Free Heptagon Calculator

What Is a Heptagon?

A heptagon is a polygon with seven sides and seven interior angles. The term originates from the Greek “hept-” and the Latin “sept-,” both meaning seven. When all sides and angles are equal, the heptagon is called a regular heptagon. This online heptagon calculator is designed to compute key parameters for a regular heptagon, including side length (a), perimeter (P), area (A), interior angle ($\alpha$), exterior angle ($\beta$), circumradius (R), and apothem (or inradius, r). It serves as a complete 7 sided polygon calculator for anyone needing quick and accurate geometry results.

Formulas for a Regular Heptagon

For a regular polygon with $n$ sides, the interior angle and exterior angle are:

$$\alpha = \frac{(n-2) \times 180^{\circ}}{n}, \quad \beta = \frac{360^{\circ}}{n}$$

For $n=7$:

$$\alpha = \frac{5 \times 180^{\circ}}{7} \approx 128.57^{\circ}, \quad \beta = \frac{360^{\circ}}{7} \approx 51.43^{\circ}$$

The perimeter is simply seven times the side length:

$$P = 7a$$

The area of a regular heptagon can be expressed using the side length and the cotangent function:

$$A = \frac{7}{4} a^{2} \cot\!\left(\frac{\pi}{7}\right)$$

A practical approximation often used for a heptagon area calculator is:

$$A \approx 3.634\,a^{2}$$

The heptagon circumradius (radius of the circumscribed circle) is:

$$R = \frac{a}{2 \sin\!\left(\pi/7\right)}$$

The heptagon apothem (radius of the inscribed circle, also called inradius) is:

$$r = \frac{a}{2 \tan\!\left(\pi/7\right)}$$

These formulas allow you to obtain any of the heptagon’s geometric properties from a single known side length.

How to Use the Heptagon Calculator

Using this tool is straightforward. Let’s work through an example with a side length of 8 cm.

1. Enter the side length: Set $a = 8\ \text{cm}$ in the calculator.
2. Review the perimeter: The tool automatically computes $P = 7 \times 8 = 56\ \text{cm}$.
3. View the area: Using the formula, $A = 3.634 \times 8^{2} \approx 232.58\ \text{cm}^{2}$.
4. Check the angles: The interior and exterior angles are shown as $128.57^{\circ}$ and $51.43^{\circ}$ respectively.
5. Obtain the radii: The circumradius $R$ and apothem $r$ are also calculated from the side input.

The calculator instantly updates all outputs as you change the side length, making it easy to explore different sizes of regular heptagons.

Beyond a Single Shape

This tool is not limited to heptagons. By selecting the “Try other regular polygons” option, you can adjust the number of sides and compute the same set of parameters for any regular polygon. This flexibility transforms the calculator into a general-purpose regular polygon side and area tool.

Whether you need a quick area check, a heptagon perimeter verification, or a deeper investigation into heptagon angles, this heptagon area and perimeter online resource delivers precise results without manual formula work.