Electrostatic Force Calculator

Coulomb's Law states that the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them: F = k × |q₁ × q₂| / r². It was formulated by Charles-Augustin de Coulomb in 1785.

Coulomb's constant k = 1/(4πε₀) ≈ 8.9876 × 10⁹ N·m²/C², where ε₀ = 8.854 × 10⁻¹² F/m is the permittivity of free space. This constant determines the strength of the electromagnetic force in a vacuum.

When the two charges have opposite signs (one positive, one negative), the force is attractive — the charges pull toward each other. When both charges have the same sign (both positive or both negative), the force is repulsive — the charges push away from each other. Coulomb's Law gives the magnitude of the force; the direction depends on the signs.

The electrostatic force follows an inverse-square law: doubling the distance reduces the force by a factor of four (2² = 4). Tripling the distance reduces it by a factor of nine. This rapid decrease with distance is why macroscopic objects rarely feel noticeable electrostatic forces unless the charges are very large.

Relative permittivity εr (also called the dielectric constant) measures how much a material reduces the electrostatic force compared to a vacuum. For vacuum and air εr ≈ 1, for water εr ≈ 80. A higher εr means the material shields the charges more strongly, reducing the force by a factor of εr.

The calculator uses coulombs (C) as the SI unit of electric charge. In practice, most everyday charges are much smaller: 1 microcoulomb (µC) = 10⁻⁶ C, 1 nanocoulomb (nC) = 10⁻⁹ C. The elementary charge of a proton or electron is approximately 1.602 × 10⁻¹⁹ C.

Inside a conductor in electrostatic equilibrium, the electric field is zero and free charges redistribute on the surface. Coulomb's Law still holds for individual charge interactions, but the macroscopic field inside the conductor cancels out. The law is most directly applied to point charges in free space or insulating media.

The electrostatic force is enormously stronger than gravity at the atomic scale. The ratio of the electrostatic to gravitational force between two protons is approximately 10³⁶. However, large objects tend to be electrically neutral, so gravity dominates at macroscopic scales despite being fundamentally much weaker.

Yes. For a system of multiple charges, the principle of superposition applies: the total force on any one charge is the vector sum of the forces exerted by every other charge individually. The calculator computes the force between exactly two charges; for more complex systems, each pair must be calculated and vectors added.

Coulomb's Law is a classical approximation valid for stationary point charges in the non-relativistic regime and at distances much larger than atomic nuclei. At very small distances (sub-nanometer), quantum mechanical effects (exchange interaction, Pauli exclusion) dominate. For moving charges, the full Maxwell's equations or relativistic electrodynamics must be used.