Polygon coordinate area

Calculate simple planar polygon area, perimeter and centroid from ordered vertices, rejecting crossing boundaries.

Your input

Outputs are cleared when the input changes.

Result

Enter your data or use the example, then run the tool.

Worked example

(0,0),(2,0),(2,2),(0,2) give area 4, perimeter 8 and centroid (1,1).

Reversing vertex order changes orientation, while absolute area remains 4. Crossing bow-tie boundaries are rejected.

Method

The shoelace cross-product sum yields signed area; absolute area is reported alongside orientation.

Cross-product weighted coordinates give the centroid; edge lengths sum to perimeter. Non-adjacent edge intersections are checked.

Limits

Simple polygons only: no holes, self-intersections, zero-area shapes or consecutive duplicate vertices.

Coordinates are planar, not longitude/latitude. Floating-point arithmetic can be sensitive near collinearity; not a certified land survey.

Sources

MIT OpenCourseWare: shoelace formula

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