What this calculator does
Coulomb's law gives the electrostatic force between two point charges: F = kq₁q₂/r², where k is Coulomb's constant, q₁ and q₂ are the charges and r is the distance separating them. Like charges push apart and opposite charges pull together, and the force falls off with the square of the distance, so doubling the separation cuts the force to a quarter.
This is a force calculation between two specific charges, not a field calculation from a single one. A single point charge sets up an electric field and potential in the space around it regardless of whether a second charge is there to feel it; Coulomb's law is what happens once that second charge is actually placed in the field, and a real force results between the pair.
The formula
Multiply the two charges together, multiply by Coulomb's constant k = 8.9875517923×10⁹ N·m²/C², and divide by the square of the separation: F = kq₁q₂/r². The sign of the result shows the nature of the force: a negative product (opposite-sign charges) gives an attractive force, and a positive product (same-sign charges) gives a repulsive one.
| Term | Meaning |
|---|---|
| F | The electrostatic force between the two charges, in newtons. |
| k | Coulomb's constant, 8.9875517923×10⁹ N·m²/C², sometimes written as 1/(4πε₀). |
| q₁, q₂ | The two point charges, in coulombs, each carrying its own sign. |
| r | The distance separating the two charges, in metres. |
The inputs explained
| Field | What to enter |
|---|---|
| Charge 1 (C) | The first charge, in coulombs. Use a negative value for a negative charge. |
| Charge 2 (C) | The second charge, in coulombs. Use a negative value for a negative charge; opposite signs to charge 1 give an attractive force. |
| Separation (m) | The straight-line distance between the two charges. |
When to use it
Working out whether two charges attract or repel
The sign of the two charges alone decides the direction: same sign always repels, opposite sign always attracts, regardless of how large either charge is. This calculator states that outcome directly alongside the force magnitude.
Checking how force changes as charges move apart or together
Because the force follows an inverse-square relationship, a small change in separation at close range has a much bigger effect than the same change at a larger distance, which matters when judging how sensitive a setup is to positioning.
Working a textbook or lab electrostatics problem
Coulomb's law problems typically give two charge values and a separation and ask for the resulting force; this calculator does that arithmetic directly and also reports the force at double the separation for comparison.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the force changes with separation, for a fixed pair of charges
The same two charges, moved to a range of separations.
| Separation | Force magnitude | Direction |
|---|---|---|
| 0.02 m | 44.9378 N | Attractive (opposite charges) |
| 0.05 m | 7.1900 N | Attractive (opposite charges) |
| 0.1 m | 1.7975 N | Attractive (opposite charges) |
| 0.2 m | 0.449378 N | Attractive (opposite charges) |
| 0.5 m | 0.071900 N | Attractive (opposite charges) |
| 1 m | 0.017975 N | Attractive (opposite charges) |
How the force changes with the size of one charge, the other held fixed
A steady 1 µC second charge, against a range of sizes for the first charge.
| First charge | Force magnitude | Direction |
|---|---|---|
| 0.5 µC | 0.449378 N | Repulsive (like charges) |
| 1 µC | 0.898755 N | Repulsive (like charges) |
| 2 µC | 1.7975 N | Repulsive (like charges) |
| 5 µC | 4.4938 N | Repulsive (like charges) |
| 10 µC | 8.9876 N | Repulsive (like charges) |
Questions
What is the Coulomb's law formula?
F = kq₁q₂/r², where k is Coulomb's constant (8.9875517923×10⁹ N·m²/C²), q₁ and q₂ are the two point charges and r is the distance between them. The sign of the product q₁q₂ shows whether the resulting force is attractive or repulsive.
How is Coulomb's law different from the electric field of a point charge?
Coulomb's law calculates the force between two specific charges. A single charge on its own sets up an electric field and potential around it, which is what the electric field calculator works out; Coulomb's law is what happens once a second charge is placed in that field and a real force results.
Why is the force sometimes shown as negative?
A negative signed force here means the force is attractive, which happens whenever the two charges have opposite signs. A positive signed force means the charges are repelling each other. The force magnitude is always reported as a positive number regardless.
Does Coulomb's law work at any distance?
The formula holds for point charges, or for charged objects small enough relative to their separation to be treated as points, at any distance apart, provided the charges are stationary. It does not account for magnetic effects that arise once charges are moving relative to each other.
For the electric field and potential a single charge sets up on its own, see the electric field of a point charge calculator. For gravitational force between two masses, which follows the same inverse-square shape, see the Newton's law of gravitation calculator.