Mathematics · Statistics

Symmetric Mean Absolute Percentage Error sum of absolute actual-plus-forecast magnitudes Solver

Rearrange the symmetric mean absolute percentage error relationship and solve for sum of absolute actual-plus-forecast magnitudes.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
sum of absolute actual-plus-forecast magnitudes10,000
Reconstructed sMAPE percentage0.84

Calculation steps

  1. Use b=2a/c with sMAPE percentage=0.84 and one-hundred times summed absolute errors=4200.
  2. sum of absolute actual-plus-forecast magnitudes=10000.
  3. Substitution into c=2a/b reconstructs 0.84.

Understand Symmetric Mean Absolute Percentage Error: solve sum of absolute actual-plus-forecast magnitudes

One idea, three depths

Choose how deeply to explain Symmetric Mean Absolute Percentage Error: solve sum of absolute actual-plus-forecast magnitudes

Symmetric Mean Absolute Percentage Error: solve sum of absolute actual-plus-forecast magnitudes: Rearrange the symmetric mean absolute percentage error relationship and solve for 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: solve sum of absolute actual-plus-forecast magnitudes to answer this question: rearrange the symmetric mean absolute percentage error relationship and solve for sum of absolute actual-plus-forecast magnitudes? Enter sMAPE percentage and one-hundred times summed absolute errors; the calculator shows sum of absolute actual-plus-forecast magnitudes. 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 sum of absolute actual-plus-forecast magnitudes.

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 isolates sum of absolute actual-plus-forecast magnitudes and verifies it in the original relationship. The rule is b=2a/c. Its input values are sMAPE percentage, one-hundred times summed absolute errors, and the main result is sum of absolute actual-plus-forecast magnitudes. 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: solve sum of absolute actual-plus-forecast magnitudes relation over the valid real-number domain stated below. The implemented relation is b=2a/c, evaluated from sMAPE percentage, one-hundred times summed absolute errors to produce sum of absolute actual-plus-forecast magnitudes. A common sMAPE convention is two hundred times summed absolute error divided by summed absolute actual-plus-forecast magnitudes. This page isolates sum of absolute actual-plus-forecast magnitudes and verifies it in the original relationship. Several sMAPE scaling conventions exist, so report the exact factor and aggregation rule.

Inputs and valid domain

  • sMAPE percentage must be a finite real number.
  • one-hundred times summed absolute errors must be a finite real number.

Important boundary: Several sMAPE scaling conventions exist, so report the exact factor and aggregation rule.

The formula

b=2a/c

How the calculator works through it

It substitutes sMAPE percentage, one-hundred times summed absolute errors into the formula and exposes every numerical step above. The main output is sum of absolute actual-plus-forecast magnitudes, accompanied by Reconstructed sMAPE percentage.

Read the result correctly

The sum of absolute actual-plus-forecast magnitudes is the direct answer to “rearrange the symmetric mean absolute percentage error relationship and solve for 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: solve sum of absolute actual-plus-forecast magnitudes 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: solve sum of absolute actual-plus-forecast magnitudes uses b=2a/c. 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: solve sum of absolute actual-plus-forecast magnitudes 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: solve sum of absolute actual-plus-forecast magnitudes formula, but it helps you judge how stable a reported result may be.

    Review this foundation about 6 min
Learn the missing foundationsI already know these — show the code

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

  1. Read sMAPE percentage, one-hundred times summed absolute errors.
  2. Evaluate the principal relationship: b=2a/c.
  3. Return sum of absolute actual-plus-forecast magnitudes and check the domain conditions described above.
Python
            from math import *

def symmetric_mean_absolute_percentage_error_solve_b(c, a) -> float:
    return ((2.0 * a) / c)

assert abs(symmetric_mean_absolute_percentage_error_solve_b(0.84, 4200) - 10000) < 1e-6 * max(1.0, abs(10000))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double symmetric_mean_absolute_percentage_error_solve_b(double c, double a) {
    return ((2.0 * a) / c);
}

int main(void) {
    const double expected = 10000;
    const double actual = symmetric_mean_absolute_percentage_error_solve_b(0.84, 4200);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double symmetric_mean_absolute_percentage_error_solve_b(double c, double a) {
    return ((2.0 * a) / c);
}

int main() {
    constexpr double expected = 10000;
    const double actual = symmetric_mean_absolute_percentage_error_solve_b(0.84, 4200);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double symmetric_mean_absolute_percentage_error_solve_b(double c, double a)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global symmetric_mean_absolute_percentage_error_solve_b
section .text

symmetric_mean_absolute_percentage_error_solve_b:
    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-16]
    movsd [rbp-32], xmm0
    movsd xmm0, [rbp-32]
    divsd xmm0, [rbp-8]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = symmetric_mean_absolute_percentage_error_solve_b(c, a)
    result = ((2.0 * a) / c);
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[c_, a_] := ((2.0 * a) / c);
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

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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 textbook
Cite 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 sum of absolute actual-plus-forecast magnitudes Solver. MW SysArc Tools. https://math.mwsysarc.com/statistics/symmetric-mean-absolute-percentage-error-sum-of-absolute-actual-plus-forecast-magnitudes-solver

MLA 9

MW SysArc. “Symmetric Mean Absolute Percentage Error sum of absolute actual-plus-forecast magnitudes Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/symmetric-mean-absolute-percentage-error-sum-of-absolute-actual-plus-forecast-magnitudes-solver. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Symmetric Mean Absolute Percentage Error sum of absolute actual-plus-forecast magnitudes Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/symmetric-mean-absolute-percentage-error-sum-of-absolute-actual-plus-forecast-magnitudes-solver.

Harvard

MW SysArc (2026) ‘Symmetric Mean Absolute Percentage Error sum of absolute actual-plus-forecast magnitudes Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/symmetric-mean-absolute-percentage-error-sum-of-absolute-actual-plus-forecast-magnitudes-solver (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_symmetric_mean_absolute_percentage_error_solve_b_2026,
  author = {{MW SysArc}},
  title = {Symmetric Mean Absolute Percentage Error sum of absolute actual-plus-forecast magnitudes Solver},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/statistics/symmetric-mean-absolute-percentage-error-sum-of-absolute-actual-plus-forecast-magnitudes-solver},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Symmetric Mean Absolute Percentage Error sum of absolute actual-plus-forecast magnitudes Solver
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-sum-of-absolute-actual-plus-forecast-magnitudes-solver
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Symmetric Mean Absolute Percentage Error: solve sum of absolute actual-plus-forecast magnitudes do?

Rearrange the symmetric mean absolute percentage error relationship and solve for sum of absolute actual-plus-forecast magnitudes.

How does the Symmetric Mean Absolute Percentage Error: solve sum of absolute actual-plus-forecast magnitudes work?

The calculator applies b=2a/c. A common sMAPE convention is two hundred times summed absolute error divided by summed absolute actual-plus-forecast magnitudes. This page isolates sum of absolute actual-plus-forecast magnitudes and verifies it in the original relationship.

What can I learn from the Symmetric Mean Absolute Percentage Error: solve sum of absolute actual-plus-forecast magnitudes?

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 .

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