`A = n * r^2*tan(pi/n)`

Enter a value for all fields

The Area of Polygon from Number of Sides and Inner Radius calculator computes the area of a regular polygon of n sides circumscribed around a circle of radius r.

INSTRUCTIONS: Choose units and enter the following:

• (n)  Number of Sides
• (r)  Inner Radius.  The radius of the circle inscribed inside the polygon

Polygon Segment Area (A): The calculator returns the area in square meters.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The formula for the area of a regular polygon based on the number of sides and the inner radius is:

        `A =  n * r^2*tan(pi/n)`

where:

• A = area of polygon
• n = number of sides
• r = inner radius

Polygon Calculators

• Polygon Area from Number of Sides and Length of Sides
• Polygon Area from Number of Sides and Outer Radius
• Area of Polygon Segment from Number of Sides and Inner Radius
• Area of Polygon from Number of Sides and Inner Radius
• Length of the Sides of a Polygon based on the Outer Radius and Number of Sides
• Length of a Side of a Polygon from Inner Radius and Number of Sides
• Perimeter of a Polygon from Number of Sides and Length of Sides
• Polygon Perimeter from Outer Radius and Number of Sides
• Polygon Perimeter from Inner Radius and Number of Sides
• Polygon Perimeter from the Area and Number of Sides