Mathematics · Probability
Min-Entropy from Maximum Probability Calculator
Calculate min-entropy in nats from logarithm unit scale and maximum outcome probability.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=−a ln(b) with logarithm unit scale=1 and maximum outcome probability=0.125.
- min-entropy in nats=2.0794415416798357.
Understand Min-Entropy from Maximum Probability
One idea, three depths
Choose how deeply to explain Min-Entropy from Maximum Probability
Min-Entropy from Maximum Probability: Calculate min-entropy in nats from logarithm unit scale and maximum outcome probability.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Min-Entropy from Maximum Probability to answer this question: calculate min-entropy in nats from logarithm unit scale and maximum outcome probability? Enter logarithm unit scale and maximum outcome probability; the calculator shows min-entropy in nats. For example: logarithm unit scale=1 and maximum outcome probability=0.125 produce min-entropy in nats=2.0794415416798357. The answer tells you min-entropy in nats.
Age 15Explain it to a 15-year-oldConnect it to the formula
Min-entropy is the negative natural logarithm of the largest outcome probability when the unit scale is one. This page evaluates the relationship directly. The rule is c=−a ln(b). Its input values are logarithm unit scale, maximum outcome probability, and the main result is min-entropy in nats. For example: logarithm unit scale=1 and maximum outcome probability=0.125 produce min-entropy in nats=2.0794415416798357.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated min-entropy from maximum probability relation over the valid real-number domain stated below. The implemented relation is c=−a ln(b), evaluated from logarithm unit scale, maximum outcome probability to produce min-entropy in nats. Min-entropy is the negative natural logarithm of the largest outcome probability when the unit scale is one. This page evaluates the relationship directly. For bits, divide the natural-log result by ln two or use a base-two convention.
Inputs and valid domain
- logarithm unit scale must be a finite real number.
- maximum outcome probability must be a finite real number.
Important boundary: For bits, divide the natural-log result by ln two or use a base-two convention.
The formula
c=−a ln(b)
How the calculator works through it
It substitutes logarithm unit scale, maximum outcome probability into the formula and exposes every numerical step above. The main output is min-entropy in nats.
Read the result correctly
The min-entropy in nats is the direct answer to “calculate min-entropy in nats from logarithm unit scale and maximum outcome probability.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
logarithm unit scale=1 and maximum outcome probability=0.125 produce min-entropy in nats=2.0794415416798357.
Where this model stops being reliable
For bits, divide the natural-log result by ln two or use a base-two convention.
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 Min-Entropy from Maximum Probability works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Min-Entropy from Maximum Probability uses c=−a ln(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 Min-Entropy from Maximum Probability result says about possible outcomes.
Review this foundation about 5 min
Optional enrichment
- Ordered arrangements
Counting ordered arrangements can extend Min-Entropy from Maximum Probability 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 logarithm unit scale, maximum outcome probability.
- Evaluate the principal relationship: c=−a ln(b).
- Return min-entropy in nats and check the domain conditions described above.
Python
from math import *
def min_entropy_from_maximum_probability_calculator(a, b) -> float:
return (-(a * log(b)))
assert abs(min_entropy_from_maximum_probability_calculator(1, 0.125) - 2.0794415416798357) < 1e-6 * max(1.0, abs(2.0794415416798357))
C
#include <assert.h>
#include <math.h>
double min_entropy_from_maximum_probability_calculator(double a, double b) {
return (-(a * log(b)));
}
int main(void) {
const double expected = 2.0794415416798357;
const double actual = min_entropy_from_maximum_probability_calculator(1, 0.125);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double min_entropy_from_maximum_probability_calculator(double a, double b) {
return (-(a * std::log(b)));
}
int main() {
constexpr double expected = 2.0794415416798357;
const double actual = min_entropy_from_maximum_probability_calculator(1, 0.125);
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 min_entropy_from_maximum_probability_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
extern log
global min_entropy_from_maximum_probability_calculator
section .text
min_entropy_from_maximum_probability_calculator:
push rbp
mov rbp, rsp
sub rsp, 48
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-16]
call log wrt ..plt
movsd [rbp-40], xmm0
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-40]
movsd [rbp-32], xmm0
pxor xmm0, xmm0
subsd xmm0, [rbp-32]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = min_entropy_from_maximum_probability_calculator(a, b)
result = (-(a * log(b)));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := (-(a * Log[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). Min-Entropy from Maximum Probability Calculator. MW SysArc Tools. https://math.mwsysarc.com/probability/min-entropy-from-maximum-probability-calculator
MLA 9
MW SysArc. “Min-Entropy from Maximum Probability Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/probability/min-entropy-from-maximum-probability-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Min-Entropy from Maximum Probability Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/probability/min-entropy-from-maximum-probability-calculator.
Harvard
MW SysArc (2026) ‘Min-Entropy from Maximum Probability Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/probability/min-entropy-from-maximum-probability-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_min_entropy_from_maximum_probability_calculator_2026,
author = {{MW SysArc}},
title = {Min-Entropy from Maximum Probability Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/probability/min-entropy-from-maximum-probability-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Min-Entropy from Maximum Probability Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/probability/min-entropy-from-maximum-probability-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Min-Entropy from Maximum Probability do?
Calculate min-entropy in nats from logarithm unit scale and maximum outcome probability.
How does the Min-Entropy from Maximum Probability work?
The calculator applies c=−a ln(b). Min-entropy is the negative natural logarithm of the largest outcome probability when the unit scale is one. This page evaluates the relationship directly.
What can I learn from the Min-Entropy from Maximum Probability?
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 .