What is Coulomb's Law?

Coulomb's Law states that the electrostatic force F between two stationary point charges q₁ and q₂ separated by a distance r in vacuum is F = k·|q₁·q₂|/r², where k = 8.9876×10⁹ N·m²/C² is Coulomb's constant. The force is repulsive when both charges share the same sign, and attractive when they have opposite signs.

What is the value of Coulomb's constant k?

k = 8.9875517923×10⁹ N·m²/C² in vacuum. It equals 1/(4πε₀), where ε₀ = 8.854×10⁻¹² F/m is the permittivity of free space. In a material medium, replace k with k/εᵣ where εᵣ is the relative permittivity (dielectric constant) of the medium.

How do I enter a negative charge?

Type a negative number in the charge field. For example, an electron carries approximately −1.602×10⁻¹⁹ C; enter −1.602e-19 in the C unit. The calculator uses |q₁·q₂| for the force magnitude and then reports whether the interaction is attractive or repulsive based on the signs.

Why does doubling the distance reduce the force by a factor of 4?

Because Coulomb's Law is an inverse-square law (the denominator is r²). If you double r, r² quadruples, so the force drops to 1/4 of its original value. This is the same mathematical form as Newton's Law of Gravitation — both forces obey the inverse-square rule.

Can I use this for charges in water or another dielectric?

The calculator assumes vacuum (or air, which is effectively the same). For a medium with relative permittivity εᵣ, divide the vacuum result by εᵣ. Water has εᵣ ≈ 80, so the electrostatic force in water is about 80 times weaker than in vacuum for the same charge and separation.

What units does the calculator support for charge and distance?

For charge: C, mC, μC, nC, pC. For distance: m, cm, mm, nm, Å. For force: N, kN, mN, μN, nN. Select your preferred unit from each dropdown and the calculator handles all conversions automatically — no manual power-of-ten arithmetic needed.

Coulomb's Law Calculator

Coulomb’s Law is the foundation of electrostatics and one of the most precisely tested laws in all of physics. It describes the force that two stationary point charges exert on each other through empty space — an invisible push or pull that governs everything from how atoms bond to how capacitors store energy. This calculator lets you solve for any one of the four quantities in the formula (force F, charge q₁, charge q₂, or separation distance r) given the other three, with full unit flexibility and a one-line worked solution on every calculation.

The formula

The electrostatic force between two point charges is:

F = k · |q₁ · q₂| / r²

where:

F is the magnitude of the electrostatic force, in newtons (N)
k = 8.9876×10⁹ N·m²/C² is Coulomb’s constant (= 1/4πε₀)
q₁ and q₂ are the two charges, in coulombs (C) — positive for protons, negative for electrons
r is the centre-to-centre separation distance, in metres (m)
The absolute-value bars mean you always get a positive magnitude; the signs determine whether the force is attractive (opposite signs) or repulsive (same signs)

Rearranging for each unknown:

Charge: q₁ = F · r² / (k · q₂)
Distance: r = √(k · |q₁ · q₂| / F)

How it works

Enter the three known quantities and select the variable you want to find. The unit dropdowns let you work in microcoulombs (μC), nanocoulombs (nC), ångströms (Å), millinewtons (mN) or any combination — everything is converted to SI (C, m, N) before the calculation and the result is expressed back in whichever unit you chose. The working line underneath the answer shows the full substitution in SI, so you can verify or copy it directly into a lab report.

Worked example

Two small spheres carry charges of +3 μC and −5 μC and are placed 20 cm apart in air. What force do they exert on each other?

Convert to SI: q₁ = 3×10⁻⁶ C, q₂ = −5×10⁻⁶ C, r = 0.20 m
Apply the formula: F = 8.9876×10⁹ × |3×10⁻⁶ × (−5×10⁻⁶)| / (0.20)²
Numerator: 8.9876×10⁹ × 1.5×10⁻¹¹ = 0.13481 N·m²
Denominator: 0.04 m²
F ≈ 3.37 N — attractive (opposite signs)

Set the calculator to “Solve for F”, enter q₁ = 3 μC, q₂ = −5 μC, r = 20 cm and you get the same answer with the attraction flag.

Physical constants used

Constant	Symbol	Value
Coulomb’s constant	k	8.9875517923×10⁹ N·m²/C²
Permittivity of free space	ε₀	8.8542×10⁻¹² F/m
Elementary charge	e	1.6022×10⁻¹⁹ C

All constants follow CODATA 2018 recommended values.