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Coulomb's Law Calculator

Calculate

Charge 1 (q₁) in Coulombs

Use scientific notation: 1e-6 = 0.000001

Charge 2 (q₂) in Coulombs

Distance (r) in Meters

Coulomb's Law Formula

F = k × |q₁ × q₂| / r²

Where:

F = Electrostatic force (Newtons)
k = Coulomb's constant = 8.9875 × 10⁹ N⋅m²/C²
q₁, q₂ = Electric charges (Coulombs)
r = Distance between charges (meters)

Force Direction

Like charges (both + or both −): Repulsive force (push apart)
Unlike charges (one + and one −): Attractive force (pull together)

Coulomb's Constant

k = 1/(4πε₀) where ε₀ = 8.854 × 10⁻¹² F/m is the permittivity of free space. In other media, k is reduced by the dielectric constant (relative permittivity).

What Is Coulomb's Law Calculation?

Coulomb's Law describes the electrostatic force between two charged particles. Formulated by Charles-Augustin de Coulomb in 1785, the law states: F = k × |q₁ × q₂| ÷ r², where F is force in newtons, k is Coulomb's constant (8.99 × 10⁹ N⋅m²/C²), q₁ and q₂ are charges in coulombs, and r is the distance between charges in meters. The force is attractive for opposite charges and repulsive for like charges. This fundamental law underpins electrostatics, capacitor design, semiconductor physics, and electromagnetic theory. It is analogous to Newton's law of gravitation but for electric charges.

How to Calculate Coulomb's Law Calculation

1
Enter First Charge (q₁)
Input the magnitude of the first charge in coulombs (C), microcoulombs (μC), or nanocoulombs (nC). Typical static electricity charges range from nanocoulombs to microcoulombs.
2
Enter Second Charge (q₂)
Input the second charge magnitude. For attraction, charges have opposite signs; for repulsion, same signs. The calculator uses absolute values for force magnitude.
3
Enter Distance Between Charges
Input the distance between charge centers in meters, centimeters, or millimeters. The force is inversely proportional to distance squared — doubling distance reduces force by 4×.
4
Review Force Result
The result shows electrostatic force in newtons. Compare with gravitational or mechanical forces to understand the relative strength of electrostatic interactions.

Why Coulomb's Law Calculation Matters

Electrostatic Discharge Prevention

Understanding Coulomb forces helps design ESD protection for sensitive electronics. Static charges of just nanocoulombs can generate thousands of volts, damaging semiconductor devices.

Capacitor Design

Coulomb's Law governs charge storage on capacitor plates. The attractive force between oppositely charged plates determines capacitor construction, dielectric requirements, and voltage ratings.

Particle Physics and Chemistry

Coulomb forces determine atomic structure, chemical bonding, molecular interactions, and crystal lattice formation. The balance between Coulomb attraction and electron kinetic energy defines atomic orbitals.

Lightning Protection Engineering

Understanding charge accumulation and electrostatic forces helps design lightning protection systems, grounding schemes, and charge dissipation devices for buildings and aircraft.

Electrical Safety Tips & Best Practices

Inverse Square Law

Force decreases with the square of distance. At 2× the distance, force is ¼. At 10× the distance, force is 1/100. This rapid decrease means electrostatic effects are significant only at short distances in most practical applications.

Superposition Principle

For multiple charges, calculate the force between each pair independently and add vectors. The net force on any charge is the vector sum of all individual Coulomb forces acting on it.

Medium Affects Force

Coulomb's Law in a medium uses: F = k × q₁q₂ ÷ (εᵣ × r²), where εᵣ is the relative permittivity (dielectric constant). Water (εᵣ = 80) reduces force by 80× compared to vacuum.

Point Charge Approximation

Coulomb's Law applies exactly to point charges. For extended objects, it applies when the distance between objects is much larger than their physical size, or for uniformly charged spheres (using center-to-center distance).

Common Charge Values

Particle/Unit	Symbol	Charge (C)
Electron	e⁻	-1.602e-19
Proton	p⁺	1.602e-19
Alpha Particle	α²⁺	3.204e-19
1 Microcoulomb	1 µC	1.000e-6
1 Nanocoulomb	1 nC	1.000e-9
1 Picocoulomb	1 pC	1.000e-12

Frequently Asked Questions

What is the difference between Coulomb's law and gravity?

Both are inverse-square laws, but electrostatic force can be attractive or repulsive, while gravity is always attractive. Electrostatic force is about 10³⁶ times stronger than gravity for subatomic particles.

Does Coulomb's law apply to moving charges?

Coulomb's law is strictly valid for stationary (static) charges. Moving charges create magnetic fields and are described by the Lorentz force law and Maxwell's equations.

What is a Coulomb?

One Coulomb is the charge of approximately 6.24 × 10¹⁸ electrons (or protons). It's a very large unit; typical static electricity is in the nanocoulomb to microcoulomb range.

