This Coulomb’s law calculator computes the electrostatic force between two point charges — and inverts it to solve for a charge or the separation — the inverse-square law that runs the electric half of physics.
The Electric Twin of Gravity
F = k·q₁q₂ / r², with k = 8.988×10⁹ N·m²/C² — a constant so large because the coulomb is an enormous amount of charge (a lightning bolt moves ~15 C; this calculator's microcoulombs are the laboratory scale). Same-sign charges repel, opposites attract, and the 1/r² fall-off is identical in form to the Gravitational Force Calculator's law — nature reuses its best geometry. The differences: charges come signed (gravity has only "positive mass"), and electric forces are ~10³⁶ times stronger at the particle scale, which is why chemistry — all of it — is Coulomb's law in action. Part of our Physics Calculators collection.
Worked Example (Verified)
- Two 1 µC charges, 10 cm apart: F = 8.988×10⁹ × (10⁻⁶ × 10⁻⁶) ÷ 0.01 = 0.899 N — about the weight of a small apple, from two millionths of a coulomb: a feel for k's size
- Same charges at 20 cm: 0.225 N — doubled distance, quarter force, the inverse-square signature
- The hydrogen atom, qualitatively: electron and proton at 0.053 nm attract with ≈ 8.2×10⁻⁸ N — trivial-looking, until you divide by the electron's 9.11×10⁻³¹ kg mass and get an acceleration of ~10²³ m/s². Small worlds run on enormous accelerations.
Where the Point-Charge Ideal Bends
- Charges on conducting spheres redistribute when the spheres get close — at separations comparable to their size, the point formula overestimates. Textbook problems assume r ≫ sphere radii.
- In a medium, divide by the dielectric constant (water: ~80 — electrostatic forces underwater are dramatically screened, one reason salts dissolve there).
- Superposition rules everything: forces from many charges add as vectors — the two-body formula stays exact pairwise, and patience does the rest.
Related Tools
- Gravitational Force Calculator — the inverse-square sibling
- Electric Power Calculator — charges in motion, billed
- Physics Calculators — the full collection
Frequently Asked Questions
What is Coulomb's law?
F = k q₁q₂ / r²: the force between two point charges is proportional to the product of the charges and inversely proportional to the squared distance. k ≈ 8.988×10⁹ N·m²/C² in vacuum.
How strong is 1 coulomb?
Enormous: two 1-coulomb charges one meter apart would repel with ~9×10⁹ N — the weight of a million tonnes. Real static charges are microcoulombs; a lightning strike transfers roughly 5–30 C total, spread over its duration and path.
How is Coulomb's law different from gravity?
Same shape, different world: charges are signed (attraction and repulsion), the constant is huge instead of tiny, and the source is charge rather than mass. Between an electron and a proton, the electric force exceeds gravity by ~10³⁹ — gravity wins planets only because bulk matter is electrically neutral.
Does the medium matter?
Yes: in a dielectric, replace k by k/εᵣ. Air barely changes it (εᵣ ≈ 1.0006); water slashes forces by ~80×, which reshapes everything from ion chemistry to why wet electronics misbehave.
What is an electric field in this picture?
The force per unit charge at a point: E = F/q = kQ/r² from a source charge Q. Coulomb's law computes between two charges; the field view pre-computes one charge's influence so any other charge's force is one multiplication.
Is this Coulomb's law calculator free?
Yes — free, instant, no sign-up.