Polygon Area (Coordinates)
Area, perimeter and centroid from vertex coordinates. Results update as you type.
Enter dimensions
Results
Enter your dimensions above and the results appear here.
About the Polygon Area (Coordinates)
The polygon area (coordinates) is a free online tool: area, perimeter and centroid from vertex coordinates. Enter vertices (P) and the results update instantly, alongside a labelled diagram so you always know which measurement goes where.
It runs entirely in your browser, so nothing you type is uploaded or stored. Use the share button to copy a link that restores your exact inputs.
Polygon Area (Coordinates) example
Vertices (P) = 0, 0; 8, 0; 8, 5; 4, 8; 0, 5Area = 52 cm²
Perimeter = 28 cm
Centroid = (4, 3.3076923)
Vertices = 5
Shape = Convex
Vertex order = Counter-clockwiseHow to use the Polygon Area (Coordinates)
- Enter vertices (P). Focus a field to highlight the matching label on the diagram.
- Read the results as you type. The largest card is the main answer; the others are the related measurements.
- Copy a single value, copy everything, or share a link that keeps your inputs.
Polygon Area (Coordinates) FAQ
What formulas does the polygon area (coordinates) use?
Shoelace: A = ½ |Σ (xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|; Cx = Σ (xᵢ+xᵢ₊₁)(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ) / 6A.
In what order should I list the points?
In order around the outline, clockwise or counter-clockwise. Do not jump across the shape, or the edges will cross and the area will be wrong.
Can I use different units?
Yes. Pick the input unit and, if you like, a different output unit. Area results are shown in squared units and volumes in cubed units.
Is this polygon area (coordinates) free and private?
Yes. It is free with no sign-up, and calculations happen on your device, so your numbers are never sent to a server.
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