Coulombs Law Calculator
Find electrostatic force from two charges and gap distance.
What it does
Charged objects pull or push with inverse square force. Doubling distance quarters force, doubling either charge doubles it. The constant k = 8.9875517923e9 N m2/C2 sets the scale in vacuum.
The tool above takes two microcoulomb charges and gap and returns force size, small unit force, and small gap. The defaults 10 and 10 uC at 0.1 m match the worked example, so the page opens showing 89.88 N. Switch to imperial for feet and pounds force.
Sign sets direction only. Like signs repel, opposites attract, size stays k q1 q2 / r2. Microcoulombs convert at 1e-6 coulombs each. A tenth of a meter with tens of microcoulombs gives tens of newtons, while nanocoulombs at meters give micronewtons.
Point charges in vacuum are assumed. Real insulators, conductors nearby, and dielectric fluids scale results with permittivity. Keep gaps large versus charge size for the point form to hold.
This page shows the formula, one full hand checked example at 10 uC pair over 0.1 m, a reference table, and practice checks that run through the tool in both unit systems.
How to use
- Pick Metric (m, N) or Imperial (ft, lbf).
- Type both charges in microcoulombs above 0.
- Type gap in the active unit.
- Read Force size as magnitude.
- Read small unit force for bench numbers.
- Use sign of charges for repel versus attract.
Formula
- q
- Charge size in coulombs after micro convert.
- r
- Center gap in meters.
- F
- Magnitude in N or lbf.
Feet convert at 0.3048 m, pounds force at 4.448221615 N. Vacuum assumed. Media divide by relative permittivity.
Worked example
Example: 10 uC pair at 0.1 m
Two 10 microcoulomb charges 0.1 m apart in vacuum. Find force.
- Convert: 10 uC = 10e-6 C each.
- Numerator: 8.9875517923e9 x 10e-6 x 10e-6 = 0.898755.
- Denominator: 0.1 squared = 0.01.
- Divide: 0.898755 / 0.01 = 89.88 N.
- Small: 89875.5 mN, gap 100 mm.
- Imperial mirror 0.328 ft gives 20.22 lbf.
Reference table
| Charges / gap | Force | Note |
|---|---|---|
| 10/10 uC at 0.1 m | 89.88 N | Example |
| 5/5 uC at 0.5 m | 0.9 N | Farther, weaker |
| 1/1 uC at 1 m | 0.01 N | Small lab |
| 10/10 uC at 0.328 ft | 20.22 lbf | Same gap |
Limits
- Point charges in vacuum only.
- Magnitude only. Signs set direction.
- Static only. Moving charges add magnetic terms.
- Large plates and nearby conductors need other forms.
Common mistakes
- Forgetting micro 1e-6, off by a trillion for pairs.
- Squaring after converting instead of before.
- Mixing feet with meters in r squared.
- Reading mN as N, off by 1000 times.
- Applying vacuum k inside dielectrics without dividing.
Try it yourself
Quick checks. Answers sit tucked under each question.
5/5 uC at 0.5 m?
Force 0.9 N, 898.8 mN, gap 500 mm.
1/1 uC at 1 m?
Force 0.01 N, 9 mN, gap 1000 mm.
Questions
What is Coulombs law?
k q1 q2 over r squared for point charges.
Repel or attract?
Like repel, opposite attract, same size.
10 uC pair at 0.1 m?
89.88 N.
Micro?
Times 1e-6 coulombs.
Vacuum?
Yes here. Media scale by permittivity.
Units?
N metric, lbf imperial.