Coulomb Law Calculator

What is Coulomb's Law?

Coulomb's Law describes the electrostatic force between two stationary point charges. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. For similar inverse-square law physics, see the Gravitational Force Calculator. The equation is F = k x q x q / r, where k = 8.9875517873681764 x 10 N.m/C is Coulomb's constant, q and q are the charges in coulombs, and r is the separation distance in meters.

Like charges repel each other producing a positive force, while opposite charges attract producing a negative force. This inverse-square relationship means doubling the separation distance reduces the force to one quarter. Coulomb's Law is one of the fundamental principles of electrostatics and forms the basis for understanding electric fields, circuits, and atomic structure.

Key Formula

The electrostatic force equation is mathematically identical in form to Newton's law of universal gravitation, but with charges instead of masses:

• Force: F = k x q x q / r
• Charge 1: q = F x r / (k x q)
• Charge 2: q = F x r / (k x q)
• Distance: r = sqrt(k x q x q / F)

This calculator supports multiple charge units (coulombs, millicoulombs, microcoulombs, nanocoulombs) and distance units (m, cm, mm, km). The sign of the result indicates whether the force is repulsive (positive) or attractive (negative).

How to Use the Coulomb's Law Calculator

Select the variable you want to calculate from the dropdown menu. Enter the known values in their respective fields and choose appropriate units. The calculator instantly computes the result, indicates whether the force is attractive or repulsive, and shows detailed step-by-step calculations. Default example values of 1 microcoulomb and 2 microcoulombs separated by 5 cm produce a repulsive force of approximately 7.19 N.

Real-World Applications

Coulomb's Law has numerous practical applications. Electrostatic precipitators use charged plates to remove particulates from industrial exhaust. DNA separation in electrophoresis relies on Coulomb forces to drive charged molecules through a gel. Ion traps confine charged particles using oscillating electric fields for mass spectrometry. Particle accelerators push charged particles to high energies using oscillating electric fields. Even lightning results from charge separation building Coulomb forces strong enough to ionize air across kilometers.