻⁶ / (0.1)².
- F = 8.9875×10⁹ × 10⁻¹² / 0.01 = 8.9875×10⁻³ / 0.01 = 0.89875 N.
- Both charges are positive, so the interaction is repulsive.
Electrostatic force F = 0.89875 N (Repulsive, like charges).
Key terms
- Coulomb's constant (k)
- Equal to 1/(4πε₀) ≈ 8.9875 × 10⁹ N·m²/C²; sets the strength of electrostatic interactions in a vacuum.
- Point charge
- An idealised charged object whose physical size is negligible compared to the distances involved.
- Electrostatic force
- The attractive or repulsive force between stationary electric charges, described by Coulomb's law.
- Coulomb (C)
- The SI unit of electric charge. One coulomb is the charge transported by a current of one ampere in one second.
- Permittivity of free space (ε₀)
- A physical constant ≈ 8.854 × 10⁻¹² F/m relating to how easily an electric field forms in a vacuum.
Frequently asked questions
- What is Coulomb's constant k?
- k = 1/(4πε₀) ≈ 8.9875×10⁹ N·m²/C², where ε₀ is the permittivity of free space. It appears in all electrostatic force calculations.
- What is a typical charge magnitude?
- 1 μC (1×10⁻⁶ C) is typical in electrostatics experiments. An electron carries 1.602×10⁻¹⁹ C.