CalcLibrary

Regular Polygon Calculator

Solve a regular pentagon, hexagon, octagon, decagon, or any equal-sided polygon from one known measurement. Start from side length, apothem, circumradius, perimeter, or area and get the full geometry instantly.

liveFormula
m
Examples

Start with an 8-sided layout and one side length to size the full footprint before you draw or compare options.

Area
19.31 m²
Side length
2 m
Perimeter
16 m
Apothem
2.41 m
Circumradius
2.61 m
Interior angle
135 °
Exterior angle
45 °

Started from the side length, then derived perimeter, apothem, circumradius, and area from the same regular polygon.

Regular polygons only. If your shape has unequal sides or angles, use the triangle, rectangle, or circle calculator instead.

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Examples

How It Works

Formula

P=n sP = n\,s

a=s2tan⁡(π/n)a = \frac{s}{2\tan(\pi / n)}

R=s2sin⁡(π/n)R = \frac{s}{2\sin(\pi / n)}

A=Pa2A = \frac{P a}{2}

I=(n−2)⋅180∘nI = \frac{(n - 2) \cdot 180^\circ}{n}

E=360∘nE = \frac{360^\circ}{n}

Variables

nn

Number of sides(count)

ss

Length of one side(selected unit)

aa

Apothem: center to side distance(selected unit)

RR

Circumradius: center to vertex distance(selected unit)

PP

Perimeter of the polygon(selected unit)

AA

Area enclosed by the polygon(selected unit²)

II

Interior angle(degrees)

EE

Exterior angle(degrees)

Choose the regular polygon by its number of sides, then choose the one measurement you know: side length, apothem, circumradius, perimeter, or area. The calculator solves the side length first because every other regular-polygon relationship flows from it. After that it derives perimeter with P=nsP = ns, apothem with a=s/(2tan⁡(π/n))a = s / (2\tan(\pi / n)), circumradius with R=s/(2sin⁡(π/n))R = s / (2\sin(\pi / n)), area with A=Pa/2A = Pa / 2, and the interior/exterior angles in degrees. The result is strictly for regular polygons. If your shape is not an equal-sided n-gon, jump to the triangle, rectangle, or circle calculators below.

Frequently Asked Questions

01What shapes does this regular polygon calculator cover?
It covers regular polygons only: equal sides and equal angles, with at least 5 sides. That includes regular pentagons, hexagons, octagons, decagons, and similar n-gons.
02What is the difference between the apothem and the circumradius?
The apothem runs from the center straight to the middle of a side. The circumradius runs from the center to a vertex. In a regular polygon they are related, but they are not the same measurement.
03Can I solve the polygon from area or perimeter only?
Yes. The calculator first reverse-solves the side length from your chosen measure, then derives perimeter, apothem, circumradius, area, and both angle values from the finished regular polygon.
04Why must the number of sides be a whole number of at least 5?
A polygon must have a whole number of sides, and this tool intentionally starts at regular pentagons. If your shape is a triangle, rectangle, or circle problem, use those dedicated calculators instead.
05Can I use this to estimate materials or fabrication tolerances?
No. This tool handles clean geometry from the dimensions you provide. It is helpful for sketches, homework, and planning checks, but it does not estimate waste, material quantities, or CAD-grade tolerances.

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