Hendecagon Calculator

Complete set of formulas for a regular 11‑sided polygon: side, circumradius, inradius, area, perimeter, interior & central angles. Instant update with interactive diagram.

General formulas (n = number of sides): Interior angle = (n‑2)·180°/n , side s = 2R·sin(π/n) , inradius r = R·cos(π/n) , area A = ¼·n·s²·cot(π/n)

Enter integer ≥ 3 (default 11 for hendecagon)
Positive number
Common:
triangle
square
pentagon
hexagon
octagon
decagon
hendecagon
dodecagon
Hendecagon (n=11) properties
Sides (n)
11
Side length (s)
1.000
Perimeter (P)
11.000
Area (A)
9.366
Circumradius (R)
1.775
Inradius (r)
1.703
Interior angle
147.3°
Central angle
32.73°
polygon
circumcircle (R)
incircle (r)
vertices

About the Regular Hendecagon (11‑gon)

A regular hendecagon (also called undecagon) is an eleven‑sided polygon with equal sides and equal angles. It is not constructible with compass and straightedge (due to Gauss–Wantzel theorem), but its trigonometric formulas are well defined.

Key formulas for n = 11:

  • Interior angle = 180° × (11‑2)/11 ≈ 147.27°
  • Central angle = 360° / 11 ≈ 32.727°
  • If side s = 1: Circumradius R = 1 / (2·sin(π/11)) ≈ 1.775, Inradius r = R·cos(π/11) ≈ 1.703, Area A = 11/4 · cot(π/11) ≈ 9.366
  • Perimeter P = 11·s

Why “Hendecagon”?

The name comes from Greek “hendeka” (eleven) and “gonia” (angle). It is sometimes called undecagon from Latin “undecim”.

Real‑world appearances

  • Coins: The Canadian dollar coin (loonie) is an 11‑sided Reuleaux polygon, not a regular hendecagon but reminiscent.
  • Architecture: Some modern building floor plans use 11‑sided shapes for uniqueness.
  • Mathematics: Regular hendecagon appears in problems involving trigonometric constants and roots of unity.

Frequently Asked Questions

Absolutely! Although the page highlights hendecagon, you can change the number of sides (n) to any integer from 3 to 60 – the calculator instantly adapts.

The dashed circle is the circumcircle (passing through all vertices). The dotted circle is the incircle (touching each side). Both are concentric in a regular polygon.

They involve cos(2π/11), which are roots of quintic equations. For practical purposes we use high‑precision floating point.

A = ¼ n s² cot(π/n). For n=11, A ≈ (11/4) cot(π/11) s².