Mathematics · Geometry

Rectangular Face Diagonal Calculator

Calculate face diagonal from rectangle length and rectangle width.

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
face diagonal15

Calculation steps

  1. Use c=√(a²+b²) with rectangle length=9 and rectangle width=12.
  2. face diagonal=15.

Understand Rectangular Face Diagonal

One idea, three depths

Choose how deeply to explain Rectangular Face Diagonal

Rectangular Face Diagonal: Calculate face diagonal from rectangle length and rectangle width.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Rectangular Face Diagonal to answer this question: calculate face diagonal from rectangle length and rectangle width? Enter rectangle length and rectangle width; the calculator shows face diagonal. For example: rectangle length=9 and rectangle width=12 produce face diagonal=15. The answer tells you face diagonal.

Age 15Explain it to a 15-year-oldConnect it to the formula

A rectangle's diagonal and two side lengths form a right triangle. This page evaluates the relationship directly. The rule is c=√(a²+b²). Its input values are rectangle length, rectangle width, and the main result is face diagonal. For example: rectangle length=9 and rectangle width=12 produce face diagonal=15.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated rectangular face diagonal relation over the valid real-number domain stated below. The implemented relation is c=√(a²+b²), evaluated from rectangle length, rectangle width to produce face diagonal. A rectangle's diagonal and two side lengths form a right triangle. This page evaluates the relationship directly. This is a two-dimensional face diagonal, not the space diagonal of a box.

Inputs and valid domain

  • rectangle length must be a finite real number.
  • rectangle width must be a finite real number.

Important boundary: This is a two-dimensional face diagonal, not the space diagonal of a box.

The formula

c=√(a²+b²)

How the calculator works through it

It substitutes rectangle length, rectangle width into the formula and exposes every numerical step above. The main output is face diagonal.

Read the result correctly

The face diagonal is the direct answer to “calculate face diagonal from rectangle length and rectangle width.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

rectangle length=9 and rectangle width=12 produce face diagonal=15.

Where this model stops being reliable

This is a two-dimensional face diagonal, not the space diagonal of a box.

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 Rectangular Face Diagonal works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Rectangular Face Diagonal uses c=√(a²+b²). 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

Optional enrichment

  • Angles and geometric relationships

    Angle language provides useful geometric context for extending Rectangular Face Diagonal to related shapes and constructions.

    Review this foundation about 4 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 rectangle length, rectangle width.
  2. Evaluate the principal relationship: c=√(a²+b²).
  3. Return face diagonal and check the domain conditions described above.
Python
            from math import *

def rectangular_face_diagonal_calculator(a, b) -> float:
    return sqrt(((a * a) + (b * b)))

assert abs(rectangular_face_diagonal_calculator(9, 12) - 15) < 1e-6 * max(1.0, abs(15))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double rectangular_face_diagonal_calculator(double a, double b) {
    return sqrt(((a * a) + (b * b)));
}

int main(void) {
    const double expected = 15;
    const double actual = rectangular_face_diagonal_calculator(9, 12);
    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 rectangular_face_diagonal_calculator(double a, double b) {
    return std::sqrt(((a * a) + (b * b)));
}

int main() {
    constexpr double expected = 15;
    const double actual = rectangular_face_diagonal_calculator(9, 12);
    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 rectangular_face_diagonal_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global rectangular_face_diagonal_calculator
section .text

rectangular_face_diagonal_calculator:
    push rbp
    mov rbp, rsp
    sub rsp, 48
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-8]
    mulsd xmm0, [rbp-8]
    movsd [rbp-40], xmm0
    movsd xmm0, [rbp-16]
    mulsd xmm0, [rbp-16]
    movsd [rbp-48], xmm0
    movsd xmm0, [rbp-40]
    addsd xmm0, [rbp-48]
    movsd [rbp-32], xmm0
    sqrtsd xmm0, [rbp-32]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = rectangular_face_diagonal_calculator(a, b)
    result = sqrt(((a * a) + (b * b)));
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[a_, b_] := Sqrt[((a * a) + (b * b))];
          
Current calculator valuesUpdates when you change an input above.
              
            

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 chapters
Cite 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). Rectangular Face Diagonal Calculator. MW SysArc Tools. https://math.mwsysarc.com/geometry/rectangular-face-diagonal-calculator

MLA 9

MW SysArc. “Rectangular Face Diagonal Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/geometry/rectangular-face-diagonal-calculator. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Rectangular Face Diagonal Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/geometry/rectangular-face-diagonal-calculator.

Harvard

MW SysArc (2026) ‘Rectangular Face Diagonal Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/geometry/rectangular-face-diagonal-calculator (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_rectangular_face_diagonal_calculator_2026,
  author = {{MW SysArc}},
  title = {Rectangular Face Diagonal Calculator},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/geometry/rectangular-face-diagonal-calculator},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Rectangular Face Diagonal Calculator
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/geometry/rectangular-face-diagonal-calculator
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Rectangular Face Diagonal do?

Calculate face diagonal from rectangle length and rectangle width.

How does the Rectangular Face Diagonal work?

The calculator applies c=√(a²+b²). A rectangle's diagonal and two side lengths form a right triangle. This page evaluates the relationship directly.

What can I learn from the Rectangular Face Diagonal?

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 .

MW SysArc Certified