Mathematics · Geometry
Regular Polygon Calculator
Calculate regular polygon area and perimeter from side count and side length.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Change an input to reshape this diagram.
Calculation steps
- Area=6×1²÷(4tan(π/6))=2.598076211353316.
- Report Area=2.598076211353316, Perimeter=6, Apothem=0.8660254037844387.
Understand Regular polygon
One idea, three depths
Choose how deeply to explain Regular polygon
Calculate regular polygon area and perimeter from side count and side length.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Regular polygon to answer this question: calculate regular polygon area and perimeter from side count and side length? Enter Number of sides n and Side length s; the calculator shows Area. For example: A unit regular hexagon has area about 2.598. The answer tells you Area.
Age 15Explain it to a 15-year-oldConnect it to the formula
The center divides a regular polygon into congruent isosceles triangles. The rule is A=ns²/[4tan(π/n)]. Its input values are Number of sides n, Side length s, and the main result is Area. For example: A unit regular hexagon has area about 2.598.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated regular polygon relation over the valid mixed integer and real-number domain stated below. The implemented relation is A=ns²/[4tan(π/n)], evaluated from Number of sides n, Side length s to produce Area. The center divides a regular polygon into congruent isosceles triangles. n must be at least three and all sides and angles must be equal.
Inputs and valid domain
- Number of sides n must be an integer, at least 3.
- Side length s must be a finite real number, at least 0.
Important boundary: n must be at least three and all sides and angles must be equal.
The formula
A=ns²/[4tan(π/n)]
How the calculator works through it
It substitutes Number of sides n, Side length s into the formula and exposes every numerical step above. The main output is Area, accompanied by Perimeter, Apothem.
Read the result correctly
The Area is the direct answer to “calculate regular polygon area and perimeter from side count and side length.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
A unit regular hexagon has area about 2.598.
Where this model stops being reliable
n must be at least three and all sides and angles must be equal.
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 Regular polygon works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Regular polygon uses A=ns²/[4tan(π/n)]. 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 Regular polygon.
Review this foundation about 4 min
Optional enrichment
- Angles and geometric relationships
Angle language provides useful geometric context for extending Regular polygon 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 Number of sides n, Side length s.
- Evaluate the principal relationship: A=ns²/[4tan(π/n)].
- Return Area and check the domain conditions described above.
Python
from math import *
def regular_polygon(n, a) -> float:
return ((n * (a * a)) / (4.0 * tan((pi / n))))
assert abs(regular_polygon(6, 1) - 2.598076211353316) < 1e-6 * max(1.0, abs(2.598076211353316))
C
#include <assert.h>
#include <math.h>
double regular_polygon(double n, double a) {
return ((n * (a * a)) / (4.0 * tan((3.141592653589793 / n))));
}
int main(void) {
const double expected = 2.598076211353316;
const double actual = regular_polygon(6, 1);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double regular_polygon(double n, double a) {
return ((n * (a * a)) / (4.0 * std::tan((std::numbers::pi / n))));
}
int main() {
constexpr double expected = 2.598076211353316;
const double actual = regular_polygon(6, 1);
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 regular_polygon(double n, double a)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
extern tan
global regular_polygon
section .text
regular_polygon:
push rbp
mov rbp, rsp
sub rsp, 80
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-16]
mulsd xmm0, [rbp-16]
movsd [rbp-40], xmm0
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-40]
movsd [rbp-32], xmm0
mov rax, 0x4010000000000000
movq xmm0, rax
movsd [rbp-56], xmm0
mov rax, 0x400921fb54442d18
movq xmm0, rax
movsd [rbp-80], xmm0
movsd xmm0, [rbp-80]
divsd xmm0, [rbp-8]
movsd [rbp-72], xmm0
movsd xmm0, [rbp-72]
call tan wrt ..plt
movsd [rbp-64], xmm0
movsd xmm0, [rbp-56]
mulsd xmm0, [rbp-64]
movsd [rbp-48], xmm0
movsd xmm0, [rbp-32]
divsd xmm0, [rbp-48]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = regular_polygon(n, a)
result = ((n * (a * a)) / (4.0 * tan((pi / n))));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[n_, a_] := ((n * (a * a)) / (4.0 * Tan[(Pi / n)]));
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). Regular Polygon Calculator. MW SysArc Tools. https://math.mwsysarc.com/geometry/regular-polygon-area
MLA 9
MW SysArc. “Regular Polygon Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/geometry/regular-polygon-area. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Regular Polygon Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/geometry/regular-polygon-area.
Harvard
MW SysArc (2026) ‘Regular Polygon Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/geometry/regular-polygon-area (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_regular_polygon_2026,
author = {{MW SysArc}},
title = {Regular Polygon Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/geometry/regular-polygon-area},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Regular Polygon Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/geometry/regular-polygon-area
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Regular polygon do?
Calculate regular polygon area and perimeter from side count and side length.
How does the Regular polygon work?
The calculator applies A=ns²/[4tan(π/n)]. The center divides a regular polygon into congruent isosceles triangles.
What can I learn from the Regular polygon?
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 .