Coulomb's Law Calculator

What Is a Coulomb's Law Calculator?

A Coulomb's Law calculator is used to determine the electrostatic force between two point charges, or to calculate an unknown charge or the distance between charges when the other required values are known. It applies Coulomb's Law to relate electric force, charge and separation distance.

This calculator can be useful for physics students, teachers, engineers, technicians and anyone working with electrostatics. It provides a quick way to check calculations involving charged particles and objects while automatically handling common electrical charge, distance and force units.

Why Use Coulomb's Law Calculator?

The calculator provides a convenient way to apply Coulomb's Law without manually rearranging the equation or converting every value to SI units before calculating.

How to Use Coulomb's Law Calculator

Enter the known electrical values, choose their units, select the quantity you want to calculate, and then calculate the result.

1. Choose the quantity to calculate — Select electric force, unknown charge or distance.
2. Enter the known values — Provide the required charge, force and distance values for the selected calculation.
3. Select the units — Choose the appropriate unit for each value and the desired result unit.
4. Click Calculate — Review the calculated result and the calculation details shown below the controls.

Coulomb's Law Formula and Equation

Coulomb's Law describes the magnitude of the electrostatic force between two point charges. The standard equation is F = k|q₁q₂| ÷ r², where F is the electric force, k is Coulomb's constant, q₁ and q₂ are the two charges, and r is the distance between their centres.

In SI units, force is measured in newtons (N), charge is measured in coulombs (C), and distance is measured in metres (m). Coulomb's constant is approximately 8.9875517923 × 10⁹ N·m²/C².

How to Calculate Electric Force

To calculate electric force, multiply the magnitudes of the two charges by Coulomb's constant and divide the result by the square of the distance between them. For example, two charges of 2 µC and 3 µC separated by 0.5 m produce a force of approximately 0.2157 N.

How to Calculate Charge and Distance

The Coulomb's Law equation can be rearranged to calculate an unknown charge or distance. For an unknown charge magnitude, |q| = Fr² ÷ (k|q₂|). For distance, r = √(k|q₁q₂| ÷ F). These rearrangements require a non-zero known charge, positive distance and, where applicable, a positive force magnitude.

Coulomb's Law Calculator Accuracy and Limitations

The calculator uses the defined Coulomb's constant and exact conversion factors for the supported units. The displayed result depends on the precision of the values entered. Calculations are performed using standard JavaScript number arithmetic, so extremely large or extremely small values may eventually be affected by floating-point limitations.

Coulomb's Law applies directly to idealised point charges and is also useful as an approximation when charged objects can reasonably be treated as point charges. Real systems may require additional considerations, including charge distributions, nearby conductors, dielectric materials, electric fields from multiple sources and other environmental effects. The calculator determines force magnitude; charges with the same sign repel, while charges with opposite signs attract.

Frequently Asked Questions