Mathematics · Trigonometry
Right Triangle Calculator
Solve a right triangle from its two perpendicular legs.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Change an input to reshape this diagram.
degrees
degrees
Calculation steps
- Hypotenuse = √(3² + 4²) = 5.
- Angle A = arctan(3 ÷ 4) = 36.86989764584402°.
- Angle B = 90° − 36.86989764584402° = 53.13010235415598°.
Understand Right triangle
One idea, three depths
Choose how deeply to explain Right triangle
Solve a right triangle from its two perpendicular legs.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Right triangle to answer this question: solve a right triangle from its two perpendicular legs? Enter Leg a and Leg b; the calculator shows Hypotenuse. For example: Legs 3 and 4 produce hypotenuse 5 and acute angles about 36.87° and 53.13°. The answer tells you Hypotenuse.
Age 15Explain it to a 15-year-oldConnect it to the formula
The Pythagorean theorem gives the hypotenuse and inverse tangent converts the side ratio into an acute angle. The rule is c = √(a² + b²); angle A = arctan(a ÷ b). Its input values are Leg a, Leg b, and the main result is Hypotenuse. For example: Legs 3 and 4 produce hypotenuse 5 and acute angles about 36.87° and 53.13°.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated right triangle relation over the valid real-number domain stated below. The implemented relation is c = √(a² + b²); angle A = arctan(a ÷ b), evaluated from Leg a, Leg b to produce Hypotenuse. The Pythagorean theorem gives the hypotenuse and inverse tangent converts the side ratio into an acute angle. Calculator trigonometric functions may use radians; this tool reports degrees.
Inputs and valid domain
- Leg a must be a finite real number, at least 0.000001.
- Leg b must be a finite real number, at least 0.000001.
Important boundary: Calculator trigonometric functions may use radians; this tool reports degrees.
The formula
c = √(a² + b²); angle A = arctan(a ÷ b)
How the calculator works through it
It substitutes Leg a, Leg b into the formula and exposes every numerical step above. The main output is Hypotenuse, accompanied by Angle A, Angle B.
Read the result correctly
The Hypotenuse is the direct answer to “solve a right triangle from its two perpendicular legs.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
Legs 3 and 4 produce hypotenuse 5 and acute angles about 36.87° and 53.13°.
Where this model stops being reliable
Calculator trigonometric functions may use radians; this tool reports degrees.
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 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 uses c = √(a² + b²); angle A = arctan(a ÷ 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
- Angles in degrees and radians
Interpreting the angle convention is essential for understanding the inputs and output of Right triangle.
Review this foundation about 5 min
Optional enrichment
- Functions and their graphs
Function graphs show how the Right triangle relationship changes across a full angle or period.
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 Leg a, Leg b.
- Evaluate the principal relationship: c = √(a² + b²); angle A = arctan(a ÷ b).
- Return Hypotenuse and check the domain conditions described above.
Python
from math import *
def right_triangle(a, b) -> float:
return sqrt(((a * a) + (b * b)))
assert abs(right_triangle(3, 4) - 5) < 1e-6 * max(1.0, abs(5))
C
#include <assert.h>
#include <math.h>
double right_triangle(double a, double b) {
return sqrt(((a * a) + (b * b)));
}
int main(void) {
const double expected = 5;
const double actual = right_triangle(3, 4);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double right_triangle(double a, double b) {
return std::sqrt(((a * a) + (b * b)));
}
int main() {
constexpr double expected = 5;
const double actual = right_triangle(3, 4);
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 right_triangle(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global right_triangle
section .text
right_triangle:
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
MATLAB
function result = right_triangle(a, b)
result = sqrt(((a * a) + (b * b)));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := Sqrt[((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). Right Triangle Calculator. MW SysArc Tools. https://math.mwsysarc.com/trigonometry/right-triangle-calculator
MLA 9
MW SysArc. “Right Triangle Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/trigonometry/right-triangle-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Right Triangle Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/trigonometry/right-triangle-calculator.
Harvard
MW SysArc (2026) ‘Right Triangle Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/trigonometry/right-triangle-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_right_triangle_2026,
author = {{MW SysArc}},
title = {Right Triangle Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/trigonometry/right-triangle-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Right Triangle Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/trigonometry/right-triangle-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Right triangle do?
Solve a right triangle from its two perpendicular legs.
How does the Right triangle work?
The calculator applies c = √(a² + b²); angle A = arctan(a ÷ b). The Pythagorean theorem gives the hypotenuse and inverse tangent converts the side ratio into an acute angle.
What can I learn from the Right triangle?
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 .