Polygon Calculator

vCalc Reviewed
Calculator / Last modified by KurtHeckman on 2019/01/24 01:57
Polygon Area
Polygon Area from Sides and Length
Polygon Area from Sides & Outer Radius
Segment Area from Sides and Inner Radius
Polygon Area from Sides and Inner Radius
Side Length from Number and Outer Radius
Side Length from Number and Inner Radius
Perimeter from Sides and Length
Perimeter from Sides and Outer Radius
Perimeter from Sides and Inner Radius

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

Calculator Tabs

polygon inscribed in circle.png
regular polygon segment circumscribed on circle.png        Figure 2: Inner Circle and Segment

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

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

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

Description

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.

See also