Mathematics · Statistics
Fowlkes–Mallows Classification Index Calculator
Calculate fowlkes–mallows index from positive predictive value as a decimal and sensitivity as a decimal.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=√(ab) with positive predictive value as a decimal=0.86 and sensitivity as a decimal=0.92.
- Fowlkes–Mallows index=0.8894942383174834.
Understand Fowlkes–Mallows Classification Index
One idea, three depths
Choose how deeply to explain Fowlkes–Mallows Classification Index
Fowlkes–Mallows Classification Index: Calculate fowlkes–mallows index from positive predictive value as a decimal and sensitivity as a decimal.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Fowlkes–Mallows Classification Index to answer this question: calculate fowlkes–mallows index from positive predictive value as a decimal and sensitivity as a decimal? Enter positive predictive value as a decimal and sensitivity as a decimal; the calculator shows Fowlkes–Mallows index. For example: positive predictive value as a decimal=0.86 and sensitivity as a decimal=0.92 produce Fowlkes–Mallows index=0.8894942383174834. The answer tells you Fowlkes–Mallows index.
Age 15Explain it to a 15-year-oldConnect it to the formula
The Fowlkes–Mallows index is the geometric mean of positive predictive value and sensitivity. This page evaluates the relationship directly. The rule is c=√(ab). Its input values are positive predictive value as a decimal, sensitivity as a decimal, and the main result is Fowlkes–Mallows index. For example: positive predictive value as a decimal=0.86 and sensitivity as a decimal=0.92 produce Fowlkes–Mallows index=0.8894942383174834.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated fowlkes–mallows classification index relation over the valid real-number domain stated below. The implemented relation is c=√(ab), evaluated from positive predictive value as a decimal, sensitivity as a decimal to produce Fowlkes–Mallows index. The Fowlkes–Mallows index is the geometric mean of positive predictive value and sensitivity. This page evaluates the relationship directly. Both inputs must describe the same positive class and use the same decimal scale.
Inputs and valid domain
- positive predictive value as a decimal must be a finite real number.
- sensitivity as a decimal must be a finite real number.
Important boundary: Both inputs must describe the same positive class and use the same decimal scale.
The formula
c=√(ab)
How the calculator works through it
It substitutes positive predictive value as a decimal, sensitivity as a decimal into the formula and exposes every numerical step above. The main output is Fowlkes–Mallows index.
Read the result correctly
The Fowlkes–Mallows index is the direct answer to “calculate fowlkes–mallows index from positive predictive value as a decimal and sensitivity as a decimal.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
positive predictive value as a decimal=0.86 and sensitivity as a decimal=0.92 produce Fowlkes–Mallows index=0.8894942383174834.
Where this model stops being reliable
Both inputs must describe the same positive class and use the same decimal scale.
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 Fowlkes–Mallows Classification Index works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Fowlkes–Mallows Classification Index uses c=√(ab). 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
- Averages and representative values
Representative values help you judge what the Fowlkes–Mallows Classification Index inputs summarise and what the result can legitimately describe.
Review this foundation about 5 min
Optional enrichment
- Spread and measurement variation
Variation is not always part of the Fowlkes–Mallows Classification Index formula, but it helps you judge how stable a reported result may be.
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 positive predictive value as a decimal, sensitivity as a decimal.
- Evaluate the principal relationship: c=√(ab).
- Return Fowlkes–Mallows index and check the domain conditions described above.
Python
from math import *
def fowlkes_mallows_classification_calculator(a, b) -> float:
return sqrt((a * b))
assert abs(fowlkes_mallows_classification_calculator(0.86, 0.92) - 0.8894942383174834) < 1e-6 * max(1.0, abs(0.8894942383174834))
C
#include <assert.h>
#include <math.h>
double fowlkes_mallows_classification_calculator(double a, double b) {
return sqrt((a * b));
}
int main(void) {
const double expected = 0.8894942383174834;
const double actual = fowlkes_mallows_classification_calculator(0.86, 0.92);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double fowlkes_mallows_classification_calculator(double a, double b) {
return std::sqrt((a * b));
}
int main() {
constexpr double expected = 0.8894942383174834;
const double actual = fowlkes_mallows_classification_calculator(0.86, 0.92);
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 fowlkes_mallows_classification_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global fowlkes_mallows_classification_calculator
section .text
fowlkes_mallows_classification_calculator:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-16]
movsd [rbp-32], xmm0
sqrtsd xmm0, [rbp-32]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = fowlkes_mallows_classification_calculator(a, b)
result = sqrt((a * b));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := Sqrt[(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.
Introductory Statistics 2e
Read the free OpenStax statistics textbookCite this book
- APA 7
- Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
- MLA 9
- Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
- Chicago author-date
- Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/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). Fowlkes–Mallows Classification Index Calculator. MW SysArc Tools. https://math.mwsysarc.com/statistics/fowlkes-mallows-classification-calculator
MLA 9
MW SysArc. “Fowlkes–Mallows Classification Index Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/fowlkes-mallows-classification-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Fowlkes–Mallows Classification Index Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/fowlkes-mallows-classification-calculator.
Harvard
MW SysArc (2026) ‘Fowlkes–Mallows Classification Index Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/fowlkes-mallows-classification-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_fowlkes_mallows_classification_calculator_2026,
author = {{MW SysArc}},
title = {Fowlkes–Mallows Classification Index Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/statistics/fowlkes-mallows-classification-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Fowlkes–Mallows Classification Index Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/statistics/fowlkes-mallows-classification-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Fowlkes–Mallows Classification Index do?
Calculate fowlkes–mallows index from positive predictive value as a decimal and sensitivity as a decimal.
How does the Fowlkes–Mallows Classification Index work?
The calculator applies c=√(ab). The Fowlkes–Mallows index is the geometric mean of positive predictive value and sensitivity. This page evaluates the relationship directly.
What can I learn from the Fowlkes–Mallows Classification Index?
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 .