Coulomb's Law
Calculate electrostatic force between two charges using Coulomb's law. Get accurate results with formula substitution and step-by-step output.
Key formula
F = k(q1q2 / r^2)
How do you use Coulomb's law?
Electrostatic force magnitude is F = k |q₁ q₂| / r². Multiply the charges, multiply by k, divide by r squared. Direction: opposite charges attract; like charges repel along the line joining them. Rearrange to r = √(k|q₁q₂|/F) when force is given.
About this tool
Coulomb’s law gives the electrostatic force between two point charges. This page keeps F = k q₁q₂ / r² visible so you can solve for force, charge, or separation without mixing µC with C.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: two charges
q₁ = q₂ = 2.0 × 10⁻⁶ C, r = 0.10 m, k = 9.0 × 10⁹. F = (9e9)(2e-6)(2e-6)/(0.01) = (9e9)(4e-12)/0.01 = 3.6 N (repulsive if same sign).
Example 2: convert µC
q₁ = 3.0 µC = 3.0 × 10⁻⁶ C, q₂ = −1.0 µC = −1.0 × 10⁻⁶ C, r = 0.050 m. |F| = (9e9)(3e-6)(1e-6)/(0.0025) = 10.8 N attractive.
Example 3: find separation
F = 0.90 N, |q₁q₂| = 1.0 × 10⁻¹² C², k = 9.0 × 10⁹. r² = k|q₁q₂|/F = (9e9)(1e-12)/0.90 = 0.01. r = 0.10 m.
Frequently asked questions
What is Coulomb's law formula?
F = k q₁ q₂ / r² for the magnitude (use absolute values for size, then assign attract/repel). k ≈ 9.0 × 10⁹ N·m²/C² in vacuum.
How do I convert microcoulombs?
1 µC = 10⁻⁶ C. Convert before substituting. Leaving µC as if they were C inflates force by 10¹².
Is the force attractive or repulsive?
Like signs (both + or both −) repel. Opposite signs attract. The formula magnitude is positive; direction is along the line between charges.
How is this like gravity?
Both are inverse-square laws. Gravity is always attractive (masses positive). Coulomb force can attract or repel depending on charge signs.
What if the charges are not point charges?
Coulomb’s law as F = kq₁q₂/r² is for point charges or spherical symmetry with r between centers. Extended charge distributions need integration or Gauss’s law.