Coulomb's Law Calculator

What is Electrostatic Physics?

Coulomb's Law is the fundamental principle of electrostatics. It quantifies the amount of force between two stationary, electrically charged particles. This invisible force is what holds electrons in orbit around atomic nuclei, governs chemical bonds, and is the underlying cause behind everyday static electricity shocks.

Mathematical Foundation

Coulomb's Law of Electrostatic Force

F = k \times \frac{q_1 \times q_2}{r^2}

F

= Electrostatic Force (Newtons)

k

= Coulomb's Constant (8.9875 × 10⁹ N·m²/C²)

q_1, q_2

= Magnitudes of the interacting charges (Coulombs)

r

= Distance between the centers of the charges (meters)

Laws & Principles

Opposites Attract, Likes Repel: If the calculated Force (F) is negative (one positive charge, one negative charge), the force is attractive. If F is positive (both positive, or both negative), the force is repulsive.
The Inverse Square Law: The force scales inversely with the square of the distance. If you double the distance between two charges, the force doesn't drop by half—it plunges to one quarter (1/4) of its original strength.
Coulomb's Constant (k): In a vacuum, this constant is approximately 8.98755 × 10⁹ N·m²/C². Our calculator automatically applies this constant under standard vacuum/air assumptions.

Step-by-Step Example Walkthrough

" During a static electricity experiment, a student rubs a balloon on their hair, giving the balloon a negative charge of -4 µC. The student's hair gains a positive charge of +4 µC. The balloon is held 0.1 meters away from the hair. "

1. Identify Variables: q₁ = -4 × 10⁻⁶ C, q₂ = 4 × 10⁻⁶ C, r = 0.1 m.
2. Note the Constant: k = 8.9875 × 10⁹.
3. Multiply Charges: (-4 × 10⁻⁶) × (4 × 10⁻⁶) = -1.6 × 10⁻¹¹ C².
4. Square the Distance: (0.1 m)² = 0.01 m².
5. Apply Formula: F = (8.9875 × 10⁹) × (-1.6 × 10⁻¹¹) / 0.01.
6. Calculate Result: F = -14.38 Newtons.

Final Result: The force is -14.38 Newtons. The negative sign indicates it is an attractive force. The hair will be pulled vertically upward toward the balloon with approximately 3.2 pounds of physical force.

Quick Answer: How do you calculate Electrostatic Force?

To calculate electrostatic force, multiply Coulomb's Constant by the magnitude of the two charges, and then divide that by the square of the distance between them. The Coulomb's Law Calculator automatically converts micro/nano units and handles the intense scientific notation to instantly output the pulling or pushing force in standard Newtons.

Electrostatic Force Scenarios

Atomic Bonds (Hydrogen)

Specs: A single proton (nucleus) and a single electron orbit each other at roughly 0.0529 nanometers (the Bohr radius).
The Charge: The elementary charge of a proton is +1.602×10&supmin;¹&sup9; C. The electron is exactly -1.602×10&supmin;¹&sup9; C.
The Calculation: Plugging these intensely tiny numbers into Coulomb's law yields -8.23 × 10&supmin;&sup8; N.
Physicist Conclusion: This tiny attractive force is overwhelmingly powerful at the quantum scale, effortlessly trapping the electron in orbit and forming the foundational structure of the entire universe.

Thunderstorm Lightning

Specs: The base of a cumulonimbus cloud holds a massive -25 Coulomb static charge. The ground directly beneath it (2,000 meters away) holds an induced +25 Coulomb charge.
The Math: Because a full Coulomb is a massive amount of charge, the equation numerator explodes, yielding approximately -1.40 × 10&sup6; Newtons.
The Result: Millions of pounds of pure pulling force physically rip apart the air molecules separating the cloud and the ground.
Geologist Conclusion: The air's insulating resistance breaks down entirely, allowing the electrons to violently slam into the earth as a lightning strike, neutralizing the attractive force.

Scale of Electrostatic Particles

Object / Particle	Typical Charge Magnitude	Classification
Single Electron	-1.602 × 10⁻¹⁹ C	Quantum Elementary
Single Proton	+1.602 × 10⁻¹⁹ C	Quantum Elementary
Rubbed Balloon	10 to 100 nC	Macroscopic (Nano)
Van de Graaff Generator	1 to 10 µC	High Voltage (Micro)
Thundercloud Base	10 to 50 C	Geological (Full C)

Physics Law Applications

Do This

✓Respect the inverse square law geometry. Because distance is squared, moving two magnets just trivially closer together causes the pulling force to violently spike. Always secure high-charge objects physically before moving them closer.
✓Convert to scientific notation early. It is impossible to calculate an electron's orbit using decimal notations like 0.00000000000000000016. Convert all inputs to base-10 powers before multiplying them to prevent spreadsheet underrun errors.

Avoid This

✗Don't enter forces in centimeters. Coulomb's constant (k) is intrinsically locked to standard SI units. If you measure the distance between two charges as 5 centimeters, you must type it into the calculator as 0.05 meters. Failure to do so will result in an answer exactly 10,000 times weaker than reality.
✗Don't assume gravity matters. At the micro-scale of dust particles, electrons, and static electricity, the electrostatic force is trillions of times more powerful than gravity. In pure physics equations involving electrons, gravity is mathematically deleted because its impact is less than a rounding error.

Frequently Asked Questions

Why is 1 Coulomb such a massively huge charge?

It is an accident of history. A Coulomb is defined as exactly 1 Ampere of current flowing for 1 second. Because industrial wires carry intense amounts of electrons, 1 Ampere handles about 6.24 quadrillion electrons in a single second. Therefore, 1 standard Coulomb equates to a massive pile of 6.24 × 10¹⁸ electrons. If you placed a 1 C sphere and a -1 C sphere 1 meter apart, they would pull toward each other with nine billion Newtons of force—enough to effortlessly crush a battleship.

Who was Charles-Augustin de Coulomb?

He was an 18th-century French physicist and military engineer. In 1785, he published his famous memoirs defining this law. To prove the inverse square law of charges, he invented an incredibly sensitive "torsion balance" made of silk threads and lightweight pith balls to measure forces so impossibly weak no other machine on earth could register them.

Why does Coulomb's law look exactly like Newton's law of Gravity?

Both laws are "Inverse Square Laws" geometry. Imagine a lightbulb; as light spreads out in a 3D sphere, the surface area of that light bubble grows by the square of the distance (r²). Gravity and electromagnetism both radiate outward in perfect 3D spheres through space, so they naturally mathematically dilute at the exact same r² geometric rate.

Does this work if the objects are moving?

Technically, no. Coulomb's law only governs "electrostatics"—particles that are perfectly sitting still. If a charge starts moving, it generates a magnetic field. To calculate the forces of moving charges, you have to upgrade from Coulomb's Law to the much more complex Lorentz Force Law which factors in velocity and magnetism.