Dodecagon calculator
Online calculator and formulas for a regular dodecagon
This calculater returns various parameters of a dodecagon (12-gon or twelve-sided polygon).
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 dodecagon
A regular dodecagon is a polygon that consists of twelve corners and twelve sides. If all twelve sides are the same length, we speak of an equilateral dodecagon. Even if all the angles at the twelve corners are the same size, The dodecagon is called a regular dodecagon.
For a regular dodecagon, all interior angles are the same size at 150°.
The sum of the interior angles of a regular dodecagon is 1800°° (10 x 180°). This comes from a general formula for polygons, in which the number of vertices of the polygon is used as a variable \(n\):
\((n-2)· 180\ \ \ = (12-2) · 180 \ \ = 10 · 180 =1800°\)
The value of an interior angle of 150° is therefore given by the formula:
\(\displaystyle \frac{180·(n-2)}{n} \ \ =\frac{180·(12-2)}{12} ≈ 150° \)
These two formulas apply to all regular polygons. The number of corners is used for n.
Formulas for the regular dodecagon
Perimeter \(\small{P}\)
\(\displaystyle P = a · 12 \)
Area \(\small{A}\)
\(\displaystyle A = 3 · (2+\sqrt{3}) · a^2 \)
Diagonal \(\small{d_2}\)
\(\displaystyle d_2= \frac{\sqrt{6}+ \sqrt{2}}{2}·a \) \(\displaystyle \ \ = \frac{d_6}{2} \)
Diagonal \(\small{d_3}\)
\(\displaystyle d_3= (\sqrt{3}+1)·a \)
Diagonal \(\small{d_4}\)
\(\displaystyle d_4= \frac{3·\sqrt{2} +\sqrt{6}}{2} · a \)
Diagonal \(\small{d_5}\)
\(\displaystyle d_5= (2 +\sqrt{3})· a \)
Diagonal \(\small{d_6}\)
\(\displaystyle d_6= (\sqrt{2} +\sqrt{6})· a \)
Height \(\small{h}\)
\(\displaystyle h=d_5 \)
Inner circle radius \(\small{r_i}\)
\(\displaystyle r_i=\frac{ d5 }{2} \) \(\displaystyle \ \ =\frac{(2 + \sqrt{3}) ·a}{2} \)
Circumcirle radius \(\small{r_c}\)
\(\displaystyle r_c=d_2 \) \(\displaystyle \ \ =\frac{d6}{2} \)
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