⚡ Coulomb's Law Calculator

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Use a minus sign for a negative charge.

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📘 About the Coulomb's Law

Coulomb's law gives the force between two point charges: it is proportional to the product of the charges and inversely proportional to the square of the distance between them. This calculator takes the charges in microcoulombs (µC) and the distance in metres.

A positive result means the charges have the same sign and repel; a negative result means they have opposite signs and attract. The calculation assumes the charges are in air or a vacuum.

🧮 Formula

Coulomb's law
F = k q₁ q₂ ÷ r²

Where

  • F = electrostatic force (N)
  • k = 8.988 × 10⁹ N·m²/C² (= 1/4πε₀)
  • q₁, q₂ = charges (C); 1 µC = 10⁻⁶ C
  • r = distance between the charges (m)
In a medium with dielectric constant K, the force is smaller: divide the answer by K (about 80 for water).

✏️ Worked examples

+2 µC and −3 µC, 10 cm apart

You enter
Charge 1 (q₁)2 µC
Charge 2 (q₂)-3 µC
Distance between charges (r)0.1 m
You get
Size of force (N)5.39253
Force with sign (N): + repel, − attract-5.39253

They attract with a force of 5.39253 N.

Try this example →

Two +1 µC charges, 1 m apart

You enter
Charge 1 (q₁)1 µC
Charge 2 (q₂)1 µC
Distance between charges (r)1 m
You get
Size of force (N)0.00898755
Force with sign (N): + repel, − attract0.00898755

They repel with 0.00898755 N.

Try this example →

🧭 How to use this calculator

What you enter

  • Charge 1 (q₁) (µC)Use a minus sign for a negative charge.
  • Charge 2 (q₂) (µC)
  • Distance between charges (r) (m)

What you get

  • Size of force (N)
  • Force with sign (N): + repel, − attract

💡 Coulomb's law vs Newton's law of gravitation

  • Both are inverse-square laws.
  • Gravity always attracts; electric forces can attract or repel.
  • The electric force between two protons is about 10³⁶ times stronger than the gravitational force between them.

❓ Frequently asked questions

What is Coulomb's law?

The force between two point charges is F = kq₁q₂/r²: proportional to the product of the charges and inversely proportional to the square of their separation.

What is the value of k in Coulomb's law?

k = 1/(4πε₀) ≈ 8.988 × 10⁹ N·m²/C², often rounded to 9 × 10⁹.

What is the SI unit of charge?

The coulomb (C). The charge of an electron is −1.602 × 10⁻¹⁹ C.

What happens to the force if the distance is halved?

It becomes four times larger.