Coulomb's Law Calculator

How to Use the Calculator

1. Enter the value of Charge 1 (q₁) and choose its unit (nC, μC, mC, C or elementary charges). Use a minus sign for a negative charge.
2. Enter Charge 2 (q₂) with its unit in the same way.
3. Enter the Separation distance (r) between the centres of the two charges and pick a length unit (nm, μm, mm, cm, m, in or ft). The value must be greater than zero.
4. Read the result: the force magnitude in newtons (with conversions to mN, μN, kN, lbf and dynes), whether the interaction is attractive or repulsive, and a table showing every intermediate value.

What Is Coulomb's Law?

Coulomb's law, published by French physicist Charles-Augustin de Coulomb in 1785, describes the electrostatic force between two charged objects. It states that the force is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them. In many ways it mirrors Newton's law of universal gravitation — but while gravity only attracts, electric forces can attract or repel depending on the signs of the charges.

The sign of the result carries meaning. If \(q_1\) and \(q_2\) have the same sign, their product is positive and the force is repulsive: the charges push each other apart. If the signs are opposite, the product is negative and the force is attractive. The calculator reports the magnitude of the force together with this direction, so you always know both the strength and the nature of the interaction.

The inverse-square dependence on distance is the law's most important practical feature. Halving the distance makes the force four times stronger; doubling the distance makes it four times weaker. This is why electrostatic forces dominate at short range — two elementary charges 1 nm apart exert forces on the scale of chemical bonds, while the same charges a metre apart would be utterly undetectable.

Coulomb's law is the foundation of electrostatics. It underlies the structure of atoms and molecules, the behaviour of capacitors, electric fields, and technologies from laser printers to electrostatic precipitators. Once you know the force, you can combine it with Newton's second law to predict the motion of charged particles.

Assumptions, Limitations and Tips

• Point charges: the formula assumes each charge is concentrated at a single point, or is a uniformly charged sphere where r is measured between centres. For irregular charged objects at close range, the true force differs.
• Vacuum: the calculation uses the vacuum permittivity \(\varepsilon_0\). In a medium with relative permittivity \(\varepsilon_r\), the force is smaller by a factor of \(\varepsilon_r\) — about 80× weaker in water.
• Distance must be positive: two charges at exactly the same point would give an infinite force, so the calculator requires r > 0.
• Static charges: Coulomb's law applies to charges at rest. Moving charges additionally create magnetic effects described by electromagnetism.
• Realistic values: everyday static electricity involves nanocoulombs to microcoulombs. If the result comes out in kilonewtons or more, double-check your units — a millicoulomb is already a very large amount of charge.
• Force pairs: by Newton's third law, both charges experience the same force magnitude in opposite directions along the line joining them.

Once you have found the electric force, you can put it to work in other mechanics problems — for example, combine it with the Centripetal Force Calculator to analyse an electron orbiting a nucleus, check the balance with other forces using the Friction Force Calculator or Tension in Ropes Calculator, or explore the energy side of the interaction with the Potential Energy Calculator.