Physics › Electric charge
Electric charge calculations
Two charges, one distance — Coulomb's law turns that into a force, in newtons, with a direction. Drag the sliders and watch it react.
Coulomb's law calculator
F = k · q₁ · q₂ / r²
Attractive force of 0.2157 N
Same signs push apart, opposite signs pull together. Halve the distance and the force quadruples — that's the 1/r².
Coulomb's law
The force between two point charges is
F = k · q₁ · q₂ / r²
- q₁, q₂ — the two charges, in coulombs (C). A microcoulomb (µC) is 10⁻⁶ C.
- r — the distance between them, in metres.
- k — Coulomb's constant, ≈ 8.99 × 10⁹ N·m²/C².
Reading the sign
q₁·q₂ comes out positive (same signs), the force is repulsive — they push apart. If it's negative (opposite signs), it's attractive — they pull together.Why the 1/r² matters
Distance is squared, so small changes hit hard. Move the charges twice as far apart and the force drops to a quarter. Move them three times as far and it's a ninth. Same shape as Newton's gravity — both are inverse-square laws because both spread out over the surface of a sphere.
A worked example
Two +2 µC charges, 0.5 m apart:
F = (8.99×10⁹)(2×10⁻⁶)(2×10⁻⁶) / (0.5)² ≈ 0.14 N
Positive product → repulsive. Set those values on the slider and you should see the same answer.
Field, charge and force
A handy companion equation: a charge q sitting in an electric field E feels a force F = q · E. Coulomb's law is what you get when that field is the one produced by another point charge.