CalcLibrary

Polygon Area by Coordinates Calculator

Enter ordered x/y corners for an irregular polygon and get one planar area and perimeter answer, plus a point-by-point check of the outline you actually entered.

Examples

Room bay with one angled wall

A five-corner room outline measured in meters.

Length unit
Meters (m)
Ordered points
0;0 6;0 7.5;3 3;5.5 0;4
Area
31.125 m²
Perimeter
21.856 m
Vertex count
5

Examples

Room bay with one angled wallA five-corner room outline measured in meters.31.125 m²
Garden bed with offsetsA compact landscape shape entered in feet, in walking order.66 ft²
Panel sketch with negative coordinatesA CAD-style shape that crosses quadrants but stays in one flat plane.25.5 cm²

How It Works

Formula

A=12∣∑i=1n(xiyi+1−yixi+1)∣A = \frac{1}{2}\left|\sum_{i=1}^{n}(x_i y_{i+1} - y_i x_{i+1})\right|

P=∑i=1n(xi+1−xi)2+(yi+1−yi)2P = \sum_{i=1}^{n} \sqrt{(x_{i+1}-x_i)^2 + (y_{i+1}-y_i)^2}

Variables

xix_i

x-coordinate of vertex i

yiy_i

y-coordinate of vertex i

AA

Polygon area

PP

Polygon perimeter

nn

Number of vertices

Enter the vertices in boundary order around one flat outline. The calculator connects each point to the next, closes the last point back to Point 1, adds every straight-line edge for perimeter, and applies the shoelace formula for area. The headline area is shown as an absolute value so clockwise and counterclockwise entry agree on magnitude.

Frequently Asked Questions

01Why does point order matter if the area is absolute?
The calculator reports the absolute area so clockwise and counterclockwise entry give the same magnitude. Order still matters because the outline itself changes when points jump across the shape or self-intersect.
02Why does the calculator close the polygon automatically?
A polygon is a closed outline. The final side always runs from the last entered point back to Point 1, so the perimeter and area both include that closing edge.
03Can I use latitude and longitude here?
No. This tool expects planar x/y coordinates in one consistent length unit. If your data comes from GPS or a map, convert it to a projected planar coordinate system first.
04How is this different from distance, triangle, or regular polygon calculators?
Distance between two points solves one segment, triangle solvers assume exactly three corners, and regular polygon tools assume equal sides and angles. This calculator handles one arbitrary ordered outline with any number of vertices.
05Is this suitable for legal survey work?
No. It is a planar geometry worksheet for checking the coordinates you already have. It does not certify boundaries, replace a survey, or infer any accuracy beyond your own inputs.

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