Polygon geometry workspace
Calculate polygon area, perimeter and centroid from ordered vertices. Find crossing or overlapping edges and download the drawing and coordinates.
Enter 3 to 300 ordered vertices in one coordinate system. Each coordinate must be finite with magnitude no greater than 1,000,000,000. Use a decimal point, with one X,Y pair per line or a JSON array. The closing edge is added automatically; a repeated closing vertex is accepted. Adjacent duplicate vertices are rejected. Calculations are approximate and use scale-dependent tolerances. Area and centroid are not assigned to self-crossing or overlapping paths because their filled region depends on a fill rule. Zero-area paths have no centroid. Positive Y points up. Enter one X,Y pair per line, or paste a JSON array. Use a decimal point. The final edge closes automatically. Up to 200,000 characters. Review the settings before running.
Your result
How to use Polygon geometry workspace
- Enter the polygon vertices in boundary order, one X,Y pair per line. You may include the first point again at the end.
- Check the drawing and edge intersections. A simple polygon has an area and centroid; intersecting paths do not receive a fabricated filled area.
- Download complete JSON, all vertices as CSV, or the SVG diagram.
Useful next steps
Vertex order defines the boundary
The calculator connects each point to the next, then closes the final edge. It does not sort points or invent a boundary for an unordered point cloud. A rectangle with points (0,0), (4,0), (4,3), (0,3) has area 12, perimeter 14 and centroid (2,1.5).
Crossing paths need a different area definition
A self-crossing path can represent different regions depending on its fill rule. This tool reports crossing and overlapping edge pairs and draws them, but leaves area and centroid undefined. For a concave simple polygon, the centroid can lie outside its boundary.
One unit, approximate arithmetic
Use the same coordinate unit throughout. Perimeter uses that unit; area uses its square. Raw downloads preserve computed numbers while displayed results follow your language’s number format. Very small features compared with the coordinate span may fall within the numerical tolerance.