Coulomb's Law Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
The electrostatic force between two charges is calculated with F = k × q1 × q2 ÷ r², where k is Coulomb's constant (about 8.99 × 10⁹ N·m²/C²). Between two 1 µC charges 1 m apart, this force is about 0.00899 N.
Explanation
Coulomb's law describes the electrostatic force acting between two point electric charges: it's proportional to the product of the two charges and inversely proportional to the square of the distance between them — exactly the same mathematical form as Newton's law of universal gravitation (see our gravitational force calculator), with Coulomb's constant k in place of the gravitational constant G. The sign of the result carries physical meaning: a positive value indicates a repulsive force (both charges have the same sign, they push each other apart), while a negative value indicates an attractive force (charges of opposite sign, they pull toward each other). The constant k is about 8.9875 × 10⁹ N·m²/C² — it's related to the vacuum permittivity ε₀ by k = 1 ÷ (4πε₀). This calculator treats both charges as point charges (or uniformly charged spheres, for which the formula remains exact using the distance between their centers); it doesn't account for the effect of other surrounding charges or dielectric materials, which would reduce the actual force compared to a vacuum.
Example: two 1 µC charges, 1 m apart
Inputs
Charge 1: 1 µC. Charge 2: 1 µC. Distance: 1 m.
Calculation
F = 8.9875 × 10⁹ × (1 × 10⁻⁶) × (1 × 10⁻⁶) ÷ 1² = 8.9875 × 10⁹ × 10⁻¹² ≈ 0.00899 N.
Result
The repulsive electrostatic force between these two charges is about 0.00899 N.
Frequently asked questions
What does a negative result mean?
A negative result indicates an attractive force: the two charges have opposite signs (one positive, one negative) and pull toward each other. A positive result, on the other hand, indicates a repulsive force between two charges of the same sign.
What's the difference between Coulomb's law and the law of universal gravitation?
Both laws have exactly the same mathematical form (proportional to the product of two quantities, inversely proportional to the square of the distance), but they describe very different phenomena: gravitation acts between masses and is always attractive, while electrostatic force acts between electric charges and can be attractive or repulsive depending on their signs. Electrostatic force is also far stronger: between two protons, it's about 10³⁶ times stronger than their mutual gravitational attraction.
Does this formula work in any medium?
The constant k used here corresponds to a vacuum (or approximately air). In another medium (water, oil, a dielectric material), the actual force is reduced by a factor called the material's relative permittivity, specific to each substance — this calculator doesn't account for that effect.