Mathematics · Geometry
Pythagorean Leg-Square Difference Calculator
Calculate unknown leg squared from hypotenuse length and known leg length.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=a²−b² with hypotenuse length=13 and known leg length=5.
- unknown leg squared=144.
Understand Pythagorean Leg-Square Difference
One idea, three depths
Choose how deeply to explain Pythagorean Leg-Square Difference
Pythagorean Leg-Square Difference: Calculate unknown leg squared from hypotenuse length and known leg length.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Pythagorean Leg-Square Difference to answer this question: calculate unknown leg squared from hypotenuse length and known leg length? Enter hypotenuse length and known leg length; the calculator shows unknown leg squared. For example: hypotenuse length=13 and known leg length=5 produce unknown leg squared=144. The answer tells you unknown leg squared.
Age 15Explain it to a 15-year-oldConnect it to the formula
Rearranging the Pythagorean theorem gives an unknown leg square as hypotenuse square minus known-leg square. This page evaluates the relationship directly. The rule is c=a²−b². Its input values are hypotenuse length, known leg length, and the main result is unknown leg squared. For example: hypotenuse length=13 and known leg length=5 produce unknown leg squared=144.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated pythagorean leg-square difference relation over the valid real-number domain stated below. The implemented relation is c=a²−b², evaluated from hypotenuse length, known leg length to produce unknown leg squared. Rearranging the Pythagorean theorem gives an unknown leg square as hypotenuse square minus known-leg square. This page evaluates the relationship directly. The hypotenuse must be at least as long as the known leg.
Inputs and valid domain
- hypotenuse length must be a finite real number.
- known leg length must be a finite real number.
Important boundary: The hypotenuse must be at least as long as the known leg.
The formula
c=a²−b²
How the calculator works through it
It substitutes hypotenuse length, known leg length into the formula and exposes every numerical step above. The main output is unknown leg squared.
Read the result correctly
The unknown leg squared is the direct answer to “calculate unknown leg squared from hypotenuse length and known leg length.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
hypotenuse length=13 and known leg length=5 produce unknown leg squared=144.
Where this model stops being reliable
The hypotenuse must be at least as long as the known leg.
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 Pythagorean Leg-Square Difference works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Pythagorean Leg-Square Difference 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
- Ratios between measured quantities
Ratios help you check the scale, units and proportional meaning of Pythagorean Leg-Square Difference.
Review this foundation about 4 min
Optional enrichment
- Angles and geometric relationships
Angle language provides useful geometric context for extending Pythagorean Leg-Square Difference to related shapes and constructions.
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 hypotenuse length, known leg length.
- Evaluate the principal relationship: c=a²−b².
- Return unknown leg squared and check the domain conditions described above.
Python
from math import *
def pythagorean_leg_square_difference_calculator(a, b) -> float:
return ((a * a) - (b * b))
assert abs(pythagorean_leg_square_difference_calculator(13, 5) - 144) < 1e-6 * max(1.0, abs(144))
C
#include <assert.h>
#include <math.h>
double pythagorean_leg_square_difference_calculator(double a, double b) {
return ((a * a) - (b * b));
}
int main(void) {
const double expected = 144;
const double actual = pythagorean_leg_square_difference_calculator(13, 5);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double pythagorean_leg_square_difference_calculator(double a, double b) {
return ((a * a) - (b * b));
}
int main() {
constexpr double expected = 144;
const double actual = pythagorean_leg_square_difference_calculator(13, 5);
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 pythagorean_leg_square_difference_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global pythagorean_leg_square_difference_calculator
section .text
pythagorean_leg_square_difference_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-32], xmm0
movsd xmm0, [rbp-16]
mulsd xmm0, [rbp-16]
movsd [rbp-40], xmm0
movsd xmm0, [rbp-32]
subsd xmm0, [rbp-40]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = pythagorean_leg_square_difference_calculator(a, b)
result = ((a * a) - (b * b));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := ((a * a) - (b * 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.
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). Pythagorean Leg-Square Difference Calculator. MW SysArc Tools. https://math.mwsysarc.com/geometry/pythagorean-leg-square-difference-calculator
MLA 9
MW SysArc. “Pythagorean Leg-Square Difference Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/geometry/pythagorean-leg-square-difference-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Pythagorean Leg-Square Difference Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/geometry/pythagorean-leg-square-difference-calculator.
Harvard
MW SysArc (2026) ‘Pythagorean Leg-Square Difference Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/geometry/pythagorean-leg-square-difference-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_pythagorean_leg_square_difference_calculator_2026,
author = {{MW SysArc}},
title = {Pythagorean Leg-Square Difference Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/geometry/pythagorean-leg-square-difference-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Pythagorean Leg-Square Difference Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/geometry/pythagorean-leg-square-difference-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Pythagorean Leg-Square Difference do?
Calculate unknown leg squared from hypotenuse length and known leg length.
How does the Pythagorean Leg-Square Difference work?
The calculator applies c=a²−b². Rearranging the Pythagorean theorem gives an unknown leg square as hypotenuse square minus known-leg square. This page evaluates the relationship directly.
What can I learn from the Pythagorean Leg-Square Difference?
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 .