Free Coulomb's Law Calculator

Understanding Electrostatic Force with Coulomb's Law

This electrostatic force calculator, also known as an electric force calculator or charge force calculator, quickly determines the magnitude and direction of the force between two stationary point charges. The tool applies Coulomb's inverse‑square law, a cornerstone of electromagnetism.

Coulomb's law states that the electrostatic force acts along the straight line joining two charges. Its magnitude is directly proportional to the product of the charges and inversely proportional to the square of the distance separating them. The force is repulsive when both charges have the same sign and attractive when they have opposite signs.

The mathematical representation of Coulomb's law is:

$$F = k_e \dfrac{q_1 q_2}{r^2}$$

where:

• $F$ is the electrostatic force in newtons (N),
• $q_1$ and $q_2$ are the charge magnitudes in coulombs (C),
• $r$ is the distance between the charges in meters (m),
• $k_e$ is Coulomb's constant, equal to $8.98755 \times 10^9\ \text{N·m}^2/\text{C}^2$. This constant is pre‑programmed into the calculator, so no manual entry is required.

To use this point charge calculator, simply enter any three of the four values (the two charges, the distance, or the force), and the tool will automatically compute the missing quantity.

Units of Electric Charge

The SI unit of charge is the coulomb (C). One coulomb corresponds to the charge moved by a constant current of one ampere flowing for one second: $1\ \text{C} = 1\ \text{A} \cdot 1\ \text{s}$.

Conditions for Validity

Coulomb's law yields accurate results only when three key conditions are met:

• The charges must be stationary relative to each other (electrostatic regime).
• The charges must be point charges or possess spherical symmetry (e.g., a uniformly charged sphere, but not an irregular conductor).
• The charges must be distinct and non‑overlapping; a nonzero separation must exist.

Interpreting the Result

The force calculated by this Coulomb's law calculator carries a sign that indicates interaction type: a positive value signifies repulsion (like charges), while a negative value signifies attraction (opposite charges).

The calculator defaults to nanocoulombs (nC) for charge input because typical electrostatic charges fall in the microcoulomb ($10^{-6}\ \text{C}$) to nanocoulomb ($10^{-9}\ \text{C}$) range. This default reduces the need for scientific notation and streamlines data entry.