MotionLab

Coulomb's Law Calculator

The electric version of gravity — like charges repel, opposite charges attract.

Charge q₁ (C)

Charge q₂ (C)

Distance (m)

Electrostatic force (N)

1.798

F = k|q₁q₂| / r²

What you entered

Charge q₁ (C): 0.000001Charge q₂ (C): 0.000002Distance (m): 0.1

1
F = k|q₁q₂| ÷ r²
8.988e+9 × |1.00e-6 × 2.00e-6| ÷ 0.1²= 1.7975e+0 N

Result

Electrostatic force (N): 1.798

Two charges of 1.00e-6 C and 2.00e-6 C separated by 0.1 m exert a force of 1.7975e+0 N on each other.

Electrostatic force between charges

Coulomb's law: k times the product of the charges over the distance squared, with k at 8.988e9.

Charge 1 (C)	Charge 2 (C)	Distance (m)	Force (N)
1.6e-19	1.6e-19	1e-10	2.3008e-8
1e-6	1e-6	0.1	8.9876e-1
2e-6	3e-6	0.2	1.3481e+0
1e-6	2e-6	0.05	7.1900e+0
1e-3	1e-3	1	8.9876e+3

The first row is two elementary charges at roughly atomic separation, and although 2.3e-8 N sounds negligible it is around 1e36 times stronger than the gravitational attraction between the same two protons - which is why chemistry is electromagnetic and gravity is irrelevant at atomic scale. The law has the same inverse-square form as gravitation, but charges can be positive or negative so the force may attract or repel, whereas gravity only ever attracts. A coulomb is an enormous charge: the last row shows two millicoulombs a metre apart pushing with nearly 9 kN.

Same shape as gravity, vastly stronger

Coulomb's law has the same inverse-square form as Newton's gravitational law, but the electrostatic force between two protons is about 10³⁶ times stronger than their gravitational attraction — this enormous difference is why chemistry and biology are governed by electromagnetic forces, not gravity.

Sign tells you the direction

When both charges have the same sign the force is positive (repulsive), and when they have opposite signs it's negative (attractive) — the magnitude tells you how strong, and the sign tells you which way.

Frequently asked questions

Two protons in a helium nucleus are about 1 fm (10⁻¹⁵ m) apart. What electrostatic force repels them?

F = kq₁q₂/r² = 8.99×10⁹ × (1.6×10⁻¹⁹)² / (10⁻¹⁵)² = 230 N. That's about 52 pounds of repulsion — at nuclear scales, electrostatic repulsion is enormous. The strong nuclear force (even stronger) holds the nucleus together despite this.

How does Coulomb's law compare to Newton's gravity?

Same mathematical form (inverse-square), but electrostatic force is ~10³⁶ times stronger than gravity for two protons. Gravity only dominates at large scales because most matter is electrically neutral (positive and negative charges cancel), while mass never cancels. See the gravitational force calculator.

Why does electrostatic force fall off with distance squared?

The electric field spreads uniformly over a sphere of radius r. The sphere's surface area = 4πr², so field strength per unit area drops as 1/r². Double the distance = 4× the sphere area = ¼ the field intensity. This geometric argument applies to any force spreading from a point source.

Can I use Coulomb's law for charged objects that aren't point charges?

Only if the objects are small compared to their separation. For large or extended charge distributions, you need to integrate Coulomb's law over the charge distribution, or use Gauss's law. At distances much larger than the object size, treating them as point charges is an excellent approximation.

What's the force between a balloon rubbed on hair and a wall?

A rubbed balloon picks up about 10 nC (10⁻⁸ C) of charge. At 1 cm from the wall, the image-charge attraction is roughly F = kq²/(2r)² ≈ 8.99×10⁹ × (10⁻⁸)² / 0.0004 ≈ 0.002 N — just enough to overcome gravity for a light balloon.