Quick answer
Coulomb's law gives the force between point charges: F = k·q₁·q₂ ÷ r², with k = 8.9875517923 × 10⁹ N·m²/C². Two 1 µC charges 0.1 m apart repel with 0.8988 N.
Enter both charges and the distance. The calculator returns the force and whether it is attractive or repulsive.
Related tools: Charles's Law Calculator: V₁/T₁ = V₂/T₂ at constant pressure. Boyle's Law Calculator: P₁V₁ = P₂V₂ at constant temperature. Density Calculator: Solve mass, density or volume.
How to use the Coulomb's Law Calculator
- Enter charge 1 (C).
- Enter charge 2 (C).
- Enter distance (m) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Charge 1 | A number, in C | — |
| Charge 2 | A number, in C | — |
| Distance | A number, in m | > 0 |
Formula and method
Formula
F = k·q₁·q₂ ÷ r², k = 8.9875517923 × 10⁹ N·m²/C²
IEEE-754 double precision; shown to at most 6 decimal places.
Positive force repels, negative attracts.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Charge 1 = 0.000001; Charge 2 = 0.000001; Distance = 0.1.
| Result | Value |
|---|---|
| Force | 0.898755 N |
| Interaction | Repulsive |
Example 2
Inputs: Charge 1 = 0.000001; Charge 2 = -0.000001; Distance = 0.1.
| Result | Value |
|---|---|
| Force | -0.898755 N |
| Interaction | Attractive |
The first line is the headline result (force). Below it the coulomb's Law Calculator lists interaction, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Worked example
F = 8.99 × 10⁹ × (10⁻⁶)² ÷ 0.1² = 8.99 × 10⁹ × 10⁻¹² ÷ 0.01 = 0.899 N. Like charges repel; unlike charges attract. Doubling the distance cuts the force to a quarter.
Assumptions
The formula holds for point charges in a vacuum; in a medium the force is divided by the relative permittivity. Compare with gravity: the electric force between two protons is about 10³⁶ times stronger.
How the result changes with charge 1
Holding every other input at the first worked example, this table changes only charge 1. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Charge 1 | Force | Interaction |
|---|---|---|
| 5e-7 | 0.449378 N | Repulsive |
| 0.000001 | 0.898755 N | Repulsive |
| 0.000002 | 1.79751 N | Repulsive |
| 0.000004 | 3.595021 N | Repulsive |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Distance: entering "0" shows "Distance must be greater than 0." beside that field and no result.
Choosing between the Coulomb's Law Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Charles's Law Calculator](/science/charles-law/) | Final volume | |
| [Boyle's Law Calculator](/science/boyles-law/) | Final volume | |
| [Density Calculator](/science/density-calculator/) | Mass | |
| [Kinetic Energy Calculator](/science/kinetic-energy-calculator/) | mass and speed | Kinetic energy |
| [Speed Distance Time Calculator](/science/speed-distance-time-calculator/) | Distance |
Background: motion and mechanics
For constant acceleration the standard relations are v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t. Pick the equation that contains your three known quantities and the one you want. Use SI units (metres, seconds, kilograms, newtons, joules) throughout or the answer will be off by a factor.
These equations stop applying when acceleration changes during the motion, as with a rocket burning fuel; that needs calculus or numerical methods.
Assumptions and limitations
- Point charges in vacuum
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for distance to confirm this.
Frequently asked questions
What is a coulomb?
A unit of electric charge, about 6.24 × 10¹⁸ electrons.
Is the force an inverse-square law?
Yes. Doubling the distance between two charges cuts the force to a quarter, since F ∝ 1/r².
What if the charges have opposite signs?
The force is attractive.
What does the Coulomb's Law Calculator calculate?
Electrostatic force between two point charges. It returns Force and Interaction.
What formula does the Coulomb's Law Calculator use?
F = k·q₁·q₂ ÷ r², k = 8.9875517923 × 10⁹ N·m²/C². Positive force repels, negative attracts.
What do I need to enter in the coulomb's Law Calculator?
You enter Charge 1 (C), Charge 2 (C) and Distance (m).
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Point charges in vacuum.
What is an example of a coulomb's Law result?
With charge 1 0.000001, charge 2 0.000001 and distance 0.1, the force is 0.898755 N.
Where does the method come from?
The method follows: CODATA 2018 (k = 1/(4πε₀)).
Related calculators
- Charles's Law Calculator — V₁/T₁ = V₂/T₂ at constant pressure.
- Boyle's Law Calculator — P₁V₁ = P₂V₂ at constant temperature.
- Density Calculator — Solve mass, density or volume.
- Kinetic Energy Calculator — Kinetic energy and momentum of a moving mass.
- Speed Distance Time Calculator — Solve distance, speed or time.
Sources
- CODATA 2018 (k = 1/(4πε₀))
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.