Coulombs Law Calculator

1. Enter any three of force, charge 1, charge 2 and distance.
2. Use a negative value for a negative charge.
3. Leave the one you want to find blank.
4. Read the result: a positive force is repulsive, a negative one attractive.

Here is what each result means:

Coulomb's law describes the electric force between two point charges. The force grows with the size of each charge and falls with the square of the distance between them, exactly like gravity but for electric charge instead of mass. It is the rule that holds atoms together, drives every circuit and explains why a balloon sticks to a wall after rubbing.

The force equals the Coulomb constant k times the two charges divided by the distance squared. The constant k is about 8.988 x 10^9 newton meters squared per coulomb squared, which is huge, so even tiny charges can produce large forces. Charges are measured in coulombs, and because a coulomb is a very large amount of charge, everyday charges are usually in microcoulombs or smaller.

Unlike gravity, the electric force can push as well as pull. Two charges of the same sign repel, giving a positive force, while two of opposite sign attract, giving a negative one. This calculator follows that convention: enter charges with their signs, and the sign of the force tells you whether the charges repel or attract.

It rearranges Coulomb's law to solve for whichever value you leave blank.

1. For force, multiply k by both charges and divide by the distance squared.
2. For a charge, multiply force by the distance squared and divide by k times the other charge.
3. For distance, take the square root of k times both charges divided by the force.

Coulomb's law mirrors gravitation; see the gravitational force calculator and force calculator.

Two charges of 1 and 2 microcoulombs sit 0.1 meters apart.

Calculation: F = k x 1e-6 x 2e-6 / 0.01, which is about 1.8 newtons, and positive so the charges repel. Doubling the distance to 0.2 meters would quarter the force.

One law, rearranged for whatever you need to find.

All four come from F equals k q1 q2 over r squared, so any three of the values give the fourth. Solving for distance takes a square root, and needs the force sign to match the charges, since like charges must repel and opposite charges must attract.

The two great inverse-square force laws look almost identical but differ in key ways.

Because the Coulomb constant is enormous while the gravitational constant is tiny, the electric force between two charged particles is vastly stronger than the gravitational pull between them. Yet gravity dominates on the scale of planets, because large objects are electrically neutral overall.

The Charges

A larger charge gives a stronger force, in direct proportion to the product of the two charges.

The Distance

A greater separation weakens the force by the square of the distance. Twice as far is one quarter the force.

The Signs

Like charges repel and opposite charges attract, which sets whether the force is positive or negative.

Physics Homework

Solve for the force, a charge or the distance in an electrostatics problem.

Electronics and Science

Estimate the force between charged plates, particles or ions.

Understanding Atoms

See how strongly charges attract or repel over tiny distances.

1. Forgetting the Signs

Enter each charge with its sign. The sign of the force tells you attract or repel.

2. Forgetting to Square the Distance

The distance appears squared. Leaving it unsquared overstates the force.

3. Wrong Charge Units

Charges must be in coulombs. A microcoulomb is 10^-6 coulombs, so convert first.

4. Confusing K with Other Constants

The Coulomb constant is about 8.99 x 10^9, not the gravitational constant or the permittivity.

5. Expecting Only Attraction

Unlike gravity, the electric force can repel. A positive result is a real, repulsive force.

The relation is exact; only the displayed decimals are rounded, and very large or small results are shown in scientific notation.

Coulomb's law gives the electric force between two point charges: force equals k times the two charges divided by the distance squared. Two charges of 1 and 2 microcoulombs 0.1 meters apart repel with about 1.8 newtons.

Multiply the Coulomb constant k by both charges, then divide by the square of the distance. The constant k is about 8.988 x 10^9 in SI units.

The Coulomb constant k is about 8.988 x 10^9 newton meters squared per coulomb squared in a vacuum. It sets the strength of the electric force.

Look at the sign. Like charges give a positive, repulsive force; opposite charges give a negative, attractive force. Enter each charge with its correct sign.

The force falls with the square of the distance. Doubling the separation cuts the force to a quarter, and tripling it cuts the force to a ninth.

Coulombs. A microcoulomb is 10^-6 coulombs and a nanocoulomb is 10^-9, so convert small charges to coulombs before entering them.

Both are inverse-square laws: the force falls with the square of the distance. Coulomb's law uses charge and can attract or repel, while gravity uses mass and only attracts.

Yes. The Coulomb constant used here is for a vacuum. A surrounding medium such as water reduces the force by its dielectric constant, which this calculator does not apply.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Coulomb's law (Wikipedia).
• Coulomb constant (Wikipedia).
• Electric charge (Wikipedia).