Coulomb’s Law Calculator
Compute the electrostatic force between point charges: F = k·q₁·q₂ / r² with k = 8.9875517923 × 10^9 N·m²/C² (CODATA 2018). Runs entirely in the browser — no server, no signup.
Signs: charges can be negative (e.g. −5 µC). Attractive vs repulsive nature is determined automatically from the signs of both charges.
Three charges on a straight line. Enter positions x₁, x₂, x₃ (any order, as long as they differ) — the total force on the middle charge q₂ is computed.
Formula
with k = 8.9875517923 × 10^9 N·m²/C² (Coulomb constant, CODATA 2018; k = 1/(4πε₀)). F is signed: positive means the charges repel, negative means they attract.
Worked examples
Example 1. Two charges of 1 µC each, 1 m apart:
F = 8.9875517923×10^9 × 10^-6 × 10^-6 / 1² = 8.98755 × 10^-3 N = 8.98755 mN (repulsive, since both charges are positive).
Example 2 (superposition). q₁ = 2 µC at x = 0 m, q₂ = −3 µC at x = 0.4 m, q₃ = 5 µC at x = 1 m. Total force on the middle charge q₂ = 3.74481 × 10^-2 N (3.74481 × 10^1 mN) in the +x direction.
Unit reference
| Charge unit | Value in coulombs |
|---|---|
| coulomb (C) | 1 |
| millicoulomb (mC) | 10^-3 |
| microcoulomb (µC) | 10^-6 |
| nanocoulomb (nC) | 10^-9 |
| picocoulomb (pC) | 10^-12 |
Frequently asked questions
What is Coulomb’s law?
Coulomb’s law states that the magnitude of the electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation: F = k × q1 × q2 / r^2. It is the foundation of electrostatics and applies to point charges, or charged bodies whose separation is much larger than their size.
What is the value of k in Coulomb’s law?
k = 8.9875517923 × 10^9 N·m²/C². This is the CODATA 2018 value defined as k = 1/(4πε₀), where ε₀ is the vacuum permittivity. For quick estimates, 8.99 × 10^9 N·m²/C² is sufficient.
How do I know whether the force is attractive or repulsive?
Look at the sign of the product q1 × q2. If both charges have the same sign (positive-positive or negative-negative), the force is repulsive. If they have opposite signs (one positive, one negative), the force is attractive. This calculator shows an automatic badge based on the sign of the charges you enter.
Example: two 1 µC charges 1 meter apart — what is the force?
F = k × q1 × q2 / r^2 = 8.9875517923×10^9 × 10^-6 × 10^-6 / 1^2 = 8.98755 × 10^-3 N = 8.98755 mN. Since both charges have the same sign (positive), the force is repulsive.
Which units does this calculator support?
Charge: coulomb (C), millicoulomb (mC), microcoulomb (µC), nanocoulomb (nC), and picocoulomb (pC). Distance: meter (m), centimeter (cm), and millimeter (mm). The force result is automatically shown in the most fitting SI unit — N, mN, µN, nN, or pN.
What is 1D superposition mode?
The superposition principle states that the total force on one charge equals the vector sum of the forces from every other charge. In this mode three charges are placed on a line at positions x1, x2, x3, and the total force on the middle charge (q2) is computed. Example: q1 = 2 µC at x = 0 m, q2 = −3 µC at x = 0.4 m, q3 = 5 µC at x = 1 m gives a total force of 3.74481 × 10^-2 N (3.74481 × 10^1 mN) on q2 in the +x direction.
Is this calculator the same as a charge unit converter?
No. A charge unit converter only changes units (for example µC to mC) for electronics needs, while this calculator computes the electrostatic force between point charges — a different physics domain. If you need charge unit conversion, use the Electric Charge Conversion tool linked at the bottom of this page.
See also
Electric Charge Conversion Calculator — charge unit conversion (C, mC, µC, nC, pC, Ah, mAh) for electronics needs.
Scope: this tool is purely electrostatics (force between point charges). Unlike charge-converter (charge unit conversion), bridge-rectifier (bridge rectifier), and capacitive-transformerless-power-supply (transformerless power supply) which cover electronics/circuits.
Free tool by NRTechStudio