Polygon Area Calculator

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. For a hexagon of side 2 that works out to 10.392305 square units.

It finds a polygon's area from its corner coordinates by cross-multiplying each point with the next, summing those products, then halving the absolute value of the total. The name comes from the crisscross pattern of the multiplications, like lacing a shoe.

List the corners in sequence around the shape, either clockwise or counter-clockwise. Both directions give the same positive area because the tool takes the absolute value. Points listed out of order can produce a self-crossing shape and a wrong area.

Put one point per line as two numbers, separated by a comma, space or tab, for example 4, 0 or 4 0. Blank lines are ignored, and each line must contain exactly two finite numbers.

Yes. The shoelace method works for any simple polygon, convex or concave, as long as the edges do not cross themselves. That makes the coordinates mode suitable for irregular land plots and free-form outlines.

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, and a hexagon of side 2 has an apothem of about 1.732051.

Each interior angle equals the number of sides minus two, times 180 degrees, divided by the number of sides. A triangle gives 60 degrees, a square 90, a pentagon 108 and a hexagon 120.

The results are unitless, matching whatever unit you enter. If side lengths are in centimeters the area is in square centimeters; if the coordinates are in meters the area is in square meters.

Yes. Both the regular formula and the shoelace calculation run in your browser, so the dimensions and coordinates you enter are never uploaded.