Coulomb's Law Calculator
Solve F = k|q₁q₂|/r² for the electrostatic force between two point charges, or rearrange it to find a charge or the separation distance. Two 3D diagrams show how force falls off with distance and how like/opposite charges repel or attract, and charts show the inverse-square distance dependence.
Reviewed by the ToolNestr Editorial Team — July 2026
Two ideas Coulomb's law shows visually
1. Force falls off as 1/r²
Two charge pairs at different separations. The closer pair has a much bigger force arrow than the farther pair — doubling the distance cuts the force to a quarter.
2. Like charges repel, opposite charges attract
On the left, two positive charges push apart. On the right, a positive and a negative charge pull toward each other.
Coulomb force graphs
How it works
The core idea in one line: Coulomb's law says the electrostatic force between two point charges grows with the product of the charges and shrinks with the square of the distance between them — the same inverse-square shape as gravity, but able to attract or repel.
F = k |q₁ q₂| / r²
electrostatic force magnitude
k ≈ 8.9875×10⁹ N·m²/C²
Coulomb's constant, k = 1/(4πε₀)
Rearranged, F = k|q₁q₂|/r² solves any variable: |q₁| = Fr²/(k|q₂|), |q₂| = Fr²/(k|q₁|), and r = √(k|q₁q₂|/F). Because F falls off as 1/r², doubling the distance between two charges cuts the force to a quarter — the same steep drop-off that makes gravity weak at planetary distances but electric forces dominate at the atomic scale.
Worked example 1 — attractive force
Given: A charge of +2 μC (2×10⁻⁶ C) and a charge of −3 μC (3×10⁻⁶ C) are separated by 0.5 m. Find the force between them.
The charges have opposite signs, so this 0.2157 N force is attractive — each charge is pulled toward the other.
Worked example 2 — repulsive force, solving for magnitude
Given: Two charges of +5 μC each are separated by 0.2 m. Find the force between them.
Both charges are positive (like charges), so this force is repulsive — the charges push apart.
Coulomb's law vs Newton's law of gravitation
Both are inverse-square laws with an identical mathematical form, but the electric force is enormously stronger for everyday charges and masses.
| Property | Coulomb's law | Newton's gravitation |
|---|---|---|
| Formula | F = k|q₁q₂|/r² | F = Gm₁m₂/r² |
| Constant | k ≈ 8.9875×10⁹ N·m²/C² | G ≈ 6.674×10⁻¹¹ N·m²/kg² |
| Distance dependence | 1/r² (inverse square) | 1/r² (inverse square) |
| Can be attractive or repulsive | Yes — depends on charge signs | No — always attractive |
| Relative strength (proton pair) | ~10³⁶ times stronger | baseline |
For two protons, the electric repulsion is about 10³⁶ times stronger than their mutual gravitational attraction — gravity only dominates at large scales because matter is usually charge-neutral overall.
Where Coulomb's law actually matters
🔌 Electronics and capacitors
The forces between charged plates in a capacitor, and the attraction that holds charge carriers in place in circuits, both follow Coulomb's law at the microscopic level — it underlies how charge storage and electric fields behave in every circuit.
⚡ Van de Graaff generators
These build up large amounts of like charge on a metal sphere. Coulomb repulsion between the accumulated charges is strong enough to make hair stand on end or produce visible sparks when the potential gets high enough to ionise the surrounding air.
🧬 Molecular and atomic bonding
Ionic bonds, and much of the fine structure of molecular interactions, arise from Coulomb attraction between oppositely charged ions or partial charges. The strength and distance-dependence of these forces shape crystal structures and reaction chemistry.
🌩️ Lightning and static discharge
Charge separation between cloud and ground (or between your body and a doorknob) builds up an electric force described by Coulomb's law; when the resulting field is strong enough to ionise air, it discharges as a spark or lightning bolt.
Common misconceptions
"Like charges attract."
It's the opposite: like charges (two positives or two negatives) repel, and only opposite charges attract. The magnitude formula F = k|q₁q₂|/r² doesn't show this by itself — the sign of the product q₁×q₂ determines the direction, not the formula's magnitude.
"Coulomb's law only applies to point charges."
It's exact for point charges, but it also applies exactly to any spherically symmetric charge distribution (like a uniformly charged sphere) treated as a point charge at its centre — as long as the charge distributions don't overlap. This mirrors the shell theorem in gravity.
"A bigger charge always means a bigger force, no matter what."
Force depends on the product of both charges and the inverse square of distance together. A large q₁ paired with a tiny q₂, or placed very far away, can still produce a small force — all three quantities matter jointly.
"Coulomb force and gravity are basically the same strength."
They share the same 1/r² form, but for charged particles like protons the electric force is roughly 10³⁶ times stronger than gravity between the same pair. Gravity only seems to dominate at large scales because bulk matter is nearly charge-neutral.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 2 — §5.2 "Coulomb's Law" (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 21, Coulomb's Law.
- • Serway & Jewett, Physics for Scientists and Engineers — Chapter 23, Electric Fields.
F = k|q₁q₂|/r² with k ≈ 8.9875×10⁹ N·m²/C², assuming point (or spherically symmetric) charges in a vacuum or air. Results are rounded for display.
How to use this calculator
Choose the unknown
The calculator solves for force, charge 1, charge 2, or distance from the other three.
Enter charges in coulombs
Use scientific notation for lab-scale charges, e.g. 2e-6 for 2 μC.
See the force visually
The 3D diagrams show how force shrinks with distance and how like/opposite charges repel or attract.
Related tools
Frequently asked questions
What is Coulomb's law?
Coulomb's law gives the electrostatic force between two point charges: F = k|q₁q₂|/r², where k ≈ 8.9875×10⁹ N·m²/C² is Coulomb's constant, q₁ and q₂ are the charges in coulombs, and r is the separation distance in metres. The force acts along the line joining the two charges.
What does Coulomb's constant k represent?
k = 1/(4πε₀), where ε₀ ≈ 8.854×10⁻¹² C²/(N·m²) is the permittivity of free space. It sets the strength of the electric force in a vacuum (or air, to a very close approximation). Its value, k ≈ 8.9875×10⁹ N·m²/C², is often rounded to 8.99×10⁹ or 9.0×10⁹ for quick estimates.
How does the force depend on distance?
Coulomb's law is an inverse-square law: F ∝ 1/r². Doubling the separation distance cuts the force to one quarter; tripling it cuts the force to one ninth. This is the same mathematical form as Newton's law of gravitation.
Do like charges attract or repel?
Like charges (both positive or both negative) repel; opposite charges (one positive, one negative) attract. Coulomb's law as written, F = k|q₁q₂|/r², gives only the magnitude of the force — the sign of q₁×q₂ tells you the direction: positive product means repulsion, negative product means attraction.
Does Coulomb's law only work for point charges?
It is exact for point charges, and it also applies exactly to spherically symmetric charge distributions (like uniformly charged spheres) as long as the spheres don't overlap — in that case you can treat all the charge as concentrated at the centre, an electrostatic analogue of Newton's shell theorem for gravity.