Coulombs Law Calculator
Coulomb's law gives the electrostatic force between two point charges: F = k·|q1·q2| / r², where k ≈ 8.9875517873681764 × 10⁹ N·m²/C² is Coulomb's constant (equal to 1/(4·π·ε0)), q1 and q2 are the charges in coulombs and r is their separation in metres.
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How to use this calculator
- Enter the two point charges q1 and q2 in coulombs (C). Use scientific notation for small charges — for example 3e-6 for 3 microcoulombs (µC) or 5e-9 for 5 nanocoulombs (nC).
- Give one charge a minus sign (use the ± toggle) if it is negative; the calculator uses the sign of q1×q2 to report whether the force is attractive or repulsive.
- Enter the centre-to-centre separation r in metres, then read the force magnitude and its direction.
How it works
Coulomb's law gives the electrostatic force between two point charges: F = k·|q1·q2| / r², where k ≈ 8.9875517873681764 × 10⁹ N·m²/C² is Coulomb's constant (equal to 1/(4·π·ε0)), q1 and q2 are the charges in coulombs and r is their separation in metres. The result is the force each charge exerts on the other, in newtons.
The magnitude depends on the product of the charges and falls off with the square of the distance — double the separation and the force drops to a quarter. The direction comes from the signs: two like charges (product positive) repel, while opposite charges (product negative) attract. This calculator assumes point charges (or uniform spheres, where r is the distance between centres) in a vacuum or air.
Worked example
Two 3 µC charges 30 cm apart. Set q1 = 3e-6 C, q2 = 3e-6 C and r = 0.3 m. Coulomb's law gives F = k·|q1·q2|/r² = 8.98755×10⁹ × (3e-6 × 3e-6) / 0.3² = 8.98755×10⁹ × 9×10⁻¹² / 0.09 = 0.898755 N. Because both charges are positive, the product is positive, so the force is repulsive — the charges push apart along the line joining them.
Common mistakes
- Entering charges in microcoulombs or nanocoulombs as whole numbers. The formula needs coulombs — convert first: 1 µC = 1e-6 C, 1 nC = 1e-9 C.
- Giving the separation in centimetres instead of metres. Because r is squared, a 100× error in distance becomes a 10,000× error in force.
- Assuming a negative force means repulsion. This tool reports the magnitude (always positive) plus a separate direction; the sign of q1×q2 decides attractive versus repulsive, not the sign of the number.
Frequently asked questions
What is the value of Coulomb's constant k?
Coulomb's constant is k = 1/(4·π·ε0) ≈ 8.9875517873681764 × 10⁹ N·m²/C², often rounded to 8.99 × 10⁹ N·m²/C². It is the constant in F = k·q1·q2/r² and this calculator uses the full-precision value.
How does the force change if I double the distance?
The force follows an inverse-square law, so doubling the separation r divides the force by four (2² = 4). Tripling r divides it by nine. Halving r multiplies the force by four.
Does this work for charged spheres, or only point charges?
Coulomb's law is exact for point charges. It also works for two uniformly charged spheres if you use the distance between their centres as r, because a uniform sphere acts as though all its charge sits at its centre. It is not accurate for irregular or very close conductors where charge redistributes.
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