Polygon Area Calculator
Compute the area of a regular polygon from the number of sides and the side length, or the area of any polygon by entering its corner coordinates.
How to find the area of a polygon
- For a regular polygon, enter the number of sides and the side length.
- Read the area, perimeter, apothem and interior angle.
- For an irregular shape, switch to coordinates and list the corners in order.
Examples
Regular hexagon, side 2
sides = 6, side length = 2
area = 10.392305, interior angle = 120
Square by coordinates
(0,0) (4,0) (4,4) (0,4)
area = 16
Frequently asked questions
What is the formula for a regular polygon's area?
The area equals one quarter times the number of sides times the side length squared times the cotangent of pi divided by the number of sides.
What is the shoelace formula?
It finds a polygon's area from its corner coordinates by cross-multiplying neighbouring points, summing, then halving the absolute value of the total.
Does the order of coordinates matter?
List the corners in order around the shape, either clockwise or counter-clockwise. Both directions give the same positive area.
What is the apothem?
The apothem is the distance from the center of a regular polygon to the midpoint of a side. It equals the side length divided by twice the tangent of pi over the number of sides.
What is the interior angle of a regular polygon?
Each interior angle equals the number of sides minus two, times 180 degrees, divided by the number of sides. A hexagon gives 120 degrees.
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