PhysicsCalcs
Electricity

Coulomb’s Law Calculator

Calculate the electrostatic force, charge magnitude, or distance between two point charges using Coulomb’s Law. Enter known values, choose units, and see the formula with step-by-step explanation.

Interactive calculator

Coulomb\u2019s Law Calculator

Calculate electrostatic force, charge, or distance between two point charges. Enter known values and click Calculate.

First point charge (can be negative)

Second point charge (can be negative)

Distance between charges

1 for vacuum/air

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose what to calculate (force, charge, or distance).
  • Enter charge values \u2014 negative charges are allowed.
  • Relative permittivity is optional (defaults to 1).
  • Click Calculate.

Table of Contents

Key Takeaways

  • Coulomb’s Law gives the force between two point charges.
  • The force is proportional to the product of the charges and inversely proportional to the square of the distance.
  • Like charges repel; opposite charges attract.
  • The Coulomb constant k ≈ 8.99 × 10⁹ N·m²/C².
  • The calculator supports optional relative permittivity for different media.
  • Coulomb’s Law applies exactly to point charges in electrostatics.

What Is Coulomb’s Law?

Coulomb's Law describes the electrostatic force between two stationary point charges. It is one of the fundamental laws of electrostatics, first published by Charles-Augustin de Coulomb in 1785.

The law states that the force is directly proportional to the product of the charge magnitudes and inversely proportional to the square of the distance between them. Like charges repel, and opposite charges attract.

Coulomb’s Law Formula

F=k∣q1q2∣r2F=k\frac{|q_1q_2|}{r^2}

The magnitude of the electrostatic force between two point charges.

Where F is force (N), k is Coulomb's constant (≈ 8.99 × 10&sup9; N·m²/C²), q&sub1; and q&sub2; are the charges (C), and r is the distance (m).

In a medium other than vacuum, divide by the relative permittivity εr:

F=k∣q1q2∣εrr2F=k\frac{|q_1q_2|}{\varepsilon_r r^2}

Adjusted for a dielectric medium.

Coulombs Law Infographic explaining electric force

How to Use the Coulomb’s Law Calculator

  1. 1Select whether to calculate force, charge, or distance.
  2. 2Enter the known values with their units.
  3. 3For charges, enter negative values if the charge is negative.
  4. 4Relative permittivity is optional (leave blank for vacuum/air).
  5. 5Click Calculate and review the result.

Example Calculations

Force between two charges

q&sub1; = +2 μC, q&sub2; = -3 μC, r = 0.1 m. F = 8.99×10&sup9; × |2×10−&sup6; × 3×10−&sup6;| / (0.1)² ≈ 5.39 N (attractive).

Distance for a given force

q&sub1; = q&sub2; = 1 μC, F = 0.9 N. r = √(8.99×10&sup9; × 10−¹² / 0.9) ≈ 0.1 m.

Attraction vs Repulsion

The sign of the product q&sub1; × q&sub2; determines the interaction type. If both charges have the same sign, the force is repulsive and pushes them apart. If the charges have opposite signs, the force is attractive and pulls them together.

The calculator automatically detects whether the interaction is attractive or repulsive based on the signs of the entered charges.

Why Distance Matters

Coulomb's Law follows an inverse-square relationship. Doubling the distance reduces the force to one-quarter. Halving the distance quadruples the force. This strong distance dependence is why electrostatic effects are most noticeable at short range.

Coulomb’s Constant

Coulomb's constant k relates the force to the charges and distance in SI units. Its value is approximately 8.9876 × 10&sup9; N·m²/C². It can also be expressed as k = 1/(4πε&sub0;), where ε&sub0; is the permittivity of free space.

Accuracy and Limitations

This calculator uses the classical point-charge form of Coulomb's Law in electrostatics.

Limitations include: applies to point charges only, assumes electrostatic conditions, does not handle moving charges or magnetic effects, and does not account for quantum effects at atomic scales. For extended charge distributions, use integration or superposition.

Frequently Asked Questions

What is Coulomb’s Law?›

Coulomb’s Law describes the electrostatic force between two point charges. The force magnitude is proportional to the product of the charge magnitudes and inversely proportional to the square of the distance between them.

What is the formula for Coulomb’s Law?›

F = k|q₁q₂| / r², where k is Coulomb’s constant (≈ 8.99 × 10⁹ N·m²/C²).

What is Coulomb’s constant?›

Coulomb’s constant k ≈ 8.9876 × 10⁹ N·m²/C². It relates the force to the charges and distance in SI units.

How do I know if the force is attractive or repulsive?›

If both charges have the same sign (both positive or both negative), the force is repulsive. If they have opposite signs, it is attractive.

What is relative permittivity?›

Relative permittivity (εᵣ) describes how a medium weakens the electric force compared to vacuum. For vacuum or air, εᵣ ≈ 1. Water has εᵣ ≈ 80.

Does Coulomb’s Law work for more than two charges?›

Coulomb’s Law gives the force between one pair. For multiple charges, calculate each pair separately and add the forces as vectors (superposition principle).

Why does force increase so much at small distances?›

Force is inversely proportional to r². Halving the distance quadruples the force.

Is the Coulomb force related to gravity?›

Both follow an inverse-square law, but the Coulomb force acts on charges while gravity acts on masses. The Coulomb force is vastly stronger for elementary particles.

Can charges be negative?›

Yes. Electrons carry negative charge, protons carry positive charge. The sign affects whether the force is attractive or repulsive.

Does this calculator handle non-point charges?›

No. Coulomb’s Law as implemented here applies to point charges or sufficiently small charged objects.

Sources / References

  1. OpenStax College Physics 2e: Coulomb’s Law
  2. HyperPhysics: Coulomb’s Law
  3. NIST: CODATA Value of Coulomb’s Constant
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

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