Coulomb's Law Calculator

Coulomb’s Law describes the electrostatic force between two electrically charged objects. It is the foundational equation of electrostatics — the electric equivalent of Newton’s gravitational law.

Formula: F = k × (|q₁ × q₂|) ÷ r²

Where:

• F: the electrostatic force in Newtons (N). Positive = repulsive; negative = attractive.
• k: Coulomb’s constant = 8.9875 × 10⁹ N·m²/C² (in vacuum)
• q₁, q₂: the electric charges of the two objects, in Coulombs (C). Like charges (both positive or both negative) repel; unlike charges attract.
• r: the distance between the centers of the two charges, in meters.

Alternative form using permittivity: F = (1 ÷ 4πε₀) × (q₁q₂ ÷ r²) where ε₀ = 8.854 × 10⁻¹² C²/(N·m²) is the permittivity of free space.

Key relationships:

• Force doubles if either charge doubles.
• Force quadruples if distance is halved (inverse-square law: same as gravity).
• Force is always along the line connecting the two charges.

Reference: elementary charge: The charge of one electron: e = 1.602 × 10⁻¹⁹ C (negative). The charge of one proton: e = +1.602 × 10⁻¹⁹ C (positive). One Coulomb = the charge of approximately 6.24 × 10¹⁸ electrons.

Worked example: Two charged spheres: q₁ = +3 μC (3 × 10⁻⁶ C), q₂ = −2 μC (2 × 10⁻⁶ C), separated by r = 0.05 m (5 cm). F = 8.9875 × 10⁹ × (3 × 10⁻⁶ × 2 × 10⁻⁶) ÷ (0.05)² F = 8.9875 × 10⁹ × 6 × 10⁻¹² ÷ 0.0025 F = 8.9875 × 10⁹ × 2.4 × 10⁻⁹ F = 21.57 N — attractive force (opposite charges)

Real-world applications: DNA binding forces, ionic bond strength, capacitor design, van der Waals interactions, protein folding forces, and electrostatic precipitators in industrial air filtration.

Three things worth keeping in mind. First, the electrostatic force between two protons is about 10³⁶ times stronger than their gravitational pull. The reason gravity wins at planetary and astronomical scales is not strength but neutrality: bulk matter cancels its electric charges, while masses always add. Second, the formula above assumes vacuum. In a medium with relative permittivity ε_r, the force drops by that factor — water’s ε_r ≈ 80 is why ionic salts dissolve so easily. Third, the superposition principle lets you handle multi-charge systems: the total force on any one charge is the vector sum of the Coulomb forces from each other charge, calculated independently. There is no shielding or interaction term to worry about — each pair just acts as if the others weren’t there.