# Coulomb Force Calculator

Coulomb's law F = k·|q₁q₂|/r² with signed charges and unit selectors, reporting the force magnitude and whether the pair attracts or repels.

> Canonical page: https://elysiatools.com/en/tools/coulomb-force-calculator

- **Category:** Science & Education

- **Keywords:** coulombs law, electrostatic force, point charges, attraction repulsion, coulomb constant, electromagnetism

## Overview

The Coulomb Force Calculator computes the electrostatic interaction force between two point charges using Coulomb's law: F = k·|q₁q₂|/r². By supporting positive or negative values across multiple charge units (C, mC, µC, nC) and distance scales (m, cm, mm, µm, nm), it quickly provides the exact force magnitude in newtons alongside the interaction type (attractive or repulsive).

## Inputs

- **Charge q₁** (number): e.g. 1
- **Charge q₂** (number): e.g. 1
- **Charge unit** (select)
- **Separation r** (number): e.g. 1
- **Distance unit** (select)

## When to use

- Solving physics problem sets involving point charges, electrostatic fields, and force vectors.
- Analyzing atomic or molecular models, such as finding the electrostatic attraction between a nucleus and orbiting electrons.
- Evaluating electrostatic forces in laboratory setups, such as charged spheres, sensors, or electrostatic precipitators.

## How it works

- Enter the numerical values and signs for charge q₁ and charge q₂, then select the charge unit (C, mC, µC, or nC).
- Specify the separation distance r between the two charges and choose the appropriate distance unit (m, cm, mm, µm, or nm).
- The tool applies Coulomb's constant (k ≈ 8.98755 × 10⁹ N·m²/C²) to evaluate F = k·|q₁q₂|/r².
- Review the resulting electrostatic force magnitude in newtons and the determined interaction state (repulsion for like charges, attraction for opposite charges).

## Use cases

- Physics education: Verifying manual calculations for homework and electrostatics exam preparation.
- Atomic physics demonstrations: Calculating the binding force between an electron and proton at the Bohr radius.
- Engineering prototyping: Estimating electrostatic forces between micro-scale electrodes in MEMS devices.

## Frequently asked questions

### What value of Coulomb's constant (k) is used in calculations?

The calculator uses standard vacuum permittivity to apply Coulomb's constant k ≈ 8.98755 × 10⁹ N·m²/C².

### How does the tool determine attraction versus repulsion?

Charges with identical signs (both positive or both negative) repel, while charges with opposite signs attract.

### Can I input negative charge values?

Yes, you can enter signed numbers to indicate polarity, which determines whether the resulting force attracts or repels.

### Which units of distance and charge are supported?

Charges can be set in C, mC, µC, or nC, and distances can be set in m, cm, mm, µm, or nm.

### Does this tool account for dielectric medium constants?

The calculator computes forces in a vacuum (or air) using the standard electrostatic constant k without additional dielectric medium scaling.

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