Mathematics · Mathematical Physics
Coulomb Electric Force Calculator
Calculate the signed electrostatic force magnitude between two point charges.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Convert charges: 2 μC=0.000002 C; -3 μC=-0.000003 C.
- Charge product=-6e-12; distance squared=0.25.
- Force=8987551792.3×-6e-12÷0.25=-0.21570124301519997 N (attractive).
Understand Coulomb force
One idea, three depths
Choose how deeply to explain Coulomb force
Coulomb force: Calculate the signed electrostatic force magnitude between two point charges.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Coulomb force to answer this question: calculate the signed electrostatic force magnitude between two point charges? Enter First charge q₁, Second charge q₂, Separation r; the calculator shows Signed electric force. For example: Charges +2 μC and −3 μC separated by 0.5 m exert about −0.216 N, indicating attraction. The answer tells you Signed electric force.
Age 15Explain it to a 15-year-oldConnect it to the formula
Electric force follows an inverse-square law; the charge-product sign distinguishes repulsion from attraction. The rule is F=kq₁q₂/r². Its input values are First charge q₁ (μC), Second charge q₂ (μC), Separation r (m), and the main result is Signed electric force. For example: Charges +2 μC and −3 μC separated by 0.5 m exert about −0.216 N, indicating attraction.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated coulomb force relation over the valid real-number domain stated below. The implemented relation is F=kq₁q₂/r², evaluated from First charge q₁ (μC), Second charge q₂ (μC), Separation r (m) to produce Signed electric force. Electric force follows an inverse-square law; the charge-product sign distinguishes repulsion from attraction. This calculator expects charge in microcoulombs and converts it to coulombs internally.
Inputs and valid domain
- First charge q₁ must be a finite real number in μC.
- Second charge q₂ must be a finite real number in μC.
- Separation r must be a finite real number, at least 0 in m.
Important boundary: This calculator expects charge in microcoulombs and converts it to coulombs internally.
The formula
F=kq₁q₂/r²
How the calculator works through it
It substitutes First charge q₁, Second charge q₂, Separation r into the formula and exposes every numerical step above. The main output is Signed electric force, accompanied by Force magnitude, Charge product.
Read the result correctly
The Signed electric force is the direct answer to “calculate the signed electrostatic force magnitude between two point charges.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
Charges +2 μC and −3 μC separated by 0.5 m exert about −0.216 N, indicating attraction.
Where this model stops being reliable
This calculator expects charge in microcoulombs and converts it to coulombs internally.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Coulomb force works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Coulomb force uses F=kq₁q₂/r². You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Ratios, units and dimensional meaning
Tracking ratios and units keeps the Coulomb force result physically interpretable instead of merely numerical.
Review this foundation about 5 min
Optional enrichment
- Vectors and physical direction
Vector language extends Coulomb force when magnitude and direction must be treated separately.
Review this foundation about 6 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read First charge q₁, Second charge q₂, Separation r.
- Evaluate the principal relationship: F=kq₁q₂/r².
- Return Signed electric force and check the domain conditions described above.
Python
from math import *
def coulomb_force(a, b, r) -> float:
return ((8987551792.3 * ((a * 0.000001) * (b * 0.000001))) / (r * r))
assert abs(coulomb_force(2, -3, 0.5) - -0.21570124301519997) < 1e-6 * max(1.0, abs(-0.21570124301519997))
C
#include <assert.h>
#include <math.h>
double coulomb_force(double a, double b, double r) {
return ((8987551792.3 * ((a * 0.000001) * (b * 0.000001))) / (r * r));
}
int main(void) {
const double expected = -0.21570124301519997;
const double actual = coulomb_force(2, -3, 0.5);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double coulomb_force(double a, double b, double r) {
return ((8987551792.3 * ((a * 0.000001) * (b * 0.000001))) / (r * r));
}
int main() {
constexpr double expected = -0.21570124301519997;
const double actual = coulomb_force(2, -3, 0.5);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double coulomb_force(double a, double b, double r)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global coulomb_force
section .text
coulomb_force:
push rbp
mov rbp, rsp
sub rsp, 96
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd [rbp-24], xmm2
mov rax, 0x4200bd9941826666
movq xmm0, rax
movsd [rbp-48], xmm0
mov rax, 0x3eb0c6f7a0b5ed8d
movq xmm0, rax
movsd [rbp-72], xmm0
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-72]
movsd [rbp-64], xmm0
mov rax, 0x3eb0c6f7a0b5ed8d
movq xmm0, rax
movsd [rbp-88], xmm0
movsd xmm0, [rbp-16]
mulsd xmm0, [rbp-88]
movsd [rbp-80], xmm0
movsd xmm0, [rbp-64]
mulsd xmm0, [rbp-80]
movsd [rbp-56], xmm0
movsd xmm0, [rbp-48]
mulsd xmm0, [rbp-56]
movsd [rbp-40], xmm0
movsd xmm0, [rbp-24]
mulsd xmm0, [rbp-24]
movsd [rbp-96], xmm0
movsd xmm0, [rbp-40]
divsd xmm0, [rbp-96]
movsd [rbp-32], xmm0
movsd xmm0, [rbp-32]
leave
ret
MATLAB
function result = coulomb_force(a, b, r)
result = ((8987551792.3 * ((a * 0.000001) * (b * 0.000001))) / (r * r));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_, r_] := ((8987551792.3 * ((a * 0.000001) * (b * 0.000001))) / (r * r));
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
University Physics Volume 3
Read OpenStax University Physics: Quantum MechanicsCite this book
- APA 7
- Ling, S. J., Sanny, J., & Moebs, W. (2016). University physics volume 3. OpenStax. https://openstax.org/books/university-physics-volume-3/pages/1-introduction
- MLA 9
- Ling, Samuel J., et al. University Physics Volume 3. OpenStax, 2016, https://openstax.org/books/university-physics-volume-3/pages/1-introduction.
- Chicago author-date
- Ling, Samuel J., Jeff Sanny, and William Moebs. 2016. University Physics Volume 3. Houston, TX: OpenStax. https://openstax.org/books/university-physics-volume-3/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Coulomb Electric Force Calculator. MW SysArc Tools. https://math.mwsysarc.com/mathematical-physics/coulomb-electric-force
MLA 9
MW SysArc. “Coulomb Electric Force Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/mathematical-physics/coulomb-electric-force. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Coulomb Electric Force Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/mathematical-physics/coulomb-electric-force.
Harvard
MW SysArc (2026) ‘Coulomb Electric Force Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/mathematical-physics/coulomb-electric-force (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_coulomb_force_2026,
author = {{MW SysArc}},
title = {Coulomb Electric Force Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/mathematical-physics/coulomb-electric-force},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Coulomb Electric Force Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/mathematical-physics/coulomb-electric-force
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Coulomb force do?
Calculate the signed electrostatic force magnitude between two point charges.
How does the Coulomb force work?
The calculator applies F=kq₁q₂/r². Electric force follows an inverse-square law; the charge-product sign distinguishes repulsion from attraction.
What can I learn from the Coulomb force?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .