Calculators
Coulomb's Law Calculator
Calculate electrostatic force between two point charges.
Coulomb's Law Calculator tool
Loading tool…
Jump to a section
About This Tool
Coulomb's law describes the ideal electrostatic force between two stationary point charges. This calculator uses the magnitudes and signs of two charges plus their separation to find the force magnitude and whether the interaction is attractive or repulsive. It uses the vacuum Coulomb constant and performs every calculation locally in your browser.
How To Use It
- Enter each charge with its sign. Positive and negative signs determine whether the charges attract or repel.
- Choose charge units from coulombs, millicoulombs, microcoulombs, or nanocoulombs.
- Enter the straight-line separation between the charge centers and choose metres, centimetres, or millimetres.
- Choose the force output unit and read both the magnitude and interaction type.
Examples
Two 1 µC charges one metre apart
For q₁ = +1 µC, q₂ = +1 µC, and r = 1 m, the force magnitude is about 0.00899 N. Because the signs match, the interaction is repulsive.
Opposite charges
For +2 µC and -3 µC separated by 0.5 m, the force magnitude is about 0.2157 N and the interaction is attractive.
Distance has a squared effect
If both charges stay fixed and the separation doubles, Coulomb's law makes the force one quarter as large because force varies with 1/r².
Useful Notes
Coulomb's law formula
The force magnitude is F = k|q₁q₂|/r², where q₁ and q₂ are charges in coulombs, r is their separation in metres, and k = 8.9875517923 × 10⁹ N·m²/C² is the Coulomb constant used by this calculator.
Attraction and repulsion
The sign of q₁q₂ determines the interaction. Like signs produce repulsion and opposite signs produce attraction. The displayed force is a non-negative magnitude; the interaction label communicates the direction relationship.
Why distance cannot be zero
The ideal point-charge equation divides by r², so r = 0 is undefined. Real charged objects also have finite size and charge distributions, so the point-charge model should not be extended to zero separation.
Vacuum and point-charge assumptions
This calculator assumes stationary point charges in vacuum. Materials between charges can change the force through permittivity, and extended objects may require integrating over a charge distribution rather than treating all charge as concentrated at one point.
Educational scope
Use this tool for textbook electrostatics, unit checks, and idealized estimates. It does not model electric fields from many charges, moving charges, magnetic effects, dielectric geometry, breakdown, or engineering safety limits.
FAQ
What is the Coulomb constant?
This calculator uses k = 8.9875517923 × 10⁹ N·m²/C² for the vacuum Coulomb constant.
How do I know whether the force attracts or repels?
Charges with the same sign repel. Charges with opposite signs attract. If either charge is zero, this two-charge Coulomb-force model gives zero force.
Why does distance matter so much?
Coulomb force follows an inverse-square relationship. Multiplying separation by a factor of two divides the force by four; multiplying it by three divides the force by nine.
Can I use this inside a material?
Not directly if you need material effects. The calculator uses the vacuum Coulomb constant and does not apply a relative permittivity for a dielectric medium.