Calculators/Physics/Coulomb's Law

Coulomb's Law

Force between charges · attraction / repulsion

Coulomb's Law — illustration

Charges can be entered in scientific notation, e.g. 1e-6 (1 µC) or -3.2e-9. The sign decides attraction/repulsion.

F = k·|q₁·q₂| / r²
1.798 N
⟶ ⟵ Repulsion (like charges)

Coulomb's constant k = 8.99·10⁹ N·m²/C². The force decreases with the square of the distance — doubling the separation reduces it fourfold.

Coulomb's law describes the force of interaction between two point charges:

F=k∣q1 q2∣r2F=k\frac{|q_1\,q_2|}{r^2}

where k=8.99⋅109 N⋅m2C2k=8.99\cdot10^9\ \tfrac{\text{N·m}^2}{\text{C}^2}, q1,q2q_1,q_2 are the charges, and rr is the distance between them. The force decreases with the square of the distance — doubling the separation weakens it fourfold.

The sign of the product of the charges decides its character: like charges (the same sign) repel, unlike charges attract. You can enter the charges in scientific notation, e.g. 1e-6 (one microcoulomb).

Examples

q₁ = 1 µC, q₂ = 2 µC, r = 0.1 m
→ F = 8.99·10⁹·2·10⁻¹²/0.01 ≈ 1.8 N (repulsion)
Doubling the distance r
→ the force drops 4× (1/r² dependence)

Frequently asked questions

When do charges attract and when do they repel?+

Unlike charges (plus and minus) attract, like charges (two pluses or two minuses) repel. The calculator recognizes this from the signs of the charges you enter.

How does Coulomb's law resemble gravity?+

Both have the 1/r² form — the force decreases with the square of the distance. The difference: gravity always attracts, while the electric force can attract or repel.

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