Coulomb's Law Calculator

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Walk-through

How to Use This Calculator

3 steps

1

Select units and enter charges

Type charge 1 ($q_1$) and charge 2 ($q_2$) using unit prefixes like microcoulombs (µC), nanocoulombs (nC), picocoulombs (pC), elementary charges (e), or standard Coulombs (C). Positive values repel; negative values attract.

2

Enter separation distance and dielectric medium

Specify the distance between charges in meters (m), centimeters (cm), millimeters (mm), nanometers (nm), or Angstroms (Å). Select a medium like Vacuum, Air, Water, Glass, or enter a custom relative permittivity ($\varepsilon_r$).

3

Explore force, field, energy, or superposition

View the electrostatic force ($F$), electric field ($E$), and potential energy ($U$) in real time alongside an interactive vector diagram. Use the Solve tab for inverse calculations or the 3-Charge tab for linear superposition.

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Reference

Formula & Methodology

3 formulas

Coulomb's Law in Medium

F = \frac{1}{4\pi\varepsilon_0 \varepsilon_r} \frac{q_1 q_2}{r^2} = \frac{k_{CODATA}}{\varepsilon_r} \frac{q_1 q_2}{r^2}

F is electrostatic force in newtons (N), k ≈ 8.98755 × 10⁹ N·m²/C² is Coulomb's constant, εᵣ is relative permittivity (εᵣ = 1 in vacuum, 80.1 in water), q₁ and q₂ are charges in coulombs, and r is distance in meters.

Electric Field & Potential Energy

E_1 = \frac{k |q_1|}{\varepsilon_r r^2} \quad U = \frac{k q_1 q_2}{\varepsilon_r r}

Electric field strength (E) measures force per unit charge at position r (N/C). Electrostatic potential energy (U) represents work done assembling the charges (Joules or eV).

3-Charge Superposition

F_{\text{net},3} = \vec{F}_{13} + \vec{F}_{23}

The net electrostatic force on a third charge equals the vector sum of individual forces exerted independently by q₁ and q₂.

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General reference

Trust, Methodology & Sources

Written by Calculover Editorial Team · Updated 2026-07-31

Editorial accountability

Author: Calculover Editorial Team - Editor

Owner: Calculover Editorial Team - Editorial owner

Last reviewed: 2026-07-31

Last verified: 2026-07-31

Methodology

This calculator implements Coulomb's electrostatic force equation ($F = \frac{1}{4\pi\varepsilon_0 \varepsilon_r} \frac{q_1 q_2}{r^2}$) using exact 2018 CODATA fundamental constants maintained by the National Institute of Standards and Technology (NIST).

Limitations & guidance

Professional guidance:

Primary sources

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Glossary

Key Terms Explained

5 terms

Coulomb's Law The physical law governing electrostatic interactions: force is directly proportional to the product of charge magnitudes and inversely proportional to the square of their separation distance.

Relative Permittivity (εᵣ) Also known as the dielectric constant, εᵣ measures a material's ability to polarize and weaken electrostatic forces relative to vacuum (εᵣ = 1).

Electric Field (E) The vector field surrounding a charge, defining the electrostatic force exerted on a positive test charge of +1 C placed at that point (N/C or V/m).

Electrostatic Potential Energy (U) Energy stored due to the relative positions of electric charges. Positive for repulsive pairs, negative for attractive pairs.

Superposition Principle The total force on any charge in a multi-charge system equals the vector sum of forces exerted by each other individual charge acting alone.

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Scenarios

Real-World Examples

3 worked examples

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Microcoulomb Charge Pair

Two 1 µC charges separated by 10 cm in vacuum

Charge 1 1 µC Charge 2 1 µC Distance 10 cm Medium Vacuum (εᵣ = 1.0)

Produces approximately 0.899 N of repulsive force. Electric field at q₂ due to q₁ is 8.988 × 10⁵ N/C; potential energy is 0.0899 J.

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Attenuation in Water

Same 1 µC charges in water (εᵣ = 80.1)

Charge 1 1 µC Charge 2 1 µC Distance 10 cm Medium Water 20°C (εᵣ = 80.1)

Water's high dielectric constant polarizes around charges, cutting the net force down to 0.0112 N (11.2 mN) — an 80-fold reduction.

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Bohr Hydrogen Atom

Proton (+1 e) and electron (-1 e) at Bohr radius (0.529 Å)

Charge 1 +1 e Charge 2 -1 e Distance 0.529177 Å Medium Vacuum

Attractive force is 8.238 × 10⁻⁸ N (82.38 nN). Electrostatic potential energy is -4.36 × 10⁻¹⁸ J (-27.21 eV).

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Deep Dive

Electrostatic Forces & Coulomb's Law in Modern Physics

3 chapters · 2 min read

Coulomb's law forms the foundation of electrostatics, establishing how charged particles exert forces across distance. Whether analyzing atomic bonds in chemistry, capacitor dielectrics in electrical engineering, or static electricity in atmospheric science, this tool delivers precise CODATA 2018 computations.

Dielectric Mediums & Shielding Effects

In vacuum, electrostatic forces operate at maximum strength with Coulomb's constant k ≈ 8.98755 × 10⁹ N·m²/C². When charges are submerged in a material medium like water, oil, or silicon, electric dipoles in the medium align opposite to the field, partially neutralizing it. This attenuation is quantified by the relative permittivity (εᵣ), dividing the effective Coulomb constant to k_eff = k / εᵣ.

Electric Field & Energy Relationship

Electric field strength (E = F/q) describes the force intensity experienced per coulomb at a given distance. Integrating electrostatic force over distance yields potential energy U = (k q₁ q₂)/(εᵣ r). For opposite charges, U is negative, signifying a bound system requiring energy input to separate.

Linear Superposition of Charges

When three or more charges interact, Coulomb forces follow linear superposition. Each pair interacts independently as if other charges were absent. Vector summation of these individual forces determines the total net force experienced by any target charge.

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Questions

Frequently Asked Questions

4 questions

What is the formula for Coulomb's law in a medium?+

F = (1 / (4π ε₀ εᵣ)) * (q₁ q₂ / r²), where ε₀ is vacuum permittivity (8.854 × 10⁻¹² F/m) and εᵣ is the relative permittivity of the medium.

Why does water reduce electrostatic force by 80 times?+

Water molecules possess a strong permanent electric dipole. Under an electric field, they align to shield charges, reducing the net force by a factor equal to water's dielectric constant (εᵣ ≈ 80.1).

What is the CODATA 2018 value of Coulomb's constant?+

k = 1/(4π ε₀) = 8.9875517923 × 10⁹ N·m²/C².

How are electric field and force related?+

Electric field E = F / q₂. It measures the force magnitude exerted per coulomb of charge at a specific location.

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