Heptagon calculator

This function calculates various parameters of a regular heptagon, a polygon with 7 vertices.

To perform the calculation, select the required parameter in the menu and enter its value. Then click the 'Calculate' button.

Properties of a regular heptagon

A heptagon is a geometric figure that belongs to the group of polygons. It is defined by seven points. If all seven sides are the same length, it is an equilateral heptagon. If all the angles at the seven corners are the same size, the heptagon is called regular.

The side bisectors, heights and angle bisectors all intersect at the center.

The sum of the interior angles of a regular heptagon is 900° (5 x 180°). This comes from a general formula for polygons, in which the number of vertices of the polygon is used as a variable \(n\):

\((n-2)· 180\ \ \ = (7-2) · 180 \ \ = 5 · 180 =900°\)

The value of an interior angle of 108° is therefore given by the formula:

\(\displaystyle \frac{180·(n-2)}{n} \ \ =\frac{180·(7-2)}{5} ≈ 128.57° \)

These two formulas apply to all regular polygons. The number of corners is used for n.

Formulas for the equilateral heptagon

Diagonal (\(\small{e}\))

\(\displaystyle e = \frac{a}{\displaystyle 2·sin\left(\frac{π}{2 · 7}\right)} \)

Diagonal (\(\small{f}\))

\(\displaystyle f = 2 · a · cos\left( \frac{n}{7}\right) \)

Height (\(\small{h}\))

\(\displaystyle h = \frac{a}{\displaystyle 2·tan\left(\frac{π}{2· 7}\right)} \)

Perimeter (\(\small{P}\))

\(\displaystyle P = 7·a \)

Area (\(\small{A}\))

\(\displaystyle A = \frac{7}{4} · a^2 · tan\left(\frac{450°}{7}\right)≈3.63391·a^2 \)

Circumcirle radius (\(\small{r_c\))

\(\displaystyle r_c = \frac{a}{\displaystyle 2·sin\left(\frac{π}{7}\right)} \)

Inner circle radius (\(\small{r_i}\))

\(\displaystyle r_i = \frac{a}{\displaystyle 2·tan\left(\frac{π}{7}\right)} \)

Angle (\(\small{\alpha}\))

\(\displaystyle α = \frac{5}{7}·180°≈128.57° \)