Coulomb's Law Calculator
The electrostatic force between two point charges from Coulomb's law — its size, whether it attracts or repels, and how it changes with distance.
The force is k q₁ q₂ / r², with k about 8.
How the coulomb's law calculator works
The force is k q₁ q₂ / r², with k about 8.99 × 10⁹ in SI units. It falls with the square of distance, exactly like gravity, but it is some 10³⁶ times stronger for elementary particles — which is why matter holds together and why like charges never get close.
Opposite signs give a negative force, meaning attraction. Same signs repel.
Formula: F = k q₁ q₂ / r², k = 8.988 × 10⁹ N·m²/C²
Worked examples
| Inputs | Force (N) | Note |
|---|---|---|
| 2 µC and −3 µC at 5 cm | -21.5701 | 21.6 N, attractive |
| Like charges | 21.5701 | the same size, repulsive |
| In water | -0.2696 | eighty times weaker |
FAQFrequently asked questions
What is Coulomb's law?
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.
What does a negative force mean?
Attraction. The sign comes from the product of the charges: opposite signs give a negative product, and the charges pull together.
How strong is it compared with gravity?
For two protons, about 10³⁶ times stronger. Gravity only dominates at large scales because matter is electrically neutral overall.
What does the medium do?
A dielectric screens the charges and weakens the force by its relative permittivity — 80 for water, which is why salts dissolve in it.
Does it apply to charged spheres?
Yes, as long as the distance is measured between centres and the spheres are far apart compared with their radii.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Physical Laboratory — the UK's national measurement institute
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.