Coulomb's Law Calculator
Find the electrostatic force between two point charges. Enter each charge (in C, mC, µC, nC or pC) and the distance between them (m, cm, mm or km) to get the Coulomb force and whether it is attractive or repulsive.
Example: with Charge 1 1 · Charge 1 unit µC · Charge 2 1 · Charge 2 unit µC · Distance apart 1 → Electrostatic force: 8.9875 mN.
- Force in newtons8.9875e-3 N
- Nature of the forceRepulsive — the charges have the same sign
Computed by the calculator below using its default values. Change any input to see your own numbers.
Coulomb's law: F = k·q₁·q₂ / r², with Coulomb's constant k = 8.9875 × 10⁹ N·m²/C². Like charges repel, opposite charges attract, and the force falls off with the square of distance.
An inverse-square force between charges
Coulomb's law says the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them: F = k·q₁·q₂/r². Double the distance and the force drops to a quarter; halve it and the force quadruples. The constant k = 8.9875 × 10⁹ N·m²/C² sets the scale, and it is large — which is why even microcoulomb charges produce forces you can feel.
The sign of the product tells you the direction. Two like charges give a positive product and push apart; opposite charges give a negative product and pull together. The form is identical to Newton's law of gravitation, an inverse-square law with a constant out front — the key difference being that gravity only attracts, while the electric force does both.
How it’s calculated
F = k·|q₁·q₂| / r² for the magnitude, with Coulomb's constant k = 8.9875 × 10⁹ N·m²/C². Charges convert to coulombs (µC = 1e-6, nC = 1e-9, mC = 1e-3, pC = 1e-12 C) and distance to meters (cm = 1e-2, mm = 1e-3, km = 1e3 m). The sign of q₁·q₂ sets attraction or repulsion.
Point charges (or uniformly charged spheres) in a vacuum or air. A dielectric medium would reduce the force by its relative permittivity, which this tool does not apply.
Force between two 1 µC charges
| Separation | Electrostatic force |
|---|---|
| 1 mm | 8,987.5 N |
| 1 cm | 89.875 N |
| 10 cm | 0.899 N |
| 1 m | 8.9875 mN |
| 10 m | 0.0899 mN |
Computed with F = k·q₁·q₂/r², k = 8.9875 × 10⁹; rounded.
Common mistakes
- Forgetting to square the distance — the force follows 1/r², not 1/r.
- Leaving charges in µC or nC without converting to coulombs before applying k.
- Ignoring the sign: like charges repel, opposite charges attract, even though the magnitude is the same.
- Using a distance of zero, where the point-charge formula blows up to infinity.
Frequently asked questions
What is Coulomb's law formula?
F = k·q₁·q₂ / r², where k = 8.9875 × 10⁹ N·m²/C², q₁ and q₂ are the charges in coulombs, and r is the separation in meters.
What is the value of Coulomb's constant?
k ≈ 8.9875 × 10⁹ N·m²/C², sometimes written as 1/(4πε₀). It is the proportionality constant that sets the strength of the electrostatic force.
How do I know if the force is attractive or repulsive?
Check the signs of the charges. Like signs (both positive or both negative) repel; opposite signs attract. The magnitude is the same either way.
What happens to the force if I double the distance?
It drops to one quarter. The force depends on 1/r², so doubling r multiplies the force by 1/4, and halving r multiplies it by 4.