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MasterMath

Coulomb's Law Calculator

The force between two electric charges, which falls with the square of the distance — the same shape as gravity, and vastly stronger.

Result

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How this was worked out

    The formula

    F = k · q₁ · q₂ / r²

    SymbolQuantityUnit
    FElectric forceN
    q₁First chargeC
    q₂Second chargeC
    rDistance between chargesm

    What it means

    Coulomb's law gives the force between two point charges: proportional to both charges and inversely proportional to the square of the distance between them. Like charges repel, opposite charges attract.

    How to work it out by hand

    1. Multiply the two charges together
    2. Divide by the square of the distance
    3. Multiply by Coulomb's constant, about 8.99 × 10⁹

    What is worth knowing

    The inverse-square form is identical to Newton's law of gravitation, but the strengths are not remotely comparable: the electrical repulsion between two protons is about 10³⁶ times their gravitational attraction. That is why gravity is irrelevant inside an atom and dominant between planets — matter is electrically neutral in bulk, so the far stronger force cancels itself out and the weak one is left to shape the universe. Note also that the force acts along the line joining the charges, and that superposition holds: with several charges, add the individual forces as vectors.

    Frequently asked questions

    How does it compare with gravity?

    Same inverse-square shape, wildly different strength: between two protons the electric force is about 10³⁶ times the gravitational one.

    Why does gravity dominate at large scales then?

    Because bulk matter is electrically neutral, so the stronger force cancels out. Gravity has no negative charge to cancel it.

    What is Coulomb's constant?

    About 8.99 × 10⁹ N·m²/C² in a vacuum. In other media it is reduced by the material's permittivity.

    Does it work for more than two charges?

    Yes, by superposition: work out each pair separately and add the forces as vectors.