Coulomb's Law Calculator

What is Coulomb’s Law?

Coulomb’s Law describes the electric force between two point charges. The force depends on the charge magnitudes and the distance between them. It is attractive when the signs are opposite and repulsive when the signs are the same. This tool helps students solve for F, r, or a charge value, just like in school.

Constant and Units

• Coulomb constant: k ≈ 9×10⁹ N·m²/C².
• Charge units: C, µC (microcoulomb = 10⁻⁶ C), nC (nanocoulomb = 10⁻⁹ C).
• Distance units: m, cm (10⁻² m), mm (10⁻³ m).
• Force unit: N (Newton).

Core Formulas

• Find Force: F = k × |q1·q2| / r²
• Find Distance: r = √(k × |q1·q2| / F)
• Equal Charges (q1 = q2 = q): q = √((F·r²)/k)
• Unknown Charge: q2 = (F·r²) / (k·q1)
• Force Type: sign(q1·q2) < 0 ⇒ Attraction; > 0 ⇒ Repulsion; = 0 ⇒ Zero force.

How this calculator computes

1. Convert all inputs to SI: charges to C, distance to m.
2. Select the correct formula for the chosen mode (F, r, q, or q2).
3. Substitute numbers with k = 9×10⁹ (or a custom k if you uncheck default).
4. Display both scientific and normal forms of the result.
5. Determine force type from the signs (+/–) of q1 and q2.
6. Show a clear step-by-step explanation: conversions, substitution, algebra, final value.

Why no “Solve” button?

The calculator updates automatically as you type, matching the experience of our other calculators. Once inputs are valid, the result and steps appear instantly—no extra click needed.

Quick classroom example

q1 = 4 µC and q2 = 9 µC, both positive; r = 6 cm; default k. Convert: 4 µC = 4×10⁻⁶ C, 9 µC = 9×10⁻⁶ C, 6 cm = 6×10⁻² m. Substitute: F = k × |q1·q2| / r² ⇒ F ≈ 90 N. Both positive ⇒ Repulsion.

Notes & safety

• Avoid unrealistically tiny distances; results can be non-physical.
• If any charge is zero, the force is zero.
• Mind your units: µC and nC differ greatly from C.