Mathematics · Statistics
Discounted Cumulative-Gain Rank Contribution Calculator
Calculate discounted gain contribution from relevance gain at selected rank and rank discount denominator.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=a/b with relevance gain at selected rank=7 and rank discount denominator=3.
- discounted gain contribution=2.3333333333333335.
Understand Discounted Cumulative-Gain Rank Contribution
One idea, three depths
Choose how deeply to explain Discounted Cumulative-Gain Rank Contribution
Discounted Cumulative-Gain Rank Contribution: Calculate discounted gain contribution from relevance gain at selected rank and rank discount denominator.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Discounted Cumulative-Gain Rank Contribution to answer this question: calculate discounted gain contribution from relevance gain at selected rank and rank discount denominator? Enter relevance gain at selected rank and rank discount denominator; the calculator shows discounted gain contribution. For example: relevance gain at selected rank=7 and rank discount denominator=3 produce discounted gain contribution=2.3333333333333335. The answer tells you discounted gain contribution.
Age 15Explain it to a 15-year-oldConnect it to the formula
A DCG rank contribution divides relevance gain by the chosen logarithmic rank discount. This page evaluates the relationship directly. The rule is c=a/b. Its input values are relevance gain at selected rank, rank discount denominator, and the main result is discounted gain contribution. For example: relevance gain at selected rank=7 and rank discount denominator=3 produce discounted gain contribution=2.3333333333333335.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated discounted cumulative-gain rank contribution relation over the valid real-number domain stated below. The implemented relation is c=a/b, evaluated from relevance gain at selected rank, rank discount denominator to produce discounted gain contribution. A DCG rank contribution divides relevance gain by the chosen logarithmic rank discount. This page evaluates the relationship directly. Gain and discount definitions must match the reported DCG convention.
Inputs and valid domain
- relevance gain at selected rank must be a finite real number.
- rank discount denominator must be a finite real number.
Important boundary: Gain and discount definitions must match the reported DCG convention.
The formula
c=a/b
How the calculator works through it
It substitutes relevance gain at selected rank, rank discount denominator into the formula and exposes every numerical step above. The main output is discounted gain contribution.
Read the result correctly
The discounted gain contribution is the direct answer to “calculate discounted gain contribution from relevance gain at selected rank and rank discount denominator.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
relevance gain at selected rank=7 and rank discount denominator=3 produce discounted gain contribution=2.3333333333333335.
Where this model stops being reliable
Gain and discount definitions must match the reported DCG 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 Discounted Cumulative-Gain Rank Contribution works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Discounted Cumulative-Gain Rank Contribution 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
- Averages and representative values
Representative values help you judge what the Discounted Cumulative-Gain Rank Contribution 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 Discounted Cumulative-Gain Rank Contribution 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 relevance gain at selected rank, rank discount denominator.
- Evaluate the principal relationship: c=a/b.
- Return discounted gain contribution and check the domain conditions described above.
Python
from math import *
def dcg_gain_contribution_calculator(a, b) -> float:
return (a / b)
assert abs(dcg_gain_contribution_calculator(7, 3) - 2.3333333333333335) < 1e-6 * max(1.0, abs(2.3333333333333335))
C
#include <assert.h>
#include <math.h>
double dcg_gain_contribution_calculator(double a, double b) {
return (a / b);
}
int main(void) {
const double expected = 2.3333333333333335;
const double actual = dcg_gain_contribution_calculator(7, 3);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double dcg_gain_contribution_calculator(double a, double b) {
return (a / b);
}
int main() {
constexpr double expected = 2.3333333333333335;
const double actual = dcg_gain_contribution_calculator(7, 3);
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 dcg_gain_contribution_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global dcg_gain_contribution_calculator
section .text
dcg_gain_contribution_calculator:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
divsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = dcg_gain_contribution_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). Discounted Cumulative-Gain Rank Contribution Calculator. MW SysArc Tools. https://math.mwsysarc.com/statistics/dcg-gain-contribution-calculator
MLA 9
MW SysArc. “Discounted Cumulative-Gain Rank Contribution Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/dcg-gain-contribution-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Discounted Cumulative-Gain Rank Contribution Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/dcg-gain-contribution-calculator.
Harvard
MW SysArc (2026) ‘Discounted Cumulative-Gain Rank Contribution Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/dcg-gain-contribution-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_dcg_gain_contribution_calculator_2026,
author = {{MW SysArc}},
title = {Discounted Cumulative-Gain Rank Contribution Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/statistics/dcg-gain-contribution-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Discounted Cumulative-Gain Rank Contribution Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/statistics/dcg-gain-contribution-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Discounted Cumulative-Gain Rank Contribution do?
Calculate discounted gain contribution from relevance gain at selected rank and rank discount denominator.
How does the Discounted Cumulative-Gain Rank Contribution work?
The calculator applies c=a/b. A DCG rank contribution divides relevance gain by the chosen logarithmic rank discount. This page evaluates the relationship directly.
What can I learn from the Discounted Cumulative-Gain Rank Contribution?
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 .