Coulomb's Law Force Calculator

Calculator Inputs

Charge 1 value

Charge 1 unit

Charge 2 value

Charge 2 unit

Separation distance

Distance unit

Relative permittivity

Line angle in degrees

Output force unit

Decimal precision

Formula Used

The calculator uses Coulomb's law for two point charges.

F = k |q₁q₂| / r²

k = k₀ / εᵣ

Here, F is force, q₁ and q₂ are charges, r is separation distance, k₀ is 8.9875517923 × 10⁹ N·m²/C², and εᵣ is relative permittivity.

For components, the calculator uses Fx = ±F cos(θ) and Fy = ±F sin(θ). The sign depends on attraction or repulsion.

How to Use This Calculator

Enter the first charge with its correct sign.
Select the matching charge unit.
Enter the second charge with its correct sign.
Enter the center-to-center separation distance.
Choose the distance unit.
Enter relative permittivity. Use 1 for vacuum or air.
Enter the angle if vector components are needed.
Choose the force output unit.
Press the calculate button.
Download the result as CSV or PDF if needed.

Example Data Table

Charge 1	Charge 2	Distance	Relative Permittivity	Force	Interaction
+2 µC	-3 µC	5 cm	1	21.57 N	Attractive
+5 nC	+8 nC	2 cm	1	0.000899 N	Repulsive
-10 µC	-4 µC	12 cm	2.1	11.89 N	Repulsive

Understanding Coulomb Force

Coulomb force is the push or pull between two electric charges. It is one of the core ideas in electrostatics. The force grows when charge values increase. It weakens quickly when distance increases. Because distance is squared, small spacing changes can create large force changes.

Why Distance Matters

The calculator uses separation between charge centers. This distance should not be the gap between surfaces unless the charges are located there. For point charges, the model assumes each charge is concentrated at one point. This is a strong approximation for small charged objects that sit far apart compared with their own sizes.

Medium And Permittivity

Air and vacuum give almost the same result. Water, glass, oil, and other materials reduce the force by their relative permittivity. A higher relative permittivity means the material screens the electric interaction more strongly. This tool lets you enter any positive relative permittivity, so classroom examples and material studies are both supported.

Signs And Direction

Charge signs decide whether the interaction is attractive or repulsive. Like signs repel. Opposite signs attract. The calculator also accepts an angle for the line joining the charges. It then resolves the force into x and y components. This helps when a force diagram, coordinate problem, or vector balance is required.

Practical Use

Use consistent inputs and check units before trusting the answer. Microcoulombs and nanocoulombs are common in school problems. Meters are the standard distance unit. The result can be viewed in newtons or converted into smaller or larger force units. Very small charge values may produce tiny forces, so scientific notation is often helpful.

Limits Of The Model

Coulomb's law works best for stationary point charges. It does not cover moving charges, magnetic effects, charge distribution, leakage, or strong field breakdown. Real objects may have shape, humidity, and surface effects. Treat the answer as an ideal calculation unless the physical setup matches the assumptions closely.

Better Reports

The result section shows converted charge values, adjusted constant, scalar force, force direction, components, electric field, potential, and energy. These values make lab notes easier to audit. Export the CSV for spreadsheets. Use the PDF button for a clean calculation summary. It also supports repeatable physics examples for study.

FAQs

What does Coulomb's law calculate?

It calculates the ideal electrostatic force between two point charges. The force depends on both charge values, separation distance, and the medium between them.

Should charges include positive or negative signs?

Yes. Signs are important. Like signs create repulsion. Opposite signs create attraction. The magnitude uses absolute charge product, but direction uses the signs.

What distance should I enter?

Enter the center-to-center distance between the two charges. For point charge problems, this is the separation between the charge locations.

What relative permittivity should I use for air?

Use 1 for most air or vacuum classroom calculations. Air is very close to vacuum for many basic electrostatic examples.

Why does force change so quickly with distance?

Coulomb's law uses distance squared in the denominator. Doubling distance makes force one-fourth as large, assuming both charges stay unchanged.

Can this calculator handle vector components?

Yes. Enter the line angle in degrees. The calculator resolves the force into x and y components using the attraction or repulsion direction.

What happens if one charge is zero?

The electric force becomes zero. A zero charge has no charge product with the other charge, so no Coulomb force is produced.

Is this accurate for real objects?

It is accurate for ideal point charges. Real objects may have shape, charge spread, humidity, leakage, and surface effects that change measured results.