Nonagon calculator
Online calculator and formulas for a regular nonagon
This function calculates various parameters of a nonagon.
To perform the calculation, select the required parameter in the menu and enter its value. Then click the 'Calculate' button.
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Properties of a nonagon
A regular nonagon is a polygon that consists of nine corners and nine sides. If all nine sides are the same length, we speak of an equilateral nonagon. Even if all the angles at the nine corners are the same size, The nonagon is referred to as a regular nonagon.
For a regular nonagon, all interior angles are the same size at 140°.
The sum of the interior angles of a regular nonagon is 1260° (7 x 180°). This comes from a general formula for polygons, in which the number of vertices of the polygon is used as a variable \(n\):
\((n-2)· 180\ \ \ = (9-2) · 180 \ \ = 7 · 180 =1260°\)
The value of an interior angle of 140° is therefore given by the formula:
\(\displaystyle \frac{180·(n-2)}{n} \ \ =\frac{180·(9-2)}{9} =140° \)
These two formulas apply to all regular polygons. The number of corners is used for n.
Formulas for regular nonagons
Perimeter (\(\small{P}\))
\(\displaystyle P = a · 9 \)
Area (\(\small{A}\))
\(\displaystyle A = \frac{9}{2} · {r_c}^2 · sin(40°) \) \(\displaystyle \ \ = \frac{9}{2} · r_{rc}^2 · sin\left(\frac{2 · π}{9}\right) \)
Short diagonal (\(\small{d_2}\))
\(\displaystyle d_2= 2 · rc · sin(40°) \) \(\displaystyle \ \ = 2 · rc · sin\left(\frac{2 · π}{9}\right) \)
Middle diagonal (\(\small{d_3}\))
\(\displaystyle d_3 = 2 · rc · sin(60°) \) \(\displaystyle \ \ = 2 · rc · sin\left(\frac{3 · π}{9}\right) \)
Long diagonal (\(\small{d_4}\))
\(\displaystyle d_4= 2 · rc · sin(80°) \) \(\displaystyle \ \ = 2 · rc · sin\left(\frac{4 · π}{9}\right) \)
Inner circle radius (\(\small{r_i}\))
\(\displaystyle r_i=\frac{ a }{2 · tan(20°)} \) \(\displaystyle \ \ =\frac{ a }{2 · tan(π /9)} \)
Circumcirle radius (\(\small{r_c}\))
\(\displaystyle r_c=\frac{ a }{2 · sin(20°)} \) \(\displaystyle \ \ =\frac{ a }{2 · sin(π /9)} \)
Height (\(\small{h}\))
\(\displaystyle h = rc + ri \)
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