Coulomb's law calculator
The force between two point charges.
Fill in the fields and the result will appear here automatically.
Coulomb’s law estimates electrostatic force between two point charges in vacuum. Enter charges in nC and distance in cm. The main number is the force magnitude; a separate row distinguishes attraction, repulsion and zero force when a charge is zero. The first charge’s field and the pair’s potential energy separate source properties from interaction.
How it works
Formula and logic
F=k|q₁q₂|/r²; E₁=k|q₁|/r²; U=kq₁q₂/r. Multiply nC by 10⁻⁹ and cm by 0.01. k≈8.9875517862·10⁹ N·m²/C², rounded from CODATA 2022; U is zero at infinity.
Example
Charges of 1 and −1 nC 10 cm apart attract with 8.988·10⁻⁷ N.
Fields and units
- First charge — nC
- Second charge — nC
- Distance — cm
How to use
- — Enter two charges in nC. Positive, negative and zero charges are allowed; opposite signs attract and equal signs repel.
- — Enter a positive distance in centimetres:10 means 0.1 m. nC and C differ by a billion; misreading both charge units changes the force by 10¹⁸.
- — Read the force magnitude, the first charge’s field and potential energy separately. With q₂=0 the force is zero, while the first charge’s field can remain.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax §5.3: electrostatic force between point charges OpenStax §5.4: source field independent of the test charge OpenStax §7.1: energy of a charge pair with zero at infinity NIST CODATA 2022: exact h, c, e and measured ε₀
- Limitation
- The implemented model is point charges in vacuum. A homogeneous linear dielectric uses relative permittivity εᵣ, but there is no such input here.
FAQ
How is Coulomb's law like gravitation?
Both fall off as the square of the distance and scale with the product of the "charges" — electric or mass. The key difference: mass is always positive, so gravity only attracts, while electric charge comes in two signs.
Which inputs distinguish field from force?
The first charge’s field depends on q₁ and r; the force also depends on q₂. The field row is a magnitude, with direction set by the sign of q₁. A zero q₂ means zero force without removing the first charge’s field.
What is field strength?
The force that would act on a unit positive charge at that point. It does not depend on the second charge and describes the field itself rather than a pair of bodies, which makes sources comparable.
Why can potential energy be negative?
It is measured from infinity. For attracting charges you must do work to pull them infinitely apart, so their present energy sits below zero.
What changes for a medium or extended objects?
The implemented model is point charges in vacuum. A homogeneous linear dielectric uses relative permittivity εᵣ, but there is no such input here. Neighbouring charges redistribute charge on conducting spheres; centre-to-centre distance alone does not make the point formula exact.