Coulomb’s Law CalculatorF = k·q₁q₂ ÷ r²
Coulomb’s law gives the electrostatic force between two point charges: F = k·q₁q₂ ÷ r², with k = 8.988 × 10⁹ N·m²/C². Opposite charges attract and like charges repel. Enter two charges and the distance between them to get the force, whether it attracts or repels, and the electric field. You can also solve for the distance, or calculate the field around a single charge, in a vacuum, air, oil or water.
Formula verified against OpenStax — University Physics, Volume 2 · NIST — CODATA 2022 Fundamental Physical Constants
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Charges & separation
Use a minus sign for negative charges. 1 µC = 10⁻⁶ C.
Step-by-step working
What is coulomb’s law?
Coulomb’s law describes the electrostatic force between two electrically charged particles: it grows with the size of the charges and weakens with the square of the distance between them.
Charles-Augustin de Coulomb measured it with a torsion balance in 1785. It holds atoms and molecules together, makes static cling and lightning happen, and underlies all of chemistry.
Quick answers
How do you calculate the force between two charges?
Use F = k·q₁q₂ ÷ r². Two 1 µC charges 1 m apart repel with 8.99 × 10⁻³ N, about the weight of a 0.9 g paperclip.
What is the Coulomb constant k?
k = 1 ÷ 4πε₀ = 8.98755 × 10⁹ N·m²/C², where ε₀ = 8.854 × 10⁻¹² F/m is the vacuum permittivity (CODATA 2022).
How do I find the electric field from a point charge?
E = kq ÷ r². A 3 µC charge produces 2.70 × 10⁶ N/C at 10 cm, close to the field at which air breaks down and sparks.
How does Coulomb’s law compare with gravity?
Both follow the inverse-square law. Electric force is vastly stronger but can cancel, because charges come in + and −. Compare with the gravitational force calculator.
Coulomb’s law formula
In a medium, divide by its relative permittivity εr. A negative F means attraction.
| Symbol | Meaning | SI unit |
|---|---|---|
| F | Electrostatic force | N |
| k | Coulomb constant | N·m²/C² |
| q₁, q₂ | Point charges | C |
| r | Separation | m |
| εr | Relative permittivity of the medium | — |
| E | Electric field strength | N/C = V/m |
How to use Coulomb’s law
- Convert charges to coulombs (µC × 10⁻⁶, nC × 10⁻⁹).
- Convert the distance to metres and square it.
- Multiply k × q₁ × q₂ and divide by r² (and εr in a medium).
- Read the sign: negative means attraction, positive means repulsion.
Worked example: +3 µC and −5 µC, 10 cm apart
Two point charges, +3 µC and −5 µC, sit 10 cm apart in air.
F = 13.48 N, attractive
That’s about the weight of a 1.4 kg bag of sugar, from just a few microcoulombs. Inside a hydrogen atom the proton and electron attract with 8.24 × 10⁻⁸ N, about 10³⁹ times stronger than their gravitational pull.
Relative permittivity of common materials
The force between charges is divided by εr in each medium.
| Medium | εr | Force vs vacuum |
|---|---|---|
| Vacuum | 1 | 100% |
| Air (dry, 1 atm) | 1.0006 | ≈ 100% |
| Transformer oil | ≈ 2.2 | 45% |
| Glass | 5–10 | 10–20% |
| Ethanol | ≈ 24 | 4.2% |
| Water (20 °C) | ≈ 80 | 1.25% |
Common mistakes to avoid
- Forgetting the micro-prefix. 3 µC is 3 × 10⁻⁶ C. Missing it gives a force 10¹² times too large.
- Using cm in the formula. r must be in metres before squaring.
- Applying it to large charged objects. Coulomb’s law is exact for point charges and spheres measured from their centres.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Coulomb’s Law Calculator: frequently asked questions
It states that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them: F = k·q₁q₂ ÷ r².
k ≈ 8.988 × 10⁹ N·m²/C², equal to 1 ÷ 4πε₀.
When the charges have opposite signs. Like charges repel.
The coulomb (C). One electron carries −1.602176634 × 10⁻¹⁹ C, an exact value since the 2019 SI redefinition.
Yes. Insulating materials polarise and partly screen the charges, reducing the force by a factor εr. Water reduces it about 80-fold.
References & sources
- OpenStax — University Physics, Volume 2 — Ch. 5.3, Coulomb’s Law
- NIST — CODATA 2022 Fundamental Physical Constants — ε₀, elementary charge e and the Coulomb constant
- HyperPhysics, Georgia State University — Coulomb’s law
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.