How does distance affect electrostatic force?

Force decreases with the square of distance. Doubling the distance reduces the force to 1/4. Halving the distance increases force by 4×. This inverse-square relationship is fundamental to electrostatics.

What is Coulomb's constant?

Coulomb's constant k = 8.9875 × 10⁹ N⋅m²/C², also written as 1/(4πε₀) where ε₀ is the permittivity of free space (8.854 × 10⁻¹² F/m). This constant determines the strength of electrostatic interactions in vacuum and appears in all electrostatic calculations.

How strong is the electrostatic force compared to gravity?

The electrostatic force between a proton and electron is approximately 10³⁹ times stronger than their gravitational attraction. Electrostatics dominates at atomic and molecular scales, while gravity dominates at astronomical scales because large objects are electrically neutral.

What is a coulomb of charge?

One coulomb (C) equals the charge of approximately 6.242 × 10¹⁸ electrons (or protons). It is defined as the charge transported by 1 ampere of current in 1 second. Named after Charles-Augustin de Coulomb, it is the SI unit of electric charge.

Does Coulomb's Law work for moving charges?

Coulomb's Law applies to stationary charges. Moving charges create magnetic fields and require the full Lorentz force law: F = q(E + v × B). However, for charges moving slowly compared to light speed, Coulomb's Law remains a good approximation.

How is Coulomb's Law related to electric field?

The electric field E created by charge q at distance r is: E = k × q ÷ r². The force on another charge Q in this field is F = Q × E, which gives Coulomb's Law: F = k × q × Q ÷ r². Electric field is the force per unit charge.

References & Industry Standards

NIST - Fundamental Physical Constants (Coulomb constant)
Griffiths, D.J. - Introduction to Electrodynamics (Standard textbook reference)
IEEE 100 - Authoritative Dictionary of IEEE Standards Terms
IEC 60050 - International Electrotechnical Vocabulary

Last updated: 2026-02-01 | Reviewed by UnitTables Engineering Team

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Coulomb's Law Formula

F = k × |q₁ × q₂| / r²

Where:

F = Electrostatic force (Newtons)
k = Coulomb's constant = 8.9875 × 10⁹ N⋅m²/C²
q₁, q₂ = Electric charges (Coulombs)
r = Distance between charges (meters)

Force Direction

Like charges (both + or both −): Repulsive force (push apart)
Unlike charges (one + and one −): Attractive force (pull together)

Coulomb's Constant

k = 1/(4πε₀) where ε₀ = 8.854 × 10⁻¹² F/m is the permittivity of free space. In other media, k is reduced by the dielectric constant (relative permittivity).

What Is Coulomb's Law Calculation?

How to Calculate Coulomb's Law Calculation

Enter First Charge (q₁)

Input the magnitude of the first charge in coulombs (C), microcoulombs (μC), or nanocoulombs (nC). Typical static electricity charges range from nanocoulombs to microcoulombs.

Enter Second Charge (q₂)

Input the second charge magnitude. For attraction, charges have opposite signs; for repulsion, same signs. The calculator uses absolute values for force magnitude.

Enter Distance Between Charges

Input the distance between charge centers in meters, centimeters, or millimeters. The force is inversely proportional to distance squared — doubling distance reduces force by 4×.

Review Force Result

The result shows electrostatic force in newtons. Compare with gravitational or mechanical forces to understand the relative strength of electrostatic interactions.

Why Coulomb's Law Calculation Matters

Electrostatic Discharge Prevention

Understanding Coulomb forces helps design ESD protection for sensitive electronics. Static charges of just nanocoulombs can generate thousands of volts, damaging semiconductor devices.

Capacitor Design

Coulomb's Law governs charge storage on capacitor plates. The attractive force between oppositely charged plates determines capacitor construction, dielectric requirements, and voltage ratings.

Particle Physics and Chemistry

Lightning Protection Engineering

Understanding charge accumulation and electrostatic forces helps design lightning protection systems, grounding schemes, and charge dissipation devices for buildings and aircraft.

Electrical Safety Tips & Best Practices

Inverse Square Law

Superposition Principle

For multiple charges, calculate the force between each pair independently and add vectors. The net force on any charge is the vector sum of all individual Coulomb forces acting on it.

Medium Affects Force

Coulomb's Law in a medium uses: F = k × q₁q₂ ÷ (εᵣ × r²), where εᵣ is the relative permittivity (dielectric constant). Water (εᵣ = 80) reduces force by 80× compared to vacuum.

Point Charge Approximation

Particle/Unit

Symbol

Charge (C)

Electron

e⁻

-1.602e-19

Proton

p⁺

1.602e-19

Alpha Particle

α²⁺

3.204e-19

1 Microcoulomb

1 µC

1.000e-6

1 Nanocoulomb

1 nC

1.000e-9

1 Picocoulomb

1 pC

1.000e-12