Coulomb's Law Calculator — Electric Force Between Charges
Calculate the electrostatic force between two charged particles using Coulomb's Law. Covers attraction, repulsion, field strength, and real electrostatics examples.
Two charged objects exert a force on each other across empty space — no contact required. Coulomb's Law describes this force with the same inverse-square dependence as gravity, but electric forces are vastly stronger and can be either attractive or repulsive. That combination of strength and directionality is what makes electricity so central to chemistry and electronics.
The CalcHub Coulomb's Law calculator computes electric force from charge magnitudes and separation distance.
The Formula
F = k × |q₁| × |q₂| / r²- F = electric force (Newtons, N)
- k = Coulomb's constant = 8.99 × 10⁹ N·m²/C²
- q₁, q₂ = charges (Coulombs, C)
- r = separation distance (meters)
How Strong is Electric Force Compared to Gravity?
For two electrons separated by 1 meter:
- Electric force: F_e = 8.99 × 10⁹ × (1.6 × 10⁻¹⁹)² / 1² = 2.3 × 10⁻²⁸ N
- Gravitational force: F_g = 6.67 × 10⁻¹¹ × (9.1 × 10⁻³¹)² / 1² = 5.5 × 10⁻⁷¹ N
Worked Example
Two small charged spheres: q₁ = +5 μC, q₂ = −3 μC, separated by 20 cm (0.2 m).
F = (8.99 × 10⁹ × 5 × 10⁻⁶ × 3 × 10⁻⁶) / (0.2)²
= (8.99 × 10⁹ × 15 × 10⁻¹²) / 0.04
= 134.85 / 0.04
= 3.37 N
Because charges are opposite, the force is attractive. 3.37 N is roughly the weight of a 340g object — substantial for two microscopic charges.
What is permittivity and how does it affect Coulomb's Law?
Coulomb's constant k = 1/(4πε₀), where ε₀ = 8.85 × 10⁻¹² C²/(N·m²) is the permittivity of free space. In a medium with relative permittivity ε_r, the force is reduced: F = kq₁q₂/(ε_r r²). Water (ε_r ≈ 80) greatly weakens electrostatic forces, which is why ionic compounds dissolve in water.
Is Coulomb's Law exact?
For point charges in vacuum, it's exact (as far as classical electrostatics goes). For real charged objects, it applies when separation is large compared to object size. Quantum electrodynamics (QED) gives a more precise picture, but Coulomb's Law is accurate for all practical macroscopic situations.
How does Coulomb's Law relate to electric field?
Electric field E at distance r from charge q: E = kq/r². The force on a test charge Q in this field: F = QE = kqQ/r² — identical to Coulomb's Law. Electric field is a useful concept because it describes the effect of charges at every point in space, independent of what test charge you place there.