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The **Polygon Calculator** provides equations that compute the area, the length of sides, and the perimeters of various regular polygons.

**Polygon Area:** - This tab contains equations for computing the area of a regular polygon:

- Polygon Area from the Number of sides and Length of Sides
- Polygon Area from the Number of Sides and Outside Radius
- Area of a Polygon Segment (triangle) from the Number of Sides and Inscribed Radius
- Polygon Area from the Number of Sides and Inscribed Radius.

**Polygon Side:** - This tab contains equations for computing the length of the sides of a regular polygon:

- Length of a Polygon Side from the Number of Sides and Outer Radius
- Length of a Polygon Side from the Number of Sides and Inner Radius

**Polygon Perimeter:** - This tab contains equations for computing the perimeter of a regular polygon:

- Perimeter of a Polygon from Number of Sides and Length of Sides
- Perimeter of a Polygon from Number of Sides and Outer Radius
- Perimeter of a Polygon from Number of Sides and Inner Radius

A **regular polygon** is a polygon with n equal length sides. A **regular polygon** also has **n** equal angles at the **n** vertices of the polygon. Because of the symmetry of the regular polygon, all the vertices of the polygon can be constructed to touch a circle in which the regular polygon is inscribed and all the chords that are polygon sides will then obviously be of equal length . Likewise, because of the regular polygon's symmetry, a circle constructed to be inscribed in a regular polygon and touching the polygon will touch the regular polygon at the midpoint of the polygon side. As shown in the pictures, Figure 1 and Figure 2, lines from the regular polygon's vertices to the circle's center form **n** isosceles triangles of equal area.

- Area of a Polygon based on the length and number of sides.
- Area of a Polygon based on the number of sides and the outer radius.
- Area of a Polygon based on the number of sides and the inner radius.
- Perimeter of a Polygon based on the number and length of sides.
- Perimeter of a Polygon based on the number of sides and the outer radius.
- Perimeter of a Polygon based on the number of sides and the inner radius.
- Length of a Polygon Side based on Circumscribed Circle Radius
- Length of a Polygon Side based on Inscribed Circle Radius