Polygon Area Calculator

How to calculate the area of a polygon

1. Choose the vertex format. Latitude, longitude; longitude, latitude; or projected X, Y in metres such as UTM. Pick the order your data uses.
2. Paste the vertices. One vertex per line, in order around the boundary (clockwise or counter-clockwise). You do not need to repeat the first point at the end. Click Load sample to see the format.
3. Click Calculate area. The area appears in all common units, with the perimeter, vertex count and the method used. Add a regional land unit to see the same area in bigha, biswa and similar units.
4. Copy or download. Copy the results or download them as a CSV.

How the area is calculated

• Latitude and longitude input. Each edge follows the geodesic (the shortest path on the ellipsoid) between its end points, and the enclosed area is summed exactly on the WGS84 ellipsoid. The page does not project to Web Mercator, which would inflate areas, and does not treat degrees as flat x and y.
• Projected X, Y input. For coordinates already in metres in a projected system such as UTM, the page applies the shoelace formula: area = ½ Σ (x_i y_i+1 - x_i+1 y_i). This gives the area on the projection's plane, which differs slightly from the true ground area by the projection scale.

Worked example

A rectangle in Jaipur with corners at 26.9124° N, 75.7873° E; 26.9124° N, 75.7913° E; 26.9094° N, 75.7913° E; and 26.9094° N, 75.7873° E:

area      132,075.68 m²  =  13.2076 ha  =  32.6366 acres
perimeter   1,459.48 m

In Rajasthan pucca bigha (27,225 sq ft) this is 52.22 bigha. A planar example: the X, Y vertices (0, 0), (100, 0), (100, 60), (0, 60) give 6,000 m² and a perimeter of 320 m.

Why not measure in degrees or Web Mercator

• A degree of longitude is not a fixed length. It shrinks with the cosine of the latitude, so a shoelace calculation on raw degrees is wrong everywhere except near the equator.
• Web Mercator (EPSG:3857, the map-tile projection) inflates area by 1/cos² of the latitude. At 27° N that is about 26% too much, and at 60° N four times too much.
• For survey-grade work, either use this geodesic calculation or measure in a UTM zone or other local projection.

Regional land units

Pick a region to see the area in local units. The page uses the same size table as the Unit Converter, for example Rajasthan pucca bigha = 27,225 sq ft and Uttar Pradesh western bigha = 27,000 sq ft. These units differ between states and sometimes between districts and between pucca and kachcha systems. Always check the size in your local revenue records before using the figure for a sale or a record.

Common mistakes

• Vertices out of order. If the outline crosses itself like a bow tie, the area nets the loops against each other. The page warns you; check the order of the points.
• Latitude and longitude swapped. Pick the right format in the first box. Longitude-first data pasted as latitude-first is rejected when the first value exceeds 90, and otherwise gives a wrong area.
• Mixing degrees and metres. Use the X, Y format only for coordinates in metres, and the latitude/longitude formats only for degrees.
• Expecting legal accuracy. The area is as good as the coordinates. GPS points taken by phone can be several metres off, which is a large share of a small plot.

What this calculator does and does not do

• One outline. It measures a single polygon without holes. To subtract a hole, calculate it separately and subtract.
• WGS84 only. Latitude and longitude are taken as WGS84.
• Accuracy. Against GeographicLib (through pyproj) on 150 random polygons from about 40 m to 600 km across, the largest area difference was 0.00002%.
• Size limit. Up to 50,000 vertices. The self-crossing check runs up to 3,000 vertices.
• Runs in your browser. No coordinates are sent to a server.

Related calculators

For the length of one edge use distance between coordinates. To convert the result between land units, see the Unit Converter and the guide bigha and katha to acres. To draw and measure on a map, see view and measure on a map.