Polygon Area Calculator
Calculate the geographic area and perimeter of any polygon from coordinates or map drawing. Accurate spherical polygon mathematics on Earth's surface.
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How to Calculate Polygon Area
The geometry of computing spherical polygon area from geographic vertices.
Using Latitude and Longitude Coordinates
A geographic polygon is defined as an ordered sequence of vertices: [P₁, P₂, P₃, ... Pₙ], where each point consists of a latitude and longitude coordinate on the WGS 84 reference ellipsoid.
To calculate the area, the boundary ring is closed by connecting Pₙ back to P₁. You can input coordinates manually by pasting them into the coordinate input panel or click on the map.
Geographic vs. Flat-Surface Area
On a flat plane, polygon area is solved with the classical Shoelace formula. However, on the spherical Earth, degrees of longitude converge towards the poles (1° of longitude is ~111 km at the equator but shrinks to 0 km at the poles).
GeoTool uses spherical excess formulas with Turf.js, ensuring that polygons at high northern or southern latitudes are measured with high geographic accuracy without projection distortion.
Polygon Perimeter Mathematics
How linear boundary distances are calculated along geodesic arcs.
The perimeter of an n-sided polygon on Earth's surface is the sum of the great-circle arc lengths between each consecutive vertex:
Where d(Pₐ, P_b) is the geodesic distance computed via spherical trigonometry (the Haversine or Vincenty formula). GeoTool automatically converts the perimeter into kilometers, miles, meters, and feet.
GeoTool provides geographic area estimates for mapping, planning, and research. It is not a substitute for a licensed land survey or legal boundary determination.
Frequently Asked Questions
Common questions regarding polygon geometry and coordinate calculations.
How do I calculate polygon area using coordinates?
Click 'Enter or Paste Coordinate Points' in the controls, paste your list of decimal degree coordinate pairs (latitude, longitude), and click 'Plot & Calculate Area'. The tool plots the shape and computes the spherical polygon area.
What is the minimum number of vertices required?
A polygon requires at least 3 distinct non-collinear vertices to enclose an area (forming a triangle). You can add dozens or hundreds of vertices for complex boundaries.
Does the order of vertices matter?
Yes. Vertices must be arranged in sequence around the perimeter (clockwise or counterclockwise). If points are ordered randomly, the polygon edges may self-intersect, creating an irregular complex shape.
How is spherical polygon area calculated?
GeoTool computes spherical excess on the WGS 84 ellipsoid via Turf.js. Each spherical triangle component is integrated across the curved Earth surface, providing accurate results across all latitudes.
How is polygon perimeter calculated?
The perimeter is computed as the sum of great-circle geodesic distances between consecutive vertices, plus the closing line between the final vertex and the initial vertex.
Can I export or copy the vertex coordinates?
Yes. In the results panel, expand 'Inspect All Vertex Coordinates' and click 'Copy All Coordinates' to copy the formatted WGS 84 coordinate list for use in GIS software, spreadsheets, or GPS devices.
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