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Coulomb's Law Calculator
Calculate the electrostatic force between two point charges and whether it attracts or repels, or solve for either charge or the distance. Choose the medium to include its relative permittivity.
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Solve for
Use a minus sign for negative charge
Use a minus sign for negative charge
Enter your values to see the result.
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How to use the Coulomb's Law Calculator
- Choose what to solve for: force, q₁, q₂ or distance.
- Enter the known values with units; use a minus sign for negative charges.
- When solving a charge, say whether the force is attractive or repulsive.
- Pick the medium between the charges (vacuum by default).
- Read the force, field and energy, and compare distances in the table.
Coulomb's law formulas
- Force: F = k × q₁ × q₂ / (εr × r²)
- Distance: r = √(k × |q₁q₂| / (εr × F))
- Charge: |q₂| = F × εr × r² / (k × |q₁|)
- Electric field of a point charge: E = k × |q| / (εr × r²)
- Potential energy of the pair: U = k × q₁q₂ / (εr × r)
Here k = 8.9875517923 × 10⁹ N·m²/C² and the elementary charge e = 1.602176634 × 10⁻¹⁹ C. Like gravity, the force follows an inverse square law: halve the distance and the force becomes four times stronger.
Example: in a hydrogen atom the proton and electron are about 0.529 Å (5.29 × 10⁻¹¹ m) apart. F = 8.99 × 10⁹ × (1.602 × 10⁻¹⁹)² / (5.29 × 10⁻¹¹)² ≈ 8.2 × 10⁻⁸ N, attractive, and the potential energy is about −27.2 eV.
Relative permittivity of common materials
| Medium | εr (approx.) | Force vs vacuum |
|---|---|---|
| Vacuum | 1 | 100% |
| Air (dry, sea level) | 1.0006 | 99.94% |
| PTFE (Teflon) | 2.1 | 48% |
| Polyethylene | 2.25 | 44% |
| Glass (varies by type) | 4–10 | 10–25% |
| Ethanol, 25 °C | 24.5 | 4.1% |
| Water, 20 °C | 80.1 | 1.25% |
Electric vs gravitational force
Electric forces are enormously stronger than gravity. Between a proton and an electron the electric attraction is about 2 × 10³⁹ times their gravitational attraction. We rarely notice it in daily life because ordinary matter has almost exactly equal positive and negative charge, so the forces cancel.
Frequently asked questions
What is Coulomb's law?
The electrostatic force between two point charges is F = k × q₁ × q₂ / r², with k = 8.9875 × 10⁹ N·m²/C². The force is along the line joining the charges, repulsive for like charges and attractive for opposite charges.
How do I know if the force is attractive or repulsive?
Look at the signs. If q₁ and q₂ have the same sign the product is positive and the charges repel; if the signs differ the product is negative and they attract.
What is the Coulomb constant?
k = 1 / (4πε₀) ≈ 8.9875517923 × 10⁹ N·m²/C², where ε₀ ≈ 8.8541878 × 10⁻¹² F/m is the permittivity of free space.
How does the medium change the force?
In a material the force is divided by its relative permittivity εr. Water (εr ≈ 80) reduces the force between ions about 80-fold, which is why salt dissolves so readily.
What is the force between a +3 µC and −5 µC charge 10 cm apart?
F = 8.99 × 10⁹ × (3 × 10⁻⁶)(5 × 10⁻⁶) / 0.1² ≈ 13.5 N, and it is attractive.
How do you find the distance between two charges from the force?
Rearrange to r = √(k × |q₁q₂| / F). Two 1 µC charges feel 1 N of force at about 9.5 cm apart in vacuum.
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