Coulomb's Law Calculator
Electrostatic force between two point charges.
In coulombs. Use scientific notation like 1e-6 for microcoulombs.
Results update as you type.
How it works
Coulomb's law governs the force between electric charges, and this Coulomb's law calculator finds that force from the two charge values and the distance separating them. Using the electrostatic constant k of about 8.9875 billion newton-metres-squared per coulomb-squared, it returns the force in newtons for charges in coulombs and separation in metres. This force is one of the fundamental interactions of nature and shapes the world at every scale below the astronomical. It holds electrons to nuclei, binds atoms into molecules, and explains static cling, lightning, and the behaviour of capacitors. Engineers designing electronics and physicists modelling matter both need to quantify it, and a Coulomb's law calculator does so instantly without wrestling with the very large constant and the awkward powers of ten typical of charge values. The law works because each charge creates an electric field that pushes or pulls the other, with the strength falling off as the square of the distance, just like gravity. Like charges of the same sign produce a positive, repulsive force, while opposite charges give a negative result, signalling attraction. Because real charges are often measured in microcoulombs or nanocoulombs, this Coulomb's law calculator accepts scientific notation, letting students and engineers explore how dramatically the force grows as charges are brought closer together.
F = k · q₁ · q₂ ÷ r², k = 8.9875 × 10⁹ N·m²/C²
Coulomb's law says the electric force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. The product of the charges appears because each charge's field acts on the other, and the inverse-square dependence arises because the field spreads out over the surface of a sphere whose area grows with the square of the radius. The constant k sets the strength of the electrostatic interaction in a vacuum. A positive result means repulsion, a negative result attraction.
Source:Standard physics (Coulomb's law)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter charge 1, charge 2 and separation.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Electrostatic force updates instantly as you type — no button to press.
Frequently asked questions
How do I enter very small charges like microcoulombs?
Use scientific notation. One microcoulomb is 1e-6 coulombs, one nanocoulomb is 1e-9, and one picocoulomb is 1e-12. Type the value in this exponential form directly into the charge fields. Real-world charges are almost always tiny fractions of a coulomb, since one coulomb is an enormous amount of charge, so scientific notation keeps the numbers manageable and the force result accurate.
What does a negative force result mean?
The sign of the force follows the product of the two charges. If both charges have the same sign, the product is positive and the force is repulsive, pushing them apart. If the charges have opposite signs, the product is negative and the force is attractive, pulling them together. So a negative result signals attraction between opposite charges, while a positive result signals repulsion between like charges.
Why does the force fall off with the square of distance?
Coulomb's law is an inverse-square law because the electric field radiating from a point charge spreads over the surface of an expanding sphere, whose area grows with the square of the radius. Doubling the separation therefore spreads the influence over four times the area, cutting the force to a quarter. This same inverse-square geometry governs gravity and the intensity of light from a point source.
How is Coulomb's law similar to gravity?
Both are inverse-square laws with the same mathematical form: a constant times the product of the two source quantities divided by distance squared. Gravity uses masses and is always attractive, while Coulomb's law uses charges and can attract or repel. Electrostatic force is vastly stronger than gravity between fundamental particles, which is why chemistry and electronics are dominated by electric forces rather than gravitational ones.
Does this calculator work inside materials or only in a vacuum?
It uses the constant k for a vacuum, which is also very close to the value in air. Inside other materials, the surrounding medium reduces the force by a factor called the relative permittivity or dielectric constant. Water, for example, weakens electrostatic forces dramatically. For force between charges in a dielectric, divide the vacuum result by that material's dielectric constant to get the reduced value.