Coulomb's Law helps you calculate electric force without a spreadsheet. Just enter Charge 1 (μC), Charge 2 (μC) and Distance (m); Coulomb's Law updates the result as you type. Coulomb's Law puts the headline number first. Use Coulomb's Law for a reliable number, fast. Nothing typed into Coulomb's Law leaves your device or the tab. Looking for coulombs law calculator electric force or free coulombs law calculator? Coulomb's Law covers both. Coulomb's Law is designed for real people. Labels stay plain. Coulomb's Law stays bookmarked for next time.
What the defaults give
Two charges of 1 μC separated by 1 m exert 0.009 N on each other.
That is about the weight of a 1 gram mass — electrostatic force is weak at these charge levels until the distance shrinks.
The formula
F = k × q₁ × q₂ ÷ r², with k = 9 × 10⁹ N·m²/C²
Multiply the two charges, divide by the square of the separation, and scale by the Coulomb constant. The inputs here are in microcoulombs, so each charge is a millionth of a coulomb and the pair contributes 10⁻¹² to the product. That is why the force looks so small: 9 × 10⁹ × 10⁻¹² is 0.009.
Worked examples
1 μC and 1 μC at 1 m → 0.009000 N
2 μC and 1 μC at 1 m → 0.018000 N
1 μC and 2 μC at 1 m → 0.018000 N
1 μC and 1 μC at 0.5 m → 0.036000 N
1 μC and 1 μC at 2 m → 0.002250 N
0.5 μC and 0.5 μC at 1 m → 0.004500 N
Halving the distance multiplies the force by four, because r appears squared. Doubling it divides by four. The charge inputs are linear: doubling either one doubles the force, and doubling both quadruples it.
Direction and sign
Like charges repel, opposite charges attract, and the magnitude is the same in both cases. The formula gives the size only — the sign of the product tells you which way the force points along the line joining the charges. For more than two charges, calculate each pair separately and add the forces as vectors; the superposition is exact because the fields add linearly.
Why the constant is so large
k = 9 × 10⁹ is enormous compared with the gravitational constant, 6.67 × 10⁻¹¹. Two protons repel electrostatically about 10³⁶ times harder than they attract gravitationally, which is why gravity only wins on astronomical scales where charge cancels out. Everyday matter is neutral to within a tiny fraction, so the electric force that would otherwise dominate is almost entirely hidden.
At very short range, around nuclear distances, the formula stops applying and the strong force takes over. At long range in a material, the permittivity changes the effective constant, which is why the force between charges in water is much weaker than in air.
Frequently Asked Questions
What is the force between two 1 μC charges 1 m apart?
0.009 N. That is 9 × 10⁹ × 10⁻⁶ × 10⁻⁶ ÷ 1², which is 9 × 10⁻³ newtons.
What happens if I halve the distance?
The force quadruples to 0.036 N, because it depends on 1 ÷ r². Doubling the distance divides it by four.
Does the sign of the charge matter?
Only for direction. Like charges repel and opposite charges attract, but the magnitude uses the product of the magnitudes.
Why is the electrostatic force so weak here?
Microcoulombs are tiny amounts of charge. The constant is large, but 10⁻⁶ × 10⁻⁶ leaves only 10⁻¹² to multiply it by.
How do I handle three charges?
Calculate each pair separately with this formula, then add the forces on the charge you care about as vectors. The fields superpose linearly.
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