About the Coulomb's Law Calculator
This Coulomb's law calculator finds the electrostatic force between two point charges. Enter both charges (with sign) in coulombs, microcoulombs, nanocoulombs or elementary charges, and the distance between them, and it returns the size of the force, whether it is attractive or repulsive, the electric field that charge 1 creates at the position of charge 2, and the electric potential energy of the pair. A second mode works backwards from a known force to the separation distance.
It is meant for physics students working through electrostatics problems, teachers building examples, and anyone curious about the forces inside atoms or between charged objects. A chart shows how quickly the force falls away as the charges move apart — doubling the distance cuts the force to a quarter.
The calculation treats the charges as points (or uniformly charged spheres measured centre to centre) in a uniform medium. In a material other than vacuum, enter its relative permittivity (dielectric constant); air is about 1.0006 and water about 80 at room temperature, which weakens the force accordingly.
How to use the coulomb's law calculator
- 1Choose whether to find the force or the distance.
- 2Enter both charges with their signs and pick the charge unit.
- 3Enter the distance (or the force) and pick the distance unit.
- 4Change the relative permittivity if the charges are not in vacuum or air.
- 5Read the force, its direction and the field and energy values.
Formula and method
Coulomb's law says the electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. Like charges (same sign) repel and opposite charges attract; the force acts along the line joining them. Coulomb's constant k is derived from the vacuum permittivity ε₀ = 8.8541878188 × 10⁻¹² F/m (CODATA 2022).
In a uniform dielectric medium the force is reduced by its relative permittivity εr. Rearranging gives the separation for a given force, r = √(k|q₁q₂| / (εr F)). The calculator also reports the electric field of q₁ at the position of q₂, E = k|q₁|/(εr r²), and the potential energy of the pair U = kq₁q₂/(εr r), which is negative for attracting charges.
- F
- Magnitude of the electrostatic force (N)
- q₁, q₂
- Charges (C)
- r
- Distance between the charges (m)
- k
- Coulomb's constant, 8.98755 × 10⁹ N·m²/C²
- ε₀
- Vacuum permittivity
- εr
- Relative permittivity (dielectric constant) of the medium
Worked examples
+2 µC and −3 µC, 5 cm apart
F = 8.98755 × 10⁹ × (2 × 10⁻⁶ × 3 × 10⁻⁶) / 0.05² = 21.57 N. The charges have opposite signs, so the force is attractive and the potential energy is negative (−1.08 J).
Electron and proton in a hydrogen atom
At the Bohr radius of 0.0529 nm, two elementary charges (1.602 × 10⁻¹⁹ C) attract with 8.24 × 10⁻⁸ N — tiny in everyday terms, but enormous for particles with masses around 10⁻³⁰ kg.
How far apart for a 1 N force?
Two +1 µC charges repel with 1 N when r = √(8.98755 × 10⁹ × 10⁻¹² / 1) = 0.0948 m, or about 9.5 cm.
Frequently asked questions
What is Coulomb's law?+
Coulomb's law states that the force between two point charges is F = k q₁q₂ / r², where k ≈ 8.99 × 10⁹ N·m²/C². The force is attractive for opposite charges and repulsive for like charges.
What is the value of Coulomb's constant?+
k = 1/(4πε₀) ≈ 8.9875517862 × 10⁹ N·m²/C², using the CODATA 2022 vacuum permittivity ε₀ = 8.8541878188 × 10⁻¹² F/m.
How does distance affect electric force?+
The force follows an inverse-square law: doubling the distance cuts the force to one quarter, and tripling it cuts the force to one ninth. Halving the distance makes it four times stronger.
How is Coulomb’s law similar to Newton’s law of gravity?+
Both are inverse-square laws proportional to the product of two quantities (charge or mass). But electric forces can attract or repel, and they are vastly stronger — about 10³⁶ times stronger than gravity between two protons.
What does relative permittivity do?+
A dielectric medium partially shields charges, dividing the force by its relative permittivity εr. In water (εr ≈ 80) the force between ions is about 80 times weaker than in vacuum, which is why salts dissolve.