Regular Polygon Calculator

Pick a side count, type one measurement (side length, apothem, circumradius, or area) and read off the rest. The two key derived measurements are the apothem — the distance from the centre to the middle of a side, also known as the inradius — and the circumradius, the distance from the centre to a vertex. Everything runs in your browser; nothing is uploaded.

Side count (N)

3 ≤ N ≤ 1000 (integer)

Preset — choose a named polygon — Triangle (3)Square (4)Pentagon (5)Hexagon (6)Octagon (8)Decagon (10)Dodecagon (12)Hexadecagon (16)Icosagon (20)

From side length type the side s From apothem type the inradius a From circumradius type the radius R From area type the area A

Side length (s)

Result Copy

Quick reference — common regular polygons

N	Name	Interior	Exterior	Side s = 1 → area
3	Triangle	60°	120°	0.4330
4	Square	90°	90°	1.0000
5	Pentagon	108°	72°	1.7205
6	Hexagon	120°	60°	2.5981
8	Octagon	135°	45°	4.8284
10	Decagon	144°	36°	7.6942
12	Dodecagon	150°	30°	11.196
16	Hexadecagon	157.5°	22.5°	20.109
20	Icosagon	162°	18°	31.569

As the side count grows, a regular polygon approaches a circle of radius R: its circumradius stays R, the apothem approaches R from below, and the perimeter approaches the circumference 2πR. At N = 1 000 the polygon looks indistinguishable from its circumcircle in the preview.