Coulomb's Law Calculator

Coulomb's Law Calculator. Coulomb's Law describes the electrostatic force between two electrically charged objects — whether they attract or repel each other depends on their charges and how far apart they are. Enter Charge 1 (q₁) and Charge 2 (q₂) in nanocoulombs (use negative values for negative charges) and the Distance Between Charges (r) in meters to calculate the Electrostatic Force (F) in Newtons. Secondary outputs include the force in scientific notation, the interaction type (attractive or repulsive), and the Coulomb constant used. Also try the find Skin Depth (δ) with Skin Depth Calculator.

Charge 1 (q₁) *

Enter the first charge in nanocoulombs. Use negative values for negative charges.

Charge 2 (q₂) *

Enter the second charge in nanocoulombs. Use negative values for negative charges.

Distance Between Charges (r) *

Enter the separation distance between the two charges in meters.

Results

Electrostatic Force (F)

Force (Scientific Notation)

Interaction Type

Coulomb Constant (kₑ)

What is Coulomb's Law?

Coulomb's Law describes the electrostatic force between two point charges. It states that the force is proportional to the product of the two charges and inversely proportional to the square of the distance between them. The formula is F = kₑ × |q₁ × q₂| / r², where kₑ ≈ 8.9876 × 10⁹ N·m²/C². See also our Magnetic Declination Calculator.

How do I calculate the force between two charged particles?

Multiply the two charge values together (in Coulombs), multiply by the Coulomb constant (kₑ = 8.9876 × 10⁹ N·m²/C²), then divide by the square of the distance between the charges (in meters). The result is the electrostatic force in Newtons.

Is Coulomb's force attractive or repulsive?

The force is repulsive when both charges have the same sign (both positive or both negative), and attractive when the charges have opposite signs (one positive and one negative). The direction of the force always acts along the line joining the two charges.

Is Coulomb's Law an inverse square law?

Yes. Coulomb's Law is an inverse square law because the electrostatic force decreases with the square of the distance between the charges. If you double the distance, the force becomes four times weaker.

What is the force between a proton and an electron in a hydrogen atom?

In a hydrogen atom, a proton and electron are separated by approximately 5.29 × 10⁻¹¹ m (the Bohr radius). Each has a charge of magnitude 1.602 × 10⁻¹⁹ C. Using Coulomb's Law, the attractive force between them is approximately 8.2 × 10⁻⁸ N.

What units are used for charge in this calculator?

This calculator accepts charges in nanocoulombs (nC), where 1 nC = 10⁻⁹ C. This is a convenient unit for everyday electrostatics problems. The distance is entered in meters and the resulting force is displayed in Newtons.

Under what conditions is Coulomb's Law valid?

Coulomb's Law is valid for point charges (or spherically symmetric charge distributions) that are stationary or moving slowly compared to the speed of light, in a vacuum or specified medium. It does not directly apply to extended charge distributions or relativistic speeds without modification.

How does Coulomb's Law relate to electric fields?

The electric field E created by a point charge q at a distance r is defined as E = kₑ × q / r². Coulomb's Law can be seen as the force a charge q₁ experiences when placed in the electric field E created by q₂, i.e., F = q₁ × E. You might also find our Hall Coefficient Calculator useful.