Coulomb's Law Calculator
Calculate the electrostatic force between two point charges using Coulomb's law F = kq₁q₂/r². Includes attractive vs repulsive force, electric potential energy, dielectric medium, and three-charge vector sum.
μC
μC
m
Coulomb Force |F|
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Force Type —
Electric Potential Energy U —
Extended More scenarios, charts & detailed breakdown ▾
μC
μC
m
Force (N)
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Attractive / Repulsive —
Potential Energy (J) —
Professional Full parameters & maximum detail ▾
μC
μC
m
Force & Energy
Coulomb Force |F| —
Force Type —
Potential Energy U —
Advanced
Electric Field at q₂ from q₁ —
Coulomb/Gravity Ratio —
Inverse Square Check (F×r²) —
How to Use This Calculator
- Enter charge q₁ and q₂ in microcoulombs (μC). Use negative values for negative charges.
- Enter separation distance r in meters.
- Results show force magnitude, attractive/repulsive type, and electric potential energy. Use Extended tabs for three charges or dielectric medium.
Formula
F = k × |q₁ × q₂| / r²
k = 8.9875 × 10⁹ N·m²/C² | q in Coulombs | r in meters
Potential Energy: U = k × q₁ × q₂ / r
Example
Example: q₁ = +2 μC, q₂ = −3 μC, r = 0.1 m → F = 8.99×10⁹ × 2×10⁻⁶ × 3×10⁻⁶ / 0.01 = 5.39 N (attractive).
Frequently Asked Questions
- Coulomb's law states that the electrostatic force between two point charges is F = k × q₁ × q₂ / r², where k = 8.99 × 10⁹ N·m²/C², q₁ and q₂ are charges in coulombs, and r is the separation in meters.
- When the charges have opposite signs (one positive, one negative), the product q₁q₂ is negative and the force is attractive. When both charges have the same sign, the force is repulsive. The magnitude |F| = k|q₁q₂|/r² is always positive.
- Coulomb's constant k = 1/(4πε₀) = 8.9875 × 10⁹ N·m²/C². It is related to the permittivity of free space ε₀ = 8.854 × 10⁻¹² F/m. The NIST CODATA 2022 recommended value is k = 8.9875517923 × 10⁹ N·m²/C².
- In a medium with relative permittivity εᵣ, the force is reduced: F_medium = F_vacuum / εᵣ. Water (εᵣ ≈ 80) reduces Coulomb force to just 1.25% of its vacuum value, which is why ionic compounds dissolve easily in water.
- The ratio of electrostatic to gravitational force between an electron and proton at hydrogen bond distance is approximately 10³⁹. Coulomb force is vastly stronger than gravity at the atomic scale, which is why electromagnetism governs chemistry and materials.
Related Calculators
Sources & References (5) ▾
- NIST CODATA 2022 – Coulomb Constant — NIST
- OpenStax University Physics Vol. 2 Chapter 5 – Coulomb's Law — OpenStax
- HyperPhysics – Coulomb's Law — HyperPhysics / Georgia State University
- MIT OpenCourseWare 8.02 – Electromagnetism (Lewin) — MIT OCW
- Halliday D, Resnick R, Walker J — Fundamentals of Physics, 11th Ed. — Wiley