Mathematics · Geometry

Right-Triangle Leg Relationship Calculator

Calculate hypotenuse from first leg and second leg.

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
hypotenuse15

Calculation steps

  1. Use c=√(a²+b²) with first leg=9 and second leg=12.
  2. hypotenuse=15.

Understand Right-Triangle Leg Relationship

One idea, three depths

Choose how deeply to explain Right-Triangle Leg Relationship

Right-Triangle Leg Relationship: Calculate hypotenuse from first leg and second leg.

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

Imagine using Right-Triangle Leg Relationship to answer this question: calculate hypotenuse from first leg and second leg? Enter first leg and second leg; the calculator shows hypotenuse. For example: first leg=9 and second leg=12 produce hypotenuse=15. The answer tells you hypotenuse.

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

The Pythagorean theorem links the two perpendicular legs and the hypotenuse. This page evaluates the relationship directly. The rule is c=√(a²+b²). Its input values are first leg, second leg, and the main result is hypotenuse. For example: first leg=9 and second leg=12 produce hypotenuse=15.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated right-triangle leg relationship relation over the valid real-number domain stated below. The implemented relation is c=√(a²+b²), evaluated from first leg, second leg to produce hypotenuse. The Pythagorean theorem links the two perpendicular legs and the hypotenuse. This page evaluates the relationship directly. The solved hypotenuse must be the side opposite the right angle.

Inputs and valid domain

  • first leg must be a finite real number.
  • second leg must be a finite real number.

Important boundary: The solved hypotenuse must be the side opposite the right angle.

The formula

c=√(a²+b²)

How the calculator works through it

It substitutes first leg, second leg into the formula and exposes every numerical step above. The main output is hypotenuse.

Read the result correctly

The hypotenuse is the direct answer to “calculate hypotenuse from first leg and second leg.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

first leg=9 and second leg=12 produce hypotenuse=15.

Where this model stops being reliable

The solved hypotenuse must be the side opposite the right angle.

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 Right-Triangle Leg Relationship works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Right-Triangle Leg Relationship 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 Right-Triangle Leg Relationship 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 first leg, second leg.
  2. Evaluate the principal relationship: c=√(a²+b²).
  3. Return hypotenuse and check the domain conditions described above.
Python
            from math import *

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

assert abs(right_triangle_legs_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 right_triangle_legs_calculator(double a, double b) {
    return sqrt(((a * a) + (b * b)));
}

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

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

right_triangle_legs_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 = right_triangle_legs_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). Right-Triangle Leg Relationship Calculator. MW SysArc Tools. https://math.mwsysarc.com/geometry/right-triangle-legs-calculator

MLA 9

MW SysArc. “Right-Triangle Leg Relationship Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/geometry/right-triangle-legs-calculator. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Right-Triangle Leg Relationship Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/geometry/right-triangle-legs-calculator.

Harvard

MW SysArc (2026) ‘Right-Triangle Leg Relationship Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/geometry/right-triangle-legs-calculator (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_right_triangle_legs_calculator_2026,
  author = {{MW SysArc}},
  title = {Right-Triangle Leg Relationship Calculator},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/geometry/right-triangle-legs-calculator},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Right-Triangle Leg Relationship Calculator
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/geometry/right-triangle-legs-calculator
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Right-Triangle Leg Relationship do?

Calculate hypotenuse from first leg and second leg.

How does the Right-Triangle Leg Relationship work?

The calculator applies c=√(a²+b²). The Pythagorean theorem links the two perpendicular legs and the hypotenuse. This page evaluates the relationship directly.

What can I learn from the Right-Triangle Leg Relationship?

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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