Mathematics · Probability

Jensen–Shannon Entropy Gap Calculator

Calculate jensen-shannon divergence from mixture-distribution entropy and weighted component-entropy mean.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
Jensen-Shannon divergence0.5

Calculation steps

  1. Use c=a−b with mixture-distribution entropy=2.4 and weighted component-entropy mean=1.9.
  2. Jensen-Shannon divergence=0.5.

Understand Jensen–Shannon Entropy Gap

One idea, three depths

Choose how deeply to explain Jensen–Shannon Entropy Gap

Jensen–Shannon Entropy Gap: Calculate jensen-shannon divergence from mixture-distribution entropy and weighted component-entropy mean.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Jensen–Shannon Entropy Gap to answer this question: calculate jensen-shannon divergence from mixture-distribution entropy and weighted component-entropy mean? Enter mixture-distribution entropy and weighted component-entropy mean; the calculator shows Jensen-Shannon divergence. For example: mixture-distribution entropy=2.4 and weighted component-entropy mean=1.9 produce Jensen-Shannon divergence=0.5. The answer tells you Jensen-Shannon divergence.

Age 15Explain it to a 15-year-oldConnect it to the formula

Jensen-Shannon divergence is mixture entropy minus the weighted mean of component entropies. This page evaluates the relationship directly. The rule is c=a−b. Its input values are mixture-distribution entropy, weighted component-entropy mean, and the main result is Jensen-Shannon divergence. For example: mixture-distribution entropy=2.4 and weighted component-entropy mean=1.9 produce Jensen-Shannon divergence=0.5.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated jensen–shannon entropy gap relation over the valid real-number domain stated below. The implemented relation is c=a−b, evaluated from mixture-distribution entropy, weighted component-entropy mean to produce Jensen-Shannon divergence. Jensen-Shannon divergence is mixture entropy minus the weighted mean of component entropies. This page evaluates the relationship directly. The component weights must sum to one and use the same logarithm base.

Inputs and valid domain

  • mixture-distribution entropy must be a finite real number.
  • weighted component-entropy mean must be a finite real number.

Important boundary: The component weights must sum to one and use the same logarithm base.

The formula

c=a−b

How the calculator works through it

It substitutes mixture-distribution entropy, weighted component-entropy mean into the formula and exposes every numerical step above. The main output is Jensen-Shannon divergence.

Read the result correctly

The Jensen-Shannon divergence is the direct answer to “calculate jensen-shannon divergence from mixture-distribution entropy and weighted component-entropy mean.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

mixture-distribution entropy=2.4 and weighted component-entropy mean=1.9 produce Jensen-Shannon divergence=0.5.

Where this model stops being reliable

The component weights must sum to one and use the same logarithm base.

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 Jensen–Shannon Entropy Gap works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Jensen–Shannon Entropy Gap 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 Jensen–Shannon Entropy Gap result says about possible outcomes.

    Review this foundation about 5 min

Optional enrichment

Learn the missing foundationsI already know these — show the code

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

  1. Read mixture-distribution entropy, weighted component-entropy mean.
  2. Evaluate the principal relationship: c=a−b.
  3. Return Jensen-Shannon divergence and check the domain conditions described above.
Python
            from math import *

def jensen_shannon_entropy_gap_calculator(a, b) -> float:
    return (a - b)

assert abs(jensen_shannon_entropy_gap_calculator(2.4, 1.9) - 0.5) < 1e-6 * max(1.0, abs(0.5))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double jensen_shannon_entropy_gap_calculator(double a, double b) {
    return (a - b);
}

int main(void) {
    const double expected = 0.5;
    const double actual = jensen_shannon_entropy_gap_calculator(2.4, 1.9);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double jensen_shannon_entropy_gap_calculator(double a, double b) {
    return (a - b);
}

int main() {
    constexpr double expected = 0.5;
    const double actual = jensen_shannon_entropy_gap_calculator(2.4, 1.9);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double jensen_shannon_entropy_gap_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global jensen_shannon_entropy_gap_calculator
section .text

jensen_shannon_entropy_gap_calculator:
    push rbp
    mov rbp, rsp
    sub rsp, 32
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-8]
    subsd xmm0, [rbp-16]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = jensen_shannon_entropy_gap_calculator(a, b)
    result = (a - b);
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a - b);
          
Current calculator valuesUpdates when you change an input above.
              
            

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 textbook
Cite 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). Jensen–Shannon Entropy Gap Calculator. MW SysArc Tools. https://math.mwsysarc.com/probability/jensen-shannon-entropy-gap-calculator

MLA 9

MW SysArc. “Jensen–Shannon Entropy Gap Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/probability/jensen-shannon-entropy-gap-calculator. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Jensen–Shannon Entropy Gap Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/probability/jensen-shannon-entropy-gap-calculator.

Harvard

MW SysArc (2026) ‘Jensen–Shannon Entropy Gap Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/probability/jensen-shannon-entropy-gap-calculator (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_jensen_shannon_entropy_gap_calculator_2026,
  author = {{MW SysArc}},
  title = {Jensen–Shannon Entropy Gap Calculator},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/probability/jensen-shannon-entropy-gap-calculator},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Jensen–Shannon Entropy Gap Calculator
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/probability/jensen-shannon-entropy-gap-calculator
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Jensen–Shannon Entropy Gap do?

Calculate jensen-shannon divergence from mixture-distribution entropy and weighted component-entropy mean.

How does the Jensen–Shannon Entropy Gap work?

The calculator applies c=a−b. Jensen-Shannon divergence is mixture entropy minus the weighted mean of component entropies. This page evaluates the relationship directly.

What can I learn from the Jensen–Shannon Entropy Gap?

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 .

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