Coulomb's Law Calculator

Compute the magnitude and direction of electrostatic force between two point charges. Supports µC, nC, C and distance in meters or centimeters.

Coulomb constant k = 8.9875517923 × 10⁹ N·m²/C² (CODATA 2018)
⚡ Repulsive (both +2µC, r=0.1m)
? Attractive (+2µC, -1µC, r=5cm)
? 5nC & 10nC, r=2cm
⚙️ 1C & 1C, r=1m (huge force)
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Coulomb's Law: Fundamental Law of Electrostatics

Coulomb's law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them. The force acts along the line joining the charges. This calculator applies the precise formula F = k · |q₁·q₂| / r² and determines whether the interaction is repulsive (same sign) or attractive (opposite signs).

$$ F = k \frac{|q_1 q_2|}{r^2}, \quad k = 8.9875517923 \times 10^9 \ \text{N·m}^2/\text{C}^2 $$

$$ Vector form: \vec{F}_{12} = k \frac{q_1 q_2}{r^2} \hat{r}_{12} $$

The law was first published by French physicist Charles-Augustin de Coulomb in 1785 and was essential to the development of the theory of electromagnetism. Along with Gauss's law, it forms the basis of electrostatics. Our tool uses the CODATA internationally recommended value of the Coulomb constant, ensuring high precision for scientific and educational purposes.

How to Use the Interactive Coulomb Calculator

  • Enter the numeric values of charges q₁ and q₂ (positive or negative).
  • Select appropriate units: microcoulombs (µC), nanocoulombs (nC) or coulombs (C).
  • Input the separation distance r in meters or centimeters.
  • Press "Calculate Force" to get the force magnitude in newtons (N) and the type of interaction.
  • The diagram shows two charged spheres with force vectors (red for repulsion, green arrows pointing inward for attraction).
Real-World Application: Molecular Interactions

In chemistry, Coulomb's law explains ionic bonding: the attractive force between Na⁺ and Cl⁻ ions in salt. For a typical ion pair at distance ≈ 0.28 nm, using q = ±1.6×10⁻¹⁹ C gives a force of several nano-Newtons. This calculator can model such interactions by entering appropriate charge units (nC) and small distances (converted to meters). Students can verify that ionic bond strength decreases with distance squared, influencing lattice energy in crystals.

Deep Dive: Derivation and Vector Nature

The scalar form gives magnitude only. For two charges, the force on q₁ due to q₂ is directed along the line from q₁ to q₂: repulsive if q₁·q₂ > 0, attractive if product is negative. Our algorithm calculates the force magnitude and determines direction based on sign analysis. Additionally, the force obeys Newton's third law: F₁₂ = -F₂₁. The tool also displays the effective interaction (attract/repel) for visual understanding.

Unit Conversions & Practical Tips

The standard SI unit for charge is coulomb (C), but many lab-scale charges are in µC (10⁻⁶ C) or nC (10⁻⁹ C). The calculator automatically converts to coulombs before applying the formula. Distance must be in meters for correct force output (1 cm = 0.01 m). The result is shown in newtons, which can be converted to millinewtons or micronewtons for convenience using standard prefixes.

Example scenario q₁, q₂ (converted) r (m) Force magnitude Type
Two protons (elementary charge) 1.602×10⁻¹⁹ C 1.0×10⁻¹⁰ m 2.307×10⁻⁸ N Repulsive
Electron & proton in hydrogen atom +1.6e-19 C, -1.6e-19 C 5.3×10⁻¹¹ m 8.2×10⁻⁸ N Attractive
2 µC and 5 µC, distance 10 cm 2e-6 C , 5e-6 C 0.1 m 8.988 N Repulsive

Common Misconceptions and Clarifications

  • Force becomes infinite when r → 0: Coulomb's law applies to point charges; real charges have finite size, and at very short distances other nuclear forces dominate.
  • Sign of force indicates direction: The scalar law uses absolute values for magnitude; our result displays direction separately using the sign of q₁·q₂.
  • k changes in different media: In a dielectric, the effective force reduces by a factor of the relative permittivity. Our calculator assumes vacuum (or air, approximately).

The Coulomb Constant: Precision and History

k = 8.9875517923(14) × 10⁹ N·m²/C² is derived from the speed of light and magnetic constant: k = 1/(4πε₀). Its value is known to high precision due to modern experiments. The calculator uses the recommended 2018 CODATA value for accuracy in research-grade applications.

Frequently Asked Questions

Electrostatic force can be attractive or repulsive and is generally much stronger than gravity. The gravitational force is always attractive and depends on masses, not charge.

For multiple point charges, the net force is the vector sum of individual Coulomb forces. This calculator focuses on a two‑charge system; for multiple charges consider superposition manually.

Distance zero would lead to division by zero. The calculator validates input and displays an error. Physically, charges cannot occupy the same point.

Results use double‑precision arithmetic with the latest CODATA k value. Typical rounding errors are below 1e-12 relative.

Scientific basis and review – This Coulomb's Law calculator references standard electrodynamics literature (Griffiths, Jackson) and NIST reference constants. The tool is developed by getzenquery tech team for educational accuracy. Last revised: June 2026.

References: NIST CODATA (2018); Griffith, D.J. "Introduction to Electrodynamics"; Coulomb, C. A. (1785) – "Premier mémoire sur l’électricité et le magnétisme".