Polygon Area Calculator (Coordinates)

How it is calculated

For vertices listed in order, the tool sums xᵢ × yᵢ₊₁ − xᵢ₊₁ × yᵢ over every edge, closing the shape by joining the last point back to the first, and takes area = |sum| ÷ 2. The perimeter is the sum of the straight-line edge lengths, √(Δx² + Δy²). Put one point per line or separate points with semicolons, with x and y split by a comma or a space. Lines that do not start with two numbers, such as a header, are skipped and do not stop the calculation. At least three points are needed. Area comes out in the square of the coordinate unit and perimeter in the coordinate unit itself. Clockwise or anticlockwise order gives the same area. The count of vertices used is also shown.

Common mistakes

• Listing the points in the wrong order, such as jumping across the shape. Points must follow the outline; with a crossed order like a bow tie the signed areas cancel, and the tool can report 0.00 for a non-empty shape.
• Repeating the first point at the end. The closing is automatic, and the extra copy is counted as another vertex, although the area and perimeter stay the same.
• Mixing units between coordinates, such as x in metres and y in feet. Every coordinate must use one unit, and the area is then in that unit squared.
• Using latitude and longitude directly. Degrees are not a flat grid, so convert to a projected system in metres first, or the area will not be in a usable unit.
• Applying it to shapes with holes or edges that cross. The formula gives the area of one simple outline only.