Mathematics · Mathematical Physics
Two-Particle Reduced Mass Calculator
Calculate reduced mass from first particle mass and second particle mass.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=ab/(a+b) with first particle mass=4 and second particle mass=12.
- reduced mass=3.
Understand Two-Particle Reduced Mass
One idea, three depths
Choose how deeply to explain Two-Particle Reduced Mass
Two-Particle Reduced Mass: Calculate reduced mass from first particle mass and second particle mass.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Two-Particle Reduced Mass to answer this question: calculate reduced mass from first particle mass and second particle mass? Enter first particle mass and second particle mass; the calculator shows reduced mass. For example: first particle mass=4 and second particle mass=12 produce reduced mass=3. The answer tells you reduced mass.
Age 15Explain it to a 15-year-oldConnect it to the formula
Reduced mass converts a two-body relative-motion problem into an equivalent one-body form. This page evaluates the relationship directly. The rule is c=ab/(a+b). Its input values are first particle mass, second particle mass, and the main result is reduced mass. For example: first particle mass=4 and second particle mass=12 produce reduced mass=3.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated two-particle reduced mass relation over the valid real-number domain stated below. The implemented relation is c=ab/(a+b), evaluated from first particle mass, second particle mass to produce reduced mass. Reduced mass converts a two-body relative-motion problem into an equivalent one-body form. This page evaluates the relationship directly. Both masses must exceed the reduced mass, and physical units must match.
Inputs and valid domain
- first particle mass must be a finite real number.
- second particle mass must be a finite real number.
Important boundary: Both masses must exceed the reduced mass, and physical units must match.
The formula
c=ab/(a+b)
How the calculator works through it
It substitutes first particle mass, second particle mass into the formula and exposes every numerical step above. The main output is reduced mass.
Read the result correctly
The reduced mass is the direct answer to “calculate reduced mass from first particle mass and second particle mass.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
first particle mass=4 and second particle mass=12 produce reduced mass=3.
Where this model stops being reliable
Both masses must exceed the reduced mass, and physical units must match.
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 Two-Particle Reduced Mass works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Two-Particle Reduced Mass uses c=ab/(a+b). 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 Two-Particle Reduced Mass result physically interpretable instead of merely numerical.
Review this foundation about 5 min
Optional enrichment
- Vectors and physical direction
Vector language extends Two-Particle Reduced Mass 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 particle mass, second particle mass.
- Evaluate the principal relationship: c=ab/(a+b).
- Return reduced mass and check the domain conditions described above.
Python
from math import *
def two_particle_reduced_mass_calculator(a, b) -> float:
return ((a * b) / (a + b))
assert abs(two_particle_reduced_mass_calculator(4, 12) - 3) < 1e-6 * max(1.0, abs(3))
C
#include <assert.h>
#include <math.h>
double two_particle_reduced_mass_calculator(double a, double b) {
return ((a * b) / (a + b));
}
int main(void) {
const double expected = 3;
const double actual = two_particle_reduced_mass_calculator(4, 12);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double two_particle_reduced_mass_calculator(double a, double b) {
return ((a * b) / (a + b));
}
int main() {
constexpr double expected = 3;
const double actual = two_particle_reduced_mass_calculator(4, 12);
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 two_particle_reduced_mass_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global two_particle_reduced_mass_calculator
section .text
two_particle_reduced_mass_calculator:
push rbp
mov rbp, rsp
sub rsp, 48
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-16]
movsd [rbp-32], xmm0
movsd xmm0, [rbp-8]
addsd xmm0, [rbp-16]
movsd [rbp-40], xmm0
movsd xmm0, [rbp-32]
divsd xmm0, [rbp-40]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = two_particle_reduced_mass_calculator(a, b)
result = ((a * b) / (a + b));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := ((a * b) / (a + b));
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). Two-Particle Reduced Mass Calculator. MW SysArc Tools. https://math.mwsysarc.com/mathematical-physics/two-particle-reduced-mass-calculator
MLA 9
MW SysArc. “Two-Particle Reduced Mass Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/mathematical-physics/two-particle-reduced-mass-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Two-Particle Reduced Mass Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/mathematical-physics/two-particle-reduced-mass-calculator.
Harvard
MW SysArc (2026) ‘Two-Particle Reduced Mass Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/mathematical-physics/two-particle-reduced-mass-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_two_particle_reduced_mass_calculator_2026,
author = {{MW SysArc}},
title = {Two-Particle Reduced Mass Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/mathematical-physics/two-particle-reduced-mass-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Two-Particle Reduced Mass Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/mathematical-physics/two-particle-reduced-mass-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Two-Particle Reduced Mass do?
Calculate reduced mass from first particle mass and second particle mass.
How does the Two-Particle Reduced Mass work?
The calculator applies c=ab/(a+b). Reduced mass converts a two-body relative-motion problem into an equivalent one-body form. This page evaluates the relationship directly.
What can I learn from the Two-Particle Reduced Mass?
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 .