Electric Force Calculator: Formula & How to Use
The calculator for this page is switched off while it is checked. The formula is below, and the worked example in the article shows how to use it by hand.
An electric force calculator computes the magnitude of the electrostatic force between two point charges using Coulomb’s law. You enter the charge of each object (in coulombs) and the distance between them (in meters), and the calculator returns the force in newtons. It also shows the direction (attractive or repulsive) based on the signs of the charges.
Formula
Coulomb’s law is the foundation of electrostatics. The formula is:
F = k * |q1 * q2| / r²
Where:
- F = magnitude of the electric force (newtons, N)
- k = Coulomb’s constant ≈ 8.9875517923 × 10â�¹ N·m²/C²
- q1, q2 = magnitudes of the two point charges (coulombs, C)
- r = distance between the centers of the charges (meters, m)
The force acts along the line joining the charges. If the charges have the same sign (both positive or both negative), the force is repulsive; if they have opposite signs, it is attractive. The absolute value in the numerator gives the magnitude; the sign of the product q1*q2 tells you the direction.
Worked Example
Using the default values from the calculator above:
- q1 = 2 µC = 2 × 10�� C
- q2 = -3 µC = -3 × 10�� C
- r = 5 cm = 0.05 m
Step 1: Convert charges to coulombs and distance to meters.
Step 2: Plug into Coulomb’s law:
F = (8.9875517923 × 10�) * |(2 × 10��) * (-3 × 10��)| / (0.05)²
Step 3: Multiply the charges: (2 × 10��) * (-3 × 10��) = -6 × 10�¹² C². Take absolute value: 6 × 10�¹² C².
Step 4: Square the distance: (0.05)² = 0.0025 m².
Step 5: Divide: (8.9875517923 × 10� * 6 × 10�¹²) / 0.0025 = (5.39253107538 × 10�²) / 0.0025 = 21.5701243015 N.
Rounded to three decimals, F = 21.570 N. Since q1 and q2 have opposite signs, the force is attractive.
When to Use This Calculator
Use this calculator when you need the electrostatic force between two point charges in a vacuum or air (the formula assumes a vacuum; for other media, you’d divide by the dielectric constant). Typical scenarios include:
- Physics homework or exam problems involving Coulomb’s law.
- Estimating forces in simple electrostatic experiments.
- Checking the magnitude of forces between ions in a crystal lattice (as an approximation).
- Understanding the scale of atomic forces (e.g., between a proton and an electron in a hydrogen atom).
The result is the force on each charge (Newton’s third law says they are equal and opposite). If you need the net force on a charge due to multiple other charges, you must calculate each pair separately and add them as vectors.
How to Read the Result
The calculator gives the force in newtons. A positive force magnitude with a direction label (attractive/repulsive) tells you how the charges interact. For example:
- 21.570 N attractive means each charge pulls the other toward it with that force.
- If the force is repulsive, they push each other apart.
In practice, 1 N is roughly the weight of a small apple (about 100 g). So 21.57 N is a substantial force for charges of a few microcoulombs at 5 cm—this shows how strong electrostatic forces can be. For comparison, the force between an electron and a proton in a hydrogen atom (distance ≈ 5.3 × 10�¹¹ m) is about 8.2 × 10�� N, a tiny but significant force at the atomic scale.
Common Mistakes and Limitations
Unit errors are the most frequent problem. Always convert:
- Microcoulombs (µC) to coulombs: multiply by 10��.
- Nanocoulombs (nC) to coulombs: multiply by 10��.
- Centimeters to meters: divide by 100.
- Millimeters to meters: divide by 1000.
Another mistake is forgetting that the distance is between the centers of the charges, not between their surfaces. For point charges, this is exact; for charged spheres, it’s only an approximation if the spheres are small compared to the separation.
The formula assumes charges are stationary (electrostatics). If charges are moving, magnetic forces also appear, and Coulomb’s law alone is insufficient. Also, the formula is for point charges in a vacuum; in a material like water, the force is reduced by the dielectric constant (about 80 for water).
Choosing the Right Charge Unit
In the calculator, you can enter charges in coulombs (C), microcoulombs (µC), or nanocoulombs (nC) by adjusting the unit field. The default uses microcoulombs because they are common in electrostatics problems. If you have a charge in elementary charges (e.g., 1.6 × 10�¹� C per electron), you can convert manually: multiply the number of elementary charges by 1.602 × 10�¹� C.
For distance, the calculator accepts meters, centimeters, or millimeters. Choose the unit that matches your problem. The calculator automatically converts to meters before applying the formula.
Frequently Asked Questions
What is Coulomb’s constant exactly?
Coulomb’s constant k is 8.9875517923 × 10â�¹ N·m²/C². It is derived from the speed of light and the magnetic constant, but for practical purposes, you can use 9 × 10â�¹ N·m²/C² as an approximation (about 0.1% error).
Why does the force become huge when distance is small?
Because the force is inversely proportional to the square of the distance. If you halve the distance, the force quadruples. This is why electrostatic forces dominate at atomic scales—they are much stronger than gravity.
What if I have more than two charges?
Coulomb’s law applies to each pair of charges. To find the net force on one charge, calculate the force from each other charge separately, then add them as vectors (considering direction). This is called the superposition principle.
Does the medium matter?
Yes. In a material with dielectric constant εr, the force is divided by εr. For example, in water (εr ≈ 80), the force is 80 times weaker than in a vacuum. Our calculator assumes a vacuum or air (εr ≈ 1).
Can I use this for charges in motion?
No. Coulomb’s law is for stationary charges. For moving charges, you need to account for magnetic forces (Lorentz force). However, for slow speeds, the electrostatic approximation is often adequate.
Why is the force sometimes negative?
The calculator always shows a positive magnitude. The direction is given separately as attractive or repulsive. In physics, you might see a negative sign convention for attractive forces, but it’s just a convention—the magnitude is the same.
Related
Formula used
in q1 | Charge 1 | µC | 2 | 0 in q2 | Charge 2 | µC | -3 | 0 in r | Distance | cm | 5 | 0 out F | Electric force | N | (8.9875517923e9 * (q1 * 1e-6) * (q2 * 1e-6)) / ((r * 0.01)^2) | 3 out direction | Direction | - | (q1 * q2) < 0 ? "attractive" : "repulsive" | 0
Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work
Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.