Coulomb's Law Force Calculator

Calculate electrostatic force between two charges using Coulomb's law F=kq₁q₂/r².

1μC = 1e-6 C
Negative = opposite charge
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What Coulomb's Law Says About Electric Force

Coulomb's law measures the electrostatic force between two point charges. The force grows with the size of each charge and falls very quickly as the separation increases. Because distance appears as r2 in the denominator, doubling the distance makes the force one-fourth as large, while halving the distance makes it four times as large. This inverse-square behavior is one of the most important patterns in introductory physics.

The sign of the charges determines the direction of the interaction, not the size of the force. Two positive charges or two negative charges repel; opposite charges attract. When calculating a force magnitude, use the absolute value of q1q2. Then state separately whether the interaction is attractive or repulsive. This prevents a negative sign from being mistaken for a negative force magnitude.

F = k|q1q2| / r2
SymbolMeaningWhy it appears / units
FElectrostatic force magnitudeMeasured in newtons (N).
kCoulomb constant8.99 × 109 N·m2/C2 in vacuum.
q1, q2Electric chargesEnter coulombs; 1 µC = 10−6 C.
rCenter-to-center separationMeasured in meters and squared in the denominator.

Coulomb's law is exact for point charges and is also useful for spherically symmetric charge distributions when the separation is measured between centers. For extended objects with complicated charge distributions, the total force may require integration. In routine problems, the biggest practical errors come from forgetting micro- or nano-prefix conversions and from using centimeters without converting to meters.

Worked Examples

Example 1: Two 1μC charges 10cm apart
F=8.99e9×1e-6×1e-6/0.01
Result: 0.899 N — repulsive
Like charges repel
Example 2: Proton-electron in H atom: r=0.529Å
q=1.6e-19C, r=5.29e-11m
Result: F=8.23×10⁻⁸ N — attractive
Electron attracted to proton
Example 3: Opposite charges half a meter apart
q1=+2µC, q2=−3µC, r=0.50m → F=8.99×109×(2×10−6)(3×10−6)/(0.50)2
Result: 0.216 N, attractive
The magnitude uses absolute charge values; the opposite signs tell you the force points toward the other charge.
Example 4: Doubling the separation
Keep both charges unchanged but change r from 0.50m to 1.00m → F becomes (0.50/1.00)2 of the original force
Result: 0.0539 N, one-fourth as large
This directly demonstrates the inverse-square dependence. Distance changes usually matter more than students expect.

Common Mistakes

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Using microcoulombs as if they were coulombs

A value of 2 µC is 2×10−6 C. Missing that factor changes q1q2 by enormous powers of ten.

⚠️
Forgetting to square the distance

Coulomb's law contains r2, not r. A 3-fold increase in distance reduces the force by 9, not by 3.

⚠️
Treating a negative product as a negative magnitude

Force magnitude is nonnegative. A negative q1q2 indicates attraction; it does not mean the magnitude itself is negative.

Frequently Asked Questions

Gravity vs electrostatic force?
For proton-electron: F_E/F_G = 2.3×10³⁹. Electrostatics is astronomically stronger than gravity at atomic scales, but gravity dominates at cosmic scales due to charge neutrality.
Coulomb vs Newton gravity formula?
Both follow inverse square law: F∝1/r². Gravity: F=Gm₁m₂/r² (always attractive). Coulomb: F=kq₁q₂/r² (attractive or repulsive). Same mathematical form, very different magnitudes and signs.
Why does Coulomb force decrease with the square of distance?
A point charge produces an electric field that spreads through three-dimensional space. The same field influence is distributed over spherical surfaces whose area grows as 4πr2. That geometric spreading leads to the 1/r2 dependence for an isolated point charge in three dimensions.
Can Coulomb's law be used inside a material?
Yes, but the medium changes the effective electric interaction. In a dielectric, the force is reduced relative to vacuum by the material's relative permittivity. Introductory problems usually assume vacuum or air unless a dielectric constant is supplied, so the standard value of k is normally used.
What distance should be used for charged spheres?
For two spherically symmetric charged objects that do not overlap, use the center-to-center distance. Their external electric fields behave as though the total charge were concentrated at each center. Using the gap between the surfaces instead of the center separation gives the wrong result.
How do I know the direction of the electric force?
The force lies along the line joining the two charges. Like charges push away from each other, while opposite charges pull toward each other. In vector problems, choose a coordinate direction first, calculate the magnitude, and then assign the sign from the actual force direction.

Formula Explorer connections

Interpretation: This relationship connects motion, force, momentum, work or energy in a mechanical system. Assumption: Choose a consistent reference direction and unit system. The model may assume constant acceleration, rigid bodies, negligible losses or an isolated system.

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