Coulomb's Law Calculator

What is Coulomb's Law?

Imagine holding two powerful magnets near each other. You can feel an invisible force pushing them apart or pulling them together. In the world of electricity, charges behave the same way.

Discovered by French physicist Charles-Augustin de Coulomb in 1785, Coulomb's Law quantifies the force between two stationary electrically charged particles. It is the foundation of electrostatics.

The Equation

• F (Force): The electrostatic force between the charges. Measured in Newtons (N).
• k (Coulomb's Constant): A massive proportionality constant. Value: 8.98755 × 10⁹ N·m²/C². This huge number explains why electric forces are so powerful compared to gravity.
• q₁ & q₂ (Charges): The amount of electric charge. Measured in Coulombs (C).
• r (Distance): The separation distance between the two charges. Measured in Meters (m).

The Inverse Square Law (Distance Matters)

Notice the r² (radius squared) in the denominator? This is called the Inverse Square Law.

It means that small changes in distance have massive effects on the force. If you move the charges 2x farther apart, the force doesn't just drop by half; it drops to 1/4th of its original strength.

• Double distance = 1/4 force.
• Triple distance = 1/9 force.
• Half distance = 4x force!

This explains why electrons (negative) stay locked in orbit around the nucleus (positive) of an atom—they are so close that the attractive force is incredibly strong.

Electric Force vs. Gravity

The formula for electric force looks almost identical to Newton's Law of Gravity ($F = G \frac{m_1 m_2}{r^2}$), but there is one huge difference in magnitude.

Understanding Units: The MicroCoulomb

One Coulomb is actually a terrifyingly large amount of charge. A typical lightning bolt transfers about 15 Coulombs of charge.

Because 1 C is so huge, textbook physics problems usually deal with MicroCoulombs (µC) or NanoCoulombs (nC).