Mathematics · Probability
Variation of Information Calculator
Calculate variation of information from conditional entropy h(x|y) and conditional entropy h(y|x).
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=a+b with conditional entropy H(X|Y)=1.2 and conditional entropy H(Y|X)=0.9.
- variation of information=2.1.
Understand Variation of Information
One idea, three depths
Choose how deeply to explain Variation of Information
Calculate variation of information from conditional entropy h(x|y) and conditional entropy h(y|x).
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Variation of Information to answer this question: calculate variation of information from conditional entropy h(x|y) and conditional entropy h(y|x)? Enter conditional entropy H(X|Y) and conditional entropy H(Y|X); the calculator shows variation of information. For example: conditional entropy H(X|Y)=1.2 and conditional entropy H(Y|X)=0.9 produce variation of information=2.1. The answer tells you variation of information.
Age 15Explain it to a 15-year-oldConnect it to the formula
Variation of information adds the two directional conditional entropies and defines a metric on clusterings under standard conditions. This page evaluates the relationship directly. The rule is c=a+b. Its input values are conditional entropy H(X|Y), conditional entropy H(Y|X), and the main result is variation of information. For example: conditional entropy H(X|Y)=1.2 and conditional entropy H(Y|X)=0.9 produce variation of information=2.1.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated variation of information relation over the valid real-number domain stated below. The implemented relation is c=a+b, evaluated from conditional entropy H(X|Y), conditional entropy H(Y|X) to produce variation of information. Variation of information adds the two directional conditional entropies and defines a metric on clusterings under standard conditions. This page evaluates the relationship directly. Use the same logarithm base and empirical probability convention for both terms.
Inputs and valid domain
- conditional entropy H(X|Y) must be a finite real number.
- conditional entropy H(Y|X) must be a finite real number.
Important boundary: Use the same logarithm base and empirical probability convention for both terms.
The formula
c=a+b
How the calculator works through it
It substitutes conditional entropy H(X|Y), conditional entropy H(Y|X) into the formula and exposes every numerical step above. The main output is variation of information.
Read the result correctly
The variation of information is the direct answer to “calculate variation of information from conditional entropy h(x|y) and conditional entropy h(y|x).” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
conditional entropy H(X|Y)=1.2 and conditional entropy H(Y|X)=0.9 produce variation of information=2.1.
Where this model stops being reliable
Use the same logarithm base and empirical probability convention for both terms.
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 Variation of Information works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Variation of Information uses c=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
- Probability as a modelled proportion
Probability rules are needed to interpret what the Variation of Information result says about possible outcomes.
Review this foundation about 5 min
Optional enrichment
- Ordered arrangements
Counting ordered arrangements can extend Variation of Information to more detailed sample spaces and event models.
Review this foundation about 5 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 conditional entropy H(X|Y), conditional entropy H(Y|X).
- Evaluate the principal relationship: c=a+b.
- Return variation of information and check the domain conditions described above.
Python
from math import *
def variation_of_information_calculator(a, b) -> float:
return (a + b)
assert abs(variation_of_information_calculator(1.2, 0.9) - 2.1) < 1e-6 * max(1.0, abs(2.1))
C
#include <assert.h>
#include <math.h>
double variation_of_information_calculator(double a, double b) {
return (a + b);
}
int main(void) {
const double expected = 2.1;
const double actual = variation_of_information_calculator(1.2, 0.9);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double variation_of_information_calculator(double a, double b) {
return (a + b);
}
int main() {
constexpr double expected = 2.1;
const double actual = variation_of_information_calculator(1.2, 0.9);
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 variation_of_information_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global variation_of_information_calculator
section .text
variation_of_information_calculator:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
addsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = variation_of_information_calculator(a, b)
result = (a + b);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[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.
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). Variation of Information Calculator. MW SysArc Tools. https://math.mwsysarc.com/probability/variation-of-information-calculator
MLA 9
MW SysArc. “Variation of Information Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/probability/variation-of-information-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Variation of Information Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/probability/variation-of-information-calculator.
Harvard
MW SysArc (2026) ‘Variation of Information Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/probability/variation-of-information-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_variation_of_information_calculator_2026,
author = {{MW SysArc}},
title = {Variation of Information Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/probability/variation-of-information-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Variation of Information Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/probability/variation-of-information-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Variation of Information do?
Calculate variation of information from conditional entropy h(x|y) and conditional entropy h(y|x).
How does the Variation of Information work?
The calculator applies c=a+b. Variation of information adds the two directional conditional entropies and defines a metric on clusterings under standard conditions. This page evaluates the relationship directly.
What can I learn from the Variation of Information?
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 .