Mathematics · Algebra
Percent Change Rate Calculator
Calculate percentage change from original value and new value.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=100(b−a)/a with original value=80 and new value=92.
- percentage change=15.
Understand Percent Change Rate
One idea, three depths
Choose how deeply to explain Percent Change Rate
Percent Change Rate: Calculate percentage change from original value and new value.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Percent Change Rate to answer this question: calculate percentage change from original value and new value? Enter original value and new value; the calculator shows percentage change. For example: original value=80 and new value=92 produce percentage change=15. The answer tells you percentage change.
Age 15Explain it to a 15-year-oldConnect it to the formula
Percentage change compares the signed difference between new and original values with the original value. This page evaluates the relationship directly. The rule is c=100(b−a)/a. Its input values are original value, new value, and the main result is percentage change. For example: original value=80 and new value=92 produce percentage change=15.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated percent change rate relation over the valid real-number domain stated below. The implemented relation is c=100(b−a)/a, evaluated from original value, new value to produce percentage change. Percentage change compares the signed difference between new and original values with the original value. This page evaluates the relationship directly. The original value is the denominator; swapping the two values changes the percentage and its sign.
Inputs and valid domain
- original value must be a finite real number.
- new value must be a finite real number.
Important boundary: The original value is the denominator; swapping the two values changes the percentage and its sign.
The formula
c=100(b−a)/a
How the calculator works through it
It substitutes original value, new value into the formula and exposes every numerical step above. The main output is percentage change.
Read the result correctly
The percentage change is the direct answer to “calculate percentage change from original value and new value.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
original value=80 and new value=92 produce percentage change=15.
Where this model stops being reliable
The original value is the denominator; swapping the two values changes the percentage and its sign.
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 Percent Change Rate works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Percent Change Rate uses c=100(b−a)/a. 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 Percent Change Rate result.
Review this foundation about 5 min
Optional enrichment
- Powers and exponents
Powers are not required for every Percent Change Rate 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 original value, new value.
- Evaluate the principal relationship: c=100(b−a)/a.
- Return percentage change and check the domain conditions described above.
Python
from math import *
def percent_change_rate_calculator(a, b) -> float:
return ((100.0 * (b - a)) / a)
assert abs(percent_change_rate_calculator(80, 92) - 15) < 1e-6 * max(1.0, abs(15))
C
#include <assert.h>
#include <math.h>
double percent_change_rate_calculator(double a, double b) {
return ((100.0 * (b - a)) / a);
}
int main(void) {
const double expected = 15;
const double actual = percent_change_rate_calculator(80, 92);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double percent_change_rate_calculator(double a, double b) {
return ((100.0 * (b - a)) / a);
}
int main() {
constexpr double expected = 15;
const double actual = percent_change_rate_calculator(80, 92);
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 percent_change_rate_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global percent_change_rate_calculator
section .text
percent_change_rate_calculator:
push rbp
mov rbp, rsp
sub rsp, 48
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
mov rax, 0x4059000000000000
movq xmm0, rax
movsd [rbp-40], xmm0
movsd xmm0, [rbp-16]
subsd xmm0, [rbp-8]
movsd [rbp-48], xmm0
movsd xmm0, [rbp-40]
mulsd xmm0, [rbp-48]
movsd [rbp-32], xmm0
movsd xmm0, [rbp-32]
divsd xmm0, [rbp-8]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = percent_change_rate_calculator(a, b)
result = ((100.0 * (b - a)) / a);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := ((100.0 * (b - a)) / a);
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). Percent Change Rate Calculator. MW SysArc Tools. https://math.mwsysarc.com/algebra/percent-change-rate-calculator
MLA 9
MW SysArc. “Percent Change Rate Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/algebra/percent-change-rate-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Percent Change Rate Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/algebra/percent-change-rate-calculator.
Harvard
MW SysArc (2026) ‘Percent Change Rate Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/algebra/percent-change-rate-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_percent_change_rate_calculator_2026,
author = {{MW SysArc}},
title = {Percent Change Rate Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/algebra/percent-change-rate-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Percent Change Rate Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/algebra/percent-change-rate-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Percent Change Rate do?
Calculate percentage change from original value and new value.
How does the Percent Change Rate work?
The calculator applies c=100(b−a)/a. Percentage change compares the signed difference between new and original values with the original value. This page evaluates the relationship directly.
What can I learn from the Percent Change Rate?
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 .