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physics

Coulomb's Law Calculator

Calculate the electrostatic force between two point charges using Coulomb's law. Fundamental to electricity and atomic structure.

Reviewed by Christopher FloiedUpdated

This free online coulomb's law calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Coulomb's Law Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Coulomb's Law Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Coulomb's Law Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • Use the Coulomb's Law Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
  • Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
  • Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
  • Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

About This Calculator

The Coulomb's Law Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate the electrostatic force between two point charges using Coulomb's law. Fundamental to electricity and atomic structure. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.

About Coulomb's Law Calculator

The Coulomb's Law Calculator computes the electrostatic force between two point charges. Discovered by Charles-Augustin de Coulomb in 1785, this law is analogous to Newton's gravitation but dramatically stronger — the electrostatic force between an electron and proton is about 10³⁹ times greater than their gravitational attraction.

The Math Behind It

Coulomb's law is the foundation of electrostatics. **F = k·q₁·q₂ / r²**, where k = 1/(4πε₀) = 8.9875×10⁹ N·m²/C² **Properties**: 1. Inverse square law — double distance, quarter force 2. Like charges repel, opposite attract 3. Incredibly strong compared to gravity 4. Vector nature — forces along line connecting charges **Elementary charge**: e = 1.602×10⁻¹⁹ C. 1 C = 6.24×10¹⁸ electrons. **vs Gravity**: For electron-proton: electrostatic force is ~10³⁹ times gravitational force. This is why atoms don't collapse under gravity.

Formula Reference

Coulomb's Law

F = k·q₁·q₂ / r²

Variables: k = 8.9875×10⁹ N·m²/C²

Worked Examples

Example 1: Typical Charges

Two 1 μC charges at 10 cm

Step 1:F = (8.9875×10⁹)(1×10⁻⁶)² / (0.1)²
Step 2:= 0.899 N

0.9 N repulsive force — like the weight of a 90 g object.

Example 2: Electron-Proton

At Bohr radius (5.29×10⁻¹¹ m)

Step 1:F = 8.9875×10⁹ × (1.602×10⁻¹⁹)² / (5.29×10⁻¹¹)²
Step 2:≈ 8.24×10⁻⁸ N

Tiny but huge compared to gravity at this scale.

Common Mistakes & Tips

  • !Using grams instead of coulombs.
  • !Forgetting to square the distance.
  • !Applying in conducting materials where charges redistribute.

Related Concepts

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Frequently Asked Questions

Why is Coulomb's law so much stronger than gravity?

Coulomb's constant is ~10²⁰ times Newton's G, plus charges are much larger relative to masses at atomic scale.

Why don't electrons crash into the nucleus?

Quantum mechanics — electrons occupy stable orbitals with quantized energy levels, not classical orbits.