Example 1
q1 = 1e-6, q2 = -2e-6, r = 0.1 m.
Coulomb Force Calculator
Type q₁ [C], q₂ [C] and r [m]. The calculator computes F = k q₁ q₂ / r²: 1e-6 C and −2e-6 C at 0.1 m is about 1.8 N, and two +1e-6 C at 0.05 m is about 3.6 N. Zero metres does not divide.
Field from a charge: E = k Q / r². Definition of E: E = F/q.
Result
Charge q₁ (C), Charge q₂ (C) and Distance r (m). The result shows up here.
How it works
Coulomb force between two point charges falls with distance squared: F = k q1 q2 / r². The constant k = 8.99e9 N·m²/C² is built in; you do not type it. 1 µC and −2 µC at 0.1 m give about 1.8 N and attraction, because the signs differ. Two +1 µC at 0.05 m give about 3.6 N and repulsion.
The fields want coulombs and meters. A microcoulomb is 1e-6: type 1e-6, not 1. A nanocoulomb is 1e-9. Distance r is in meters, so 10 cm is 0.1. A comma, a period, and scientific notation all parse. The result is in newtons.
r must be positive. Zero meters does not divide: the charges do not sit at the same point. Half the r is four times F, because r is squared in the denominator. The same charges at 0.2 m and at 0.4 m differ by a factor of four.
The sign of each charge sets the direction. Opposite signs: attraction. Same signs: repulsion. The calculator reports the magnitude F; you read the sense from the signs of q1 and q2.
E = k Q / r² is on the neighbouring page: there the field from one charge, here the force between two. The definition E = F/q is one step further, once you already have F and a test charge.
Charge in coulombs can come from Q = I·t if you know current and time. Here q1 and q2 are already inputs.
How to use
- In the first field enter charge q1 in coulombs, in the second q2. Type a microcoulomb as 1e-6. A minus, for example -2e-6, means a negative charge.
- In the third field enter distance r in meters. 10 cm is 0.1. r must be greater than zero.
- Click Calculate. The calculator inserts k = 8.99e9 and computes F = k q1 q2 / r². 1e-6, −2e-6 and 0.1 m give about 1.8 N.
- Opposite signs attract, same signs repel. Twice as close means four times the force.
- Want the field from one charge? Open E = k Q / r². Here it stays the force between two q.
Formula
F = k · q1 · q2 / r2
k ~ 8.99e9 N·m2/C2 (fixed). r > 0.
F, k, q₁, q₂, and r in Coulomb force
Coulomb force here is F = k q₁ q₂ / r². 1e-6 C and −2e-6 C at 0.1 m is about 1.8 N. k = 8.99e9, no field.
- F
- Force [N]. About 1.80 N at 1 µC and −2 µC at 0.1 m. The sign names attraction.
- k
- Constant 8.99e9 N·m²/C², no field. On the E-from-charge card k can be typed.
- r
- Distance [m]. 0.1 or 0.05. r must be positive.
Real-life examples
Example 2
q1 = q2 = 1e-6 C, r = 0.05 m: repulsion.
Example 3
q1 = 5e-9, q2 = -5e-9, r = 0.01 m.
Example 4
q1 = 2e-6, q2 = -1e-6, r = 1 m.
Example 5
q1 = 1e-5, q2 = 1e-5, r = 2 m: weaker force.
Example 6
q1 = 100e-9, q2 = -50e-9, r = 0.2 m.
Example 7
q1 = 1.6e-19, q2 = -1.6e-19, r = 1e-10 m.
Example 8
q1 = 3e-6, q2 = -4e-6, r = 0.5 m.
Example 9
q1 = q2 = 5e-7 C, r = 0.15 m.
Example 10
Same q, r = 0.2 m vs 0.4 m: F 4 times smaller.
Ways to use this calculator
- You compute about 1.8 N from 1 µC and −2 µC at 0.1 m.
- You check repulsion of two +1 µC at 0.05 m: about 3.6 N.
Frequently asked questions
How much F at 1e-6 C, −2e-6 C and r = 0.1 m?
Force is about 1.80 N, attraction, because the signs differ. That is k × 1e-6 × 2e-6 / 0.01.
How much with two +1e-6 C and r = 0.05 m?
Force is about 3.60 N, repulsion. Same signs and half the 0.1 m distance, so F grows four times versus a 1 µC pair at 0.1 m.
Which units do I type?
Charges q₁ and q₂ [C], distance r [m]. Result F [N]. Type 1 µC as 1e-6, not as 1.
Where do I type k?
Nowhere. k is fixed at 8.99e9 in this calculator. On the field-from-a-charge page k can be optional.
How is this different from E = k Q / r²?
Here F between two charges. There E from one Q. E = F/q for a test charge is another calculator.
Does a comma in 0.1 work?
Yes. 0.1 and 0,1 are the same r [m]. 0.1 or 1e-1 is easier.
Why is half the r four times F?
Because r is squared in the denominator. Half the distance gives four times the force at the same q.
Where is E = F/q?
On the field-strength page. Here F from two charges, not E from one Q.
Why will r = 0 not run?
You divide by r². Two point charges cannot sit at one point, and the calculator refuses it.
How do I type 1 µC?
As 1e-6. The field wants coulombs. Typed 1 is one coulomb, a million times too large for a micro.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.