Key takeaways
- Coulomb's Law is F = k × q₁ × q₂ ÷ r², measured in newtons.
- Doubling the distance between charges cuts the force to a quarter, not a half.
- Like charges repel, and opposite charges attract.
- Coulomb's constant, k, is about 8.99 × 10⁹ N·m²/C².
In this guide
What is Coulomb's Law?
Coulomb's Law calculates the electric force between two point charges. The closer the charges are, and the larger they are, the stronger the force between them.
Why does Coulomb's Law matter?
Coulomb's Law is the electric version of gravity's pull, and it explains everything from static electricity to how atoms hold together in the first place.
Two small charges of 2 µC and 5 µC, placed just 0.3 m apart, pull or push on each other with a force of about 0.9989 N, almost exactly the weight of a small apple, despite involving no contact at all.
The formula
| Symbol | What it means | Example |
|---|---|---|
| F | The electric force, in newtons (N) | 0.9989 N |
| k | Coulomb's constant, about 8.99 × 10⁹ N·m²/C² | 8.99 × 10⁹ |
| q₁, q₂ | The two electric charges, in microcoulombs (µC) | 2 µC, 5 µC |
| r | The distance between the charges, in metres (m) | 0.3 m |
How to calculate electric force step by step
- 1Find each charge. Measure them in microcoulombs.
- 2Find the distance between the charges. Measure it in metres.
- 3Multiply the two charges, then by Coulomb's constant.
k × q₁ × q₂. - 4Divide by the square of the distance. That gives the force in newtons.
Try the calculator below with your own charges and distance to see every step worked out.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Mixing up charge units. Charges are often given in microcoulombs (µC), a millionth of a coulomb — check which unit a problem uses before plugging in numbers.
- Confusing this with gravitational force. Coulomb's Law looks similar to gravity formulas but uses electric charge and Coulomb's constant instead of mass and the gravitational constant.
- Ignoring the sign of the charges. This calculator finds the strength of the force; whether it's a push or a pull depends on whether the charges match or differ in sign.
Tips and tricks
- To estimate quickly, remember the inverse-square rule: halving the distance quadruples the force.
- Working backwards from force to distance? Divide k·q₁·q₂ by the force, then take the square root:
r = √(kq₁q₂ ÷ F). - Coulomb's Law is the electric equivalent of force in Newton's laws, a push or pull, just caused by charge instead of contact.
- It describes the force between charges, separate from Ohm's Law, which describes the flow of charge once it's moving through a circuit.
Where you'll use it in real life
- Static electricity: Coulomb's Law explains why a balloon rubbed on hair sticks to a wall, or why hair stands up in dry weather.
- Chemistry: the attraction between charged particles is part of what holds atoms and molecules together.
- Electronics: engineers account for electric forces between charged components in sensitive circuit design.
- Physics education: Coulomb's Law is usually the first formula students meet for forces that act without any physical contact.
Quick summary
To find the electric force between two charges, multiply them together, multiply by Coulomb's constant, then divide by the square of the distance between them. Because distance is squared, small changes in separation make a big difference to the force. Use the calculator above to check your own numbers.
Worked example
Two small charged spheres, one with a charge of 2 µC and the other 5 µC, are placed 0.3 m apart. What is the electric force between them?
- 01F = k·q₁q₂ / r² (k = 8.99 × 10⁹ N·m²/C²)
- 02q₁ = 2 µC = 0.0000 C, q₂ = 5 µC = 0.0000 C
- 03F = 8.99×10⁹ × (0.0000 × 0.0000) / 0.3²
- 04F = 0.0899 / 0.09
- 05F = 0.9989 N
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I calculate the force between two charges?
Multiply the two charges together, multiply by Coulomb's constant (8.99 × 10⁹), then divide by the square of the distance between them: F = kq₁q₂ ÷ r².
Why does distance matter so much in Coulomb's Law?
Because the distance is squared in the formula, doubling the distance between two charges reduces the force to just a quarter of its original strength.
What happens if the charges have opposite signs?
Opposite charges attract each other, while charges with the same sign repel. This calculator uses the sizes of the charges to find the strength of that force.
What is a microcoulomb?
A microcoulomb (µC) is one millionth of a coulomb, the standard SI unit of electric charge. It's a convenient size for everyday static-electricity examples.
