Mathematics · Statistics
Symmetric Mean Absolute Percentage Error Calculator
Calculate smape percentage from one-hundred times summed absolute errors and sum of absolute actual-plus-forecast magnitudes.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=2a/b with one-hundred times summed absolute errors=4200 and sum of absolute actual-plus-forecast magnitudes=10000.
- sMAPE percentage=0.84.
Understand Symmetric Mean Absolute Percentage Error
One idea, three depths
Choose how deeply to explain Symmetric Mean Absolute Percentage Error
Symmetric Mean Absolute Percentage Error: Calculate smape percentage from one-hundred times summed absolute errors and sum of absolute actual-plus-forecast magnitudes.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Symmetric Mean Absolute Percentage Error to answer this question: calculate smape percentage from one-hundred times summed absolute errors and sum of absolute actual-plus-forecast magnitudes? Enter one-hundred times summed absolute errors and sum of absolute actual-plus-forecast magnitudes; the calculator shows sMAPE percentage. For example: one-hundred times summed absolute errors=4200 and sum of absolute actual-plus-forecast magnitudes=10000 produce sMAPE percentage=0.84. The answer tells you sMAPE percentage.
Age 15Explain it to a 15-year-oldConnect it to the formula
A common sMAPE convention is two hundred times summed absolute error divided by summed absolute actual-plus-forecast magnitudes. This page evaluates the relationship directly. The rule is c=2a/b. Its input values are one-hundred times summed absolute errors, sum of absolute actual-plus-forecast magnitudes, and the main result is sMAPE percentage. For example: one-hundred times summed absolute errors=4200 and sum of absolute actual-plus-forecast magnitudes=10000 produce sMAPE percentage=0.84.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated symmetric mean absolute percentage error relation over the valid real-number domain stated below. The implemented relation is c=2a/b, evaluated from one-hundred times summed absolute errors, sum of absolute actual-plus-forecast magnitudes to produce sMAPE percentage. A common sMAPE convention is two hundred times summed absolute error divided by summed absolute actual-plus-forecast magnitudes. This page evaluates the relationship directly. Several sMAPE scaling conventions exist, so report the exact factor and aggregation rule.
Inputs and valid domain
- one-hundred times summed absolute errors must be a finite real number.
- sum of absolute actual-plus-forecast magnitudes must be a finite real number.
Important boundary: Several sMAPE scaling conventions exist, so report the exact factor and aggregation rule.
The formula
c=2a/b
How the calculator works through it
It substitutes one-hundred times summed absolute errors, sum of absolute actual-plus-forecast magnitudes into the formula and exposes every numerical step above. The main output is sMAPE percentage.
Read the result correctly
The sMAPE percentage is the direct answer to “calculate smape percentage from one-hundred times summed absolute errors and sum of absolute actual-plus-forecast magnitudes.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
one-hundred times summed absolute errors=4200 and sum of absolute actual-plus-forecast magnitudes=10000 produce sMAPE percentage=0.84.
Where this model stops being reliable
Several sMAPE scaling conventions exist, so report the exact factor and aggregation rule.
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 Symmetric Mean Absolute Percentage Error works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Symmetric Mean Absolute Percentage Error uses c=2a/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 Symmetric Mean Absolute Percentage Error 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 Symmetric Mean Absolute Percentage Error 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 one-hundred times summed absolute errors, sum of absolute actual-plus-forecast magnitudes.
- Evaluate the principal relationship: c=2a/b.
- Return sMAPE percentage and check the domain conditions described above.
Python
from math import *
def symmetric_mean_absolute_percentage_error_calculator(a, b) -> float:
return ((2.0 * a) / b)
assert abs(symmetric_mean_absolute_percentage_error_calculator(4200, 10000) - 0.84) < 1e-6 * max(1.0, abs(0.84))
C
#include <assert.h>
#include <math.h>
double symmetric_mean_absolute_percentage_error_calculator(double a, double b) {
return ((2.0 * a) / b);
}
int main(void) {
const double expected = 0.84;
const double actual = symmetric_mean_absolute_percentage_error_calculator(4200, 10000);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double symmetric_mean_absolute_percentage_error_calculator(double a, double b) {
return ((2.0 * a) / b);
}
int main() {
constexpr double expected = 0.84;
const double actual = symmetric_mean_absolute_percentage_error_calculator(4200, 10000);
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 symmetric_mean_absolute_percentage_error_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global symmetric_mean_absolute_percentage_error_calculator
section .text
symmetric_mean_absolute_percentage_error_calculator:
push rbp
mov rbp, rsp
sub rsp, 48
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
mov rax, 0x4000000000000000
movq xmm0, rax
movsd [rbp-40], xmm0
movsd xmm0, [rbp-40]
mulsd xmm0, [rbp-8]
movsd [rbp-32], xmm0
movsd xmm0, [rbp-32]
divsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = symmetric_mean_absolute_percentage_error_calculator(a, b)
result = ((2.0 * a) / b);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := ((2.0 * 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). Symmetric Mean Absolute Percentage Error Calculator. MW SysArc Tools. https://math.mwsysarc.com/statistics/symmetric-mean-absolute-percentage-error-calculator
MLA 9
MW SysArc. “Symmetric Mean Absolute Percentage Error Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/symmetric-mean-absolute-percentage-error-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Symmetric Mean Absolute Percentage Error Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/symmetric-mean-absolute-percentage-error-calculator.
Harvard
MW SysArc (2026) ‘Symmetric Mean Absolute Percentage Error Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/symmetric-mean-absolute-percentage-error-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_symmetric_mean_absolute_percentage_error_calculator_2026,
author = {{MW SysArc}},
title = {Symmetric Mean Absolute Percentage Error Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/statistics/symmetric-mean-absolute-percentage-error-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Symmetric Mean Absolute Percentage Error Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/statistics/symmetric-mean-absolute-percentage-error-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Symmetric Mean Absolute Percentage Error do?
Calculate smape percentage from one-hundred times summed absolute errors and sum of absolute actual-plus-forecast magnitudes.
How does the Symmetric Mean Absolute Percentage Error work?
The calculator applies c=2a/b. A common sMAPE convention is two hundred times summed absolute error divided by summed absolute actual-plus-forecast magnitudes. This page evaluates the relationship directly.
What can I learn from the Symmetric Mean Absolute Percentage Error?
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 .