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.