Coulomb's Law Calculator

Both Coulomb's law and Newton's law of gravitation are inverse-square laws: force falls off as 1/r^2. Both are central forces acting along the line joining two objects. The key difference is that gravity is always attractive (mass is always positive), while electrostatic force can be either attractive (opposite charges) or repulsive (like charges). Coulomb's constant k is approximately 8.99 x 10^9 N m^2/C^2, while the gravitational constant G is about 6.67 x 10^-11 N m^2/kg^2. This means electrostatic forces between elementary particles are typically many orders of magnitude stronger than gravitational forces between the same particles.

The inverse-square dependence arises from the geometry of three-dimensional space. An electric field spreads outward from a point charge in all directions equally, like the surface of an expanding sphere. The surface area of a sphere grows as r^2, so the field strength (force per unit charge) diminishes as 1/r^2 to conserve the total flux through any sphere surrounding the charge. This is not a coincidence: it is a direct consequence of living in three spatial dimensions and is captured formally by Gauss's law.

The coulomb (C) is the SI unit of electric charge. Since the 2019 redefinition of SI units, 1 coulomb is exactly defined as (1/1.602176634 x 10^-19) elementary charges, meaning 1 coulomb is approximately 6.242 x 10^18 elementary charges (electrons or protons). In practical terms, a coulomb is a very large amount of charge: a typical capacitor stores microcoulombs to millicoulombs, and static electricity on a person might be a few hundred nanocoulombs. A lightning bolt transfers roughly 1 to 5 coulombs.

Electric force (F) is the force exerted on a specific charge q2 by the field created by charge q1. It depends on both charges. Electric field (E) is a property of space created by a source charge, independent of any test charge: E = k * |q1| / r^2, measured in newtons per coulomb (N/C) or equivalently volts per metre (V/m). The force on a test charge q2 placed in that field is F = q2 * E. The electric field concept is useful because it lets you calculate the effect on any charge placed at that location without knowing the charges in advance.

The superposition principle states that when multiple charges are present, the total force on any single charge is the vector sum of the individual forces exerted by each other charge separately. For example, if charge q3 is near both q1 and q2, the total force on q3 equals the Coulomb force from q1 plus the Coulomb force from q2, calculated independently and then added as vectors (accounting for direction). This principle holds exactly in classical electrostatics and is the foundation for calculating forces in complex charge distributions.