What 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.

What 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.

Can 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.

Why 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.

Can 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.

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.

How It Works

Formula

P = n\,s

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

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

A = \frac{P a}{2}

I = \frac{(n - 2) \cdot 180^\circ}{n}

E = \frac{360^\circ}{n}

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 $P = ns$ , apothem with $a = s / (2\tan(\pi / n))$ , circumradius with $R = s / (2\sin(\pi / n))$ , area with $A = Pa / 2$ , 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.

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