Hexadecagon calculator and formela

This function calculates various parameters of a hexadecagon.

To perform the calculation, select the property you know and enter its value. Then click the 'Calculate' button.

Hexadecagon calculation

Input

Argument type

Argument value

Decimal places

Results

Edge lenght a

Perimeter P

Area A

Diagonal d2

Diagonal d3

Diagonal d4

Diagonal d5

Diagonal d6

Diagonal d7

Diagonal d8

Inner radius ri

Outer radius ro

Formulas of the hexadecagon

Perimeter \(P\)

\(\displaystyle P = a · 16 \)

Area \(A\)

\(\displaystyle A = 4·a^2· cot\left(\frac{π}{16}\right) \)

\(\displaystyle ≈ a^2· 20.11 \)

Diagonal \(d_2\) (2 corners)

\(\displaystyle d_2=a· \frac{sin(\frac{2 ·π}{16})}{sin(\frac{π}{16})} \)

\(\displaystyle ≈ a·1.96\)

Diagonal \(d_3\) (3 corners)

\(\displaystyle d_3= a· \frac{sin(\frac{3 ·π}{16})}{sin(\frac{π}{16})} \)

\(\displaystyle ≈ a·2.85\)

Diagonal \(d_4\) (4 corners)

\(\displaystyle d_4= a·\frac{ \frac{\sqrt{2}} {2} }{ {sin(\frac{π}{16})}} \)

\(\displaystyle ≈ a·3.63\)

Diagonal \(d_5\) (5 corners)

\(\displaystyle d_5= a· \frac{sin(\frac{5 ·π}{16})}{sin(\frac{π}{16})} \)

\(\displaystyle ≈ a·4.26\)

Diagonal \(d_6\) (6 corners)

\(\displaystyle d_6= a· \frac{sin(\frac{6 ·π}{16})}{sin(\frac{π}{16})} \)

\(\displaystyle ≈ a·4.74\)

Diagonal \(d_7\) (7 corners)

\(\displaystyle d_7= a· \frac{sin(\frac{7 ·π}{16})}{sin(\frac{π}{16})} \)

\(\displaystyle ≈ a·5.03\)

Diagonal \(d_8\) (8 corners)

\(\displaystyle d_8= \frac{a}{sin(\frac{π}{16})} \)

\(\displaystyle ≈ a·5.13\)

Height \(h\)

\(\displaystyle h=d_7 \)

Inner radius \(ri\)

\(\displaystyle ri=a · \frac{1}{2}·cot\left(\frac{180°}{16}\right)\)

\(\displaystyle =a ·\frac{1}{2}·cot(11.25)\)

Outer radius \(ro\)

\(\displaystyle ri= \frac{a}{2·sin(\frac{180°}{16})} \)

\(\displaystyle = \frac{a}{2·sin(11.25)} \)

\(\displaystyle ≈\frac{a}{0.39} \)

Hexadecagon

Hexadecagon calculator

Formulas of the hexadecagon

More regular polygons