Mathematics · Algebra
Percentage Difference Calculator
Compare two values symmetrically using their average magnitude.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Difference=|80−100|=20.
- Divide by average magnitude 90 and multiply by 100: 22.22222222222222%.
Understand Percentage difference
One idea, three depths
Choose how deeply to explain Percentage difference
Percentage difference: Compare two values symmetrically using their average magnitude.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Percentage difference to answer this question: compare two values symmetrically using their average magnitude? Enter First value and Second value; the calculator shows Percentage difference. For example: 80 and 100 differ by 22.22%. The answer tells you Percentage difference.
Age 15Explain it to a 15-year-oldConnect it to the formula
Percentage difference treats both observations equally when neither is a baseline. The rule is |a−b|/((|a|+|b|)/2)×100%. Its input values are First value, Second value, and the main result is Percentage difference. For example: 80 and 100 differ by 22.22%.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated percentage difference relation over the valid real-number domain stated below. The implemented relation is |a−b|/((|a|+|b|)/2)×100%, evaluated from First value, Second value to produce Percentage difference. Percentage difference treats both observations equally when neither is a baseline. Use percentage change instead when one value is explicitly the original baseline.
Inputs and valid domain
- First value must be a finite real number.
- Second value must be a finite real number.
Important boundary: Use percentage change instead when one value is explicitly the original baseline.
The formula
|a−b|/((|a|+|b|)/2)×100%
How the calculator works through it
It substitutes First value, Second value into the formula and exposes every numerical step above. The main output is Percentage difference, accompanied by Absolute difference, Average magnitude.
Read the result correctly
The Percentage difference is the direct answer to “compare two values symmetrically using their average magnitude.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
80 and 100 differ by 22.22%.
Where this model stops being reliable
Use percentage change instead when one value is explicitly the original baseline.
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 Percentage difference works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Percentage difference uses |a−b|/((|a|+|b|)/2)×100%. 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
- Functions and input-output rules
A function viewpoint helps you see how changing an input changes the Percentage difference result.
Review this foundation about 5 min
Optional enrichment
- Powers and exponents
Powers are not required for every Percentage difference calculation, but they make related algebraic forms and code easier to read.
Review this foundation about 4 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 First value, Second value.
- Evaluate the principal relationship: |a−b|/((|a|+|b|)/2)×100%.
- Return Percentage difference and check the domain conditions described above.
Python
from math import *
def percentage_difference(a, b) -> float:
return ((fabs((a - b)) / ((fabs(a) + fabs(b)) / 2.0)) * 100.0)
assert abs(percentage_difference(80, 100) - 22.22222222222222) < 1e-6 * max(1.0, abs(22.22222222222222))
C
#include <assert.h>
#include <math.h>
double percentage_difference(double a, double b) {
return ((fabs((a - b)) / ((fabs(a) + fabs(b)) / 2.0)) * 100.0);
}
int main(void) {
const double expected = 22.22222222222222;
const double actual = percentage_difference(80, 100);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double percentage_difference(double a, double b) {
return ((std::fabs((a - b)) / ((std::fabs(a) + std::fabs(b)) / 2.0)) * 100.0);
}
int main() {
constexpr double expected = 22.22222222222222;
const double actual = percentage_difference(80, 100);
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 percentage_difference(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
extern fabs
global percentage_difference
section .text
percentage_difference:
push rbp
mov rbp, rsp
sub rsp, 96
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
subsd xmm0, [rbp-16]
movsd [rbp-48], xmm0
movsd xmm0, [rbp-48]
call fabs wrt ..plt
movsd [rbp-40], xmm0
movsd xmm0, [rbp-8]
call fabs wrt ..plt
movsd [rbp-72], xmm0
movsd xmm0, [rbp-16]
call fabs wrt ..plt
movsd [rbp-80], xmm0
movsd xmm0, [rbp-72]
addsd xmm0, [rbp-80]
movsd [rbp-64], xmm0
mov rax, 0x4000000000000000
movq xmm0, rax
movsd [rbp-88], xmm0
movsd xmm0, [rbp-64]
divsd xmm0, [rbp-88]
movsd [rbp-56], xmm0
movsd xmm0, [rbp-40]
divsd xmm0, [rbp-56]
movsd [rbp-32], xmm0
mov rax, 0x4059000000000000
movq xmm0, rax
movsd [rbp-96], xmm0
movsd xmm0, [rbp-32]
mulsd xmm0, [rbp-96]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = percentage_difference(a, b)
result = ((abs((a - b)) / ((abs(a) + abs(b)) / 2.0)) * 100.0);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := ((Abs[(a - b)] / ((Abs[a] + Abs[b]) / 2.0)) * 100.0);
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.
Algebra and Trigonometry 2e
Read the related free OpenStax mathematics chaptersCite this book
- APA 7
- Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
- MLA 9
- Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
- Chicago author-date
- Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
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). Percentage Difference Calculator. MW SysArc Tools. https://math.mwsysarc.com/algebra/percentage-difference
MLA 9
MW SysArc. “Percentage Difference Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/algebra/percentage-difference. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Percentage Difference Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/algebra/percentage-difference.
Harvard
MW SysArc (2026) ‘Percentage Difference Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/algebra/percentage-difference (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_percentage_difference_2026,
author = {{MW SysArc}},
title = {Percentage Difference Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/algebra/percentage-difference},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Percentage Difference Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/algebra/percentage-difference
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Percentage difference do?
Compare two values symmetrically using their average magnitude.
How does the Percentage difference work?
The calculator applies |a−b|/((|a|+|b|)/2)×100%. Percentage difference treats both observations equally when neither is a baseline.
What can I learn from the Percentage difference?
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 .