Calculations for a regular nonagon. The ancient Greek term for this shape, enneagon, is less common.
Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:
a = 2 * r_{c} * sin( π / 9 )
d = 2 * r_{c} * sin( 2 * π / 9 )
e = 2 * r_{c} * sin( 3 * π / 9 )
f = 2 * r_{c} * sin( 4 * π / 9 )
h = r_{c} + r_{i}
p = 9 * a
A = 9/2 * r_{c} * sin( 2 * π / 9 )
r_{i} = a / 2 * tan( π / 9 )
Angle: 140°
27 diagonals

π = 180° = 3.141592653589793...

Edge length, diagonals, height, perimeter and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

Heights, bisecting lines and median lines coincide, they meet at the centre of gravity, which is also the circumcenter and incircle center. The regular nonagon is rotationally symmetrical to this with a rotation of 360/9° or multiples thereof. Furthermore, the regular nonagon is axially symmetrical to the bisectors. It is not point symmetrical.

The regular nonagon cannot be constructed in a Euclidean manner, so it cannot be drawn using compass and ruler alone. There are approximate constructions, including one relatively simple but rather inaccurate by Albrecht Dürer. Constructions discovered later are more precise, but also more complicated.

Regular nonagons are rather rare. They are occasionally found in architecture as the floor plan for very special buildings, including the fortress city of Palmanova in the Italian region of Friuli-Venezia Giulia. The Bahai's sacred buildings are all based on this shape, including the most famous, the Lotus Temple in Delhi in India. Each side of these buildings has a gate, which is intended to symbolize openness to followers of other religions. The silver 5-euro commemorative coins from Austria also have a nonagonal shape. The name Nonagon sometimes occures in crossword puzzles, which is probably due to the rarity of the use of this unusual shape.