Coulomb’s Law Calculator computes the electric force between two point charges using their magnitudes and the distance between them. It outputs the force in newtons (and can show the direction as attraction or repulsion based on charge signs).
This article explains the exact formula, what each variable means, and how to use the calculator correctly with units like microcoulombs and meters.
What Coulomb’s Law Calculator Does
Coulomb’s Law describes the electrostatic force between two charges. The calculator takes two charge values (Q1 and Q2) and the separation distance (r) and returns the force magnitude. It also determines whether the force is attractive or repulsive.
In practical terms, this helps you estimate forces in physics homework, electronics troubleshooting, and basic experiments with charged objects.
Coulomb’s Law Formula (Core Concept)
The force between two point charges is given by:
F = k · |Q1 · Q2| / r²
- F is the force magnitude in newtons (N).
- k is Coulomb’s constant: k = 8.9875517923 × 10⁹ N·m²/C².
- Q1 and Q2 are the charges in coulombs (C).
- r is the distance between charges in meters (m).
The calculator uses the absolute value for magnitude, then uses the signs of Q1 and Q2 to label the result as attraction or repulsion.
Sign Rules: Attraction vs. Repulsion
Whether the force pulls charges together or pushes them apart depends on the charge signs.
- If Q1 and Q2 have the same sign (both positive or both negative), the force is repulsive.
- If Q1 and Q2 have opposite signs, the force is attractive.
The calculator reports this as Force type so you can interpret the physical meaning without extra steps.
Unit Conversions the Calculator Handles
Real problems often use microcoulombs (µC), nanocoulombs (nC), or picocoulombs (pC) rather than coulombs. Your inputs can be in common charge units, and the calculator converts them to coulombs internally.
Distance may be provided in meters (m) or millimeters (mm). The calculator converts distance to meters so the formula stays consistent.
| Input Quantity | Units Accepted | Converted To (Inside Calculator) |
|---|---|---|
| Charge (Q1, Q2) | µC, nC, pC, C | C (coulombs) |
| Distance (r) | m, mm | m (meters) |
Using the correct unit selector prevents common errors like mixing millimeters with meters, which can change the answer by a factor of 10⁶.
Step-by-Step: How to Use the Coulomb’s Law Calculator
- Enter Q1 and choose its unit (C, µC, nC, or pC).
- Enter Q2 and choose its unit.
- Enter the separation distance r and select the unit (m or mm).
- Click Calculate to compute force magnitude and determine attraction or repulsion.
If you enter invalid values (like zero distance), the calculator highlights the issue and shows an error message so you can fix it quickly.
Practical Example 1: Two Like Charges (Repulsion)
Suppose you have two small charges: Q1 = +2 µC and Q2 = +3 µC, separated by r = 0.10 m. Plugging these into Coulomb’s Law gives a force that is repulsive because both charges are positive.
As distance increases, the force drops quickly because of the 1/r² relationship.
Practical Example 2: Opposite Charges (Attraction)
Now consider Q1 = -5 nC and Q2 = +8 nC separated by r = 20 mm (which is 0.020 m). Because the signs are opposite, the force is attractive.
The calculator automatically converts 20 mm into meters, so you get the correct newton-scale force without manual conversion.
Common Mistakes to Avoid
- Using the wrong units: Always match the unit selector to what the number represents.
- Using r = 0: Coulomb’s Law assumes point charges at a nonzero separation. Zero distance makes the formula undefined.
- Forgetting charge signs: Magnitude uses absolute values, but sign decides attraction vs. repulsion.
- Assuming the force is always positive: The calculator reports the direction concept (attraction/repulsion) separately from magnitude.
Frequently Asked Questions
What is Coulomb’s Law, in plain language?
Coulomb’s Law states that the electric force between two charges depends on how big the charges are and how far apart they are. The force grows with charge magnitude and shrinks with the square of the distance, following F = k|Q1Q2|/r².
Why does the force change so much when distance changes?
Because Coulomb’s Law uses a 1/r² relationship, doubling the distance reduces the force by a factor of four. Tripling the distance reduces it by nine. This fast drop is why charges far apart exert very small forces.
Does Coulomb’s Law apply to any charges, or only point charges?
Coulomb’s Law is exact for point charges or situations where charges are well-approximated as points. For extended objects, you may need more advanced methods. The calculator assumes point-charge behavior to compute the force.
How do I interpret “attractive” vs. “repulsive” in the results?
Attraction means the charges pull toward each other, which happens when the charges have opposite signs. Repulsion means the charges push away from each other, which happens when the charges have the same sign. The calculator uses charge signs to label this.
What units should I use for Q1, Q2, and r?
Charges must be in coulombs (C), and distance must be in meters (m) for the standard constant k. The calculator lets you enter common charge units and meters or millimeters, then converts automatically so the computed force is in newtons.
Bottom Line
A Coulomb’s Law Calculator gives you the electric force between two charges quickly and correctly when you enter the right values and units. Use the sign information to understand whether the force is attraction or repulsion, and remember the 1/r² distance effect.