Coulombs Law Calculator
coulombs law calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Coulombs Law Calculator
Calculator
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Formula: F = kq₁q₂/r²
Worked example — 1.798 N (repulsive)
Formula
F = kq₁q₂/r²
Electrostatic force between two point charges. k = 8.9875×10⁹ N·m²/C².
Worked Examples
Example 1: Two charges
Problem:q₁=1μC, q₂=2μC, r=0.1m
Solution:F=8.99e9×1e-6×2e-6/0.01=1.798 N
Result:1.798 N (repulsive)
Frequently Asked Questions
What is Coulomb's law?
Coulomb's law states that the electrostatic force between two point charges is F = kq₁q₂/r², where k = 8.9875×10⁹ N·m²/C² is Coulomb's constant, q₁ and q₂ are the charges in coulombs, and r is the separation in meters. Like charges repel; opposite charges attract.
How do you calculate Coulomb's law force?
Use F = kq₁q₂/r². For q₁ = 1 μC and q₂ = 2 μC separated by 0.1 m: F = 8.9875×10⁹ × 1×10⁻⁶ × 2×10⁻⁶ / 0.01 = 1.798 N (repulsive, since both charges are positive). Doubling the distance reduces the force by a factor of 4.
What units does the Coulomb's law calculator use?
Charges q₁ and q₂ are entered in coulombs (C). Use scientific notation for small charges, e.g. 1e-6 for 1 microcoulomb (μC) or 1e-9 for 1 nanocoulomb (nC). Distance r is in meters (m). The output force is in Newtons (N).
How does Coulomb force compare to gravity?
For two electrons (q = 1.6×10⁻¹⁹ C, m = 9.1×10⁻³¹ kg) separated by 1 nm, Coulomb force ≈ 2.3×10⁻¹⁰ N while gravitational force ≈ 5.5×10⁻⁵² N — electrostatics is about 10⁴² times stronger. Gravity dominates at large scales only because macroscopic matter is nearly electrically neutral.
Background & Theory
Coulomb Force by the Numbers
Coulomb's law describes one of the four fundamental forces of nature, and it's structurally identical to Newton's law of gravitation — both fall off as 1/r² — but electrostatic force is vastly stronger at the particle scale. The elementary charge is 1.602×10⁻¹⁹ C, so everyday "point charges" in a physics problem (microcoulombs, nanocoulombs) already represent trillions of electrons.
| Charge pair / distance | Approx. force |
|---|---|
| Two electrons, 1 nm apart | ~2.3×10⁻¹⁰ N (repulsive) |
| Proton and electron in a hydrogen atom (0.0529 nm, Bohr radius) | ~8.2×10⁻⁸ N (attractive) |
| Two 1 μC charges, 1 cm apart | ~90 N |
| A charged balloon (~1 nC) near hair, a few cm away | micronewton range — enough to visibly lift hair strands |
The inverse-square dependence means doubling the separation cuts the force to a quarter, and halving it quadruples the force — this rapid falloff is why static electricity effects (like a balloon sticking to a wall) are only noticeable over short ranges.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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