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Area & Perimeter Calculator - Calculate Polygon Size

Geodesic polygon area calculator: WGS84 lat/lon or planar survey X/Y. Land parcel area, perimeter, Shoelace centroid in hectares, acres, m².

Geographic uses WGS84 lat/lon. Planar runs an exact Shoelace area on projected northing/easting (UTM, State Plane or local grid).

What is an Area & Perimeter Calculator?

An area and perimeter calculator computes the size and boundary length of a polygon from its vertex coordinates. This tool uses GPS coordinates (latitude/longitude) to calculate accurate area and perimeter measurements accounting for Earth's curvature.

Area and perimeter calculations are fundamental in land surveying, property measurement, agricultural planning, construction, urban planning, and geographic analysis. Accurate measurements are essential for legal documentation, resource allocation, and spatial planning.

  • Area Calculation: Compute polygon area in square meters, kilometers, acres, hectares, and square miles
  • Perimeter Calculation: Measure total boundary length in meters, kilometers, and miles
  • Centroid Location: Find the geometric center point of the polygon
  • Geodesic Accuracy: Uses great-circle distances for accurate real-world measurements

How to Use the Calculator

Follow these steps to calculate area and perimeter:

  1. Enter Vertices: Input latitude and longitude for each corner point of your polygon
  2. Add Points: Click 'Add Point' to add more vertices (minimum 3 required)
  3. Calculate: Press 'Calculate' to compute area, perimeter, and centroid
  4. View Results: See area in multiple units, perimeter, and centroid coordinates

Area Calculation Formula

The area is calculated using the spherical excess formula for geographic coordinates, which accounts for Earth's curvature:

A = R² |Σ (λ₂ - λ₁)(2 + sin φ₁ + sin φ₂)| / 2

Where R is Earth's radius (6,371 km), φ is latitude, and λ is longitude. This formula provides accurate results for polygons of any size, from small plots to large territories.

Common Use Cases

This calculator is valuable for:

  • Land Surveying: Measure property boundaries and land parcels for legal documentation
  • Agriculture: Calculate field sizes for crop planning, irrigation, and yield estimation
  • Real Estate: Determine property areas for listings, appraisals, and sales
  • Construction: Estimate material quantities and costs based on area measurements

Understanding Area Units

The calculator provides results in multiple units to suit different applications. Square meters (m²) and hectares are standard in most countries. Acres are commonly used in the US and UK real estate. Square kilometers are ideal for large areas like parks or forests.

Unit conversions: 1 hectare = 10,000 m² = 2.471 acres | 1 acre = 4,047 m² | 1 km² = 100 hectares = 247.1 acres

Geographic vs Planar (Survey) Mode

Use Geographic mode when your vertices are WGS84 latitude/longitude from GPS, Google Maps or a GeoJSON file; it integrates over the curved Earth with the spherical-excess formula. Use Planar mode when you hold projected survey coordinates — UTM, State Plane or a local site datum measured in northing/easting by total station or RTK GPS. Planar mode runs the exact Shoelace formula directly on the grid the survey was computed in, so the result matches the legal/deed value instead of forcing an error-prone unprojection back to lat/lon. Pick meters, international feet or the US survey foot for input; area is reported in m², ft², hectares, acres, km² and mi².

Worked example (planar, meters): a rectangle with corners (0,0), (50,0), (50,30), (0,30) gives a signed Shoelace area of +1500 m² (0.15 ha) and an area-centroid at X=25, Y=15. List the vertices in order around the ring — the polygon auto-closes (first vertex = last), so do not repeat the first point. A positive signed area means counter-clockwise (CCW) winding and a negative value means clockwise (CW); the tool takes the absolute value for area but shows the sign so you can verify ring orientation, which matters when exporting to GeoJSON (exterior rings must be CCW per RFC 7946).

Frequently Asked Questions

Because this tool integrates over the curved surface of the Earth using a spherical-excess (geodesic) formula on the WGS84 ellipsoid, while desktop GIS often projects coordinates first into a flat plane (UTM, State Plane, EPSG:3857 Web Mercator) and then runs a planar Shoelace formula. The two answers agree closely for small parcels far from the poles, but for large countries or polygons crossing many UTM zones the planar number can be off by several percent. Web Mercator in particular distorts area badly at high latitudes — Greenland appears the size of Africa. If you need a result that matches a legal survey, reproject to an equal-area CRS such as EPSG:6933 (NSIDC EASE-Grid 2.0) or a local Albers equal-area before comparing.

This calculator assumes WGS84 geographic coordinates (EPSG:4326), the same datum used by GPS receivers, Google Maps, OpenStreetMap, and almost every web map service. NAD83 differs from WGS84 by 1–2 meters in the continental United States, which is negligible for area calculations but can matter for survey-grade work; convert with a tool like GDAL or pyproj before entry. Local cadastral grids (British OSGB36, Australian GDA94/2020, Japanese JGD2011) need explicit transformation through a documented geoid model — do not paste their northing/easting values directly. UTM and MGRS are projected planar coordinates and must be unprojected to lat/lon first; our utm-mgrs-converter handles that conversion.

For polygons smaller than about 100 km on a side, the spherical approximation (Earth as a perfect sphere of radius 6371 km) differs from the ellipsoidal (WGS84) result by less than 0.3%. Vincenty's formulae use the actual flattening f = 1/298.257223563 and converge to millimeter accuracy for distances under 20,000 km. Karney's GeographicLib improves on Vincenty for nearly antipodal points where Vincenty can fail to converge. For a 1 km² urban parcel the difference is far below GPS precision (typically ±3 m horizontally). For a country-scale polygon the difference becomes meaningful and a proper geodesic library (PROJ, GeographicLib, Turf.js with a geodesic flag) is recommended.

Crossing the 180° meridian is the classic failure mode of every naive polygon algorithm. A polygon with vertices at longitudes 170°, 180°, and -170° looks gigantic if you treat longitude as a flat number — the algorithm thinks the shape wraps the whole planet. The correct fix is to detect crossings and add 360° to negative longitudes (or convert all to a 0–360° range), compute, then convert results back. GeoJSON RFC 7946 requires explicit polygon splitting at the antimeridian — Fiji and Russia must be encoded as multi-polygons. If your results look impossibly large for a small Pacific feature, the antimeridian is the culprit; split the polygon at 180° and recompute the two halves separately.

At the equator, one degree of latitude is about 111,320 meters, so one decimal place ≈ 11 km, four places ≈ 11 m, six places ≈ 11 cm, seven places ≈ 1.1 cm. For a 1-hectare farm plot, six decimal places give you sub-meter precision, which exceeds what consumer GPS can deliver. Pasting only four decimal places effectively quantizes your vertices into 11-meter steps and can produce area errors of a few percent on small parcels because each vertex may snap toward the wrong side. For large rural parcels (>1 km²) five decimals are plenty. For surveyor-style accuracy use eight decimals and an RTK GPS or total-station-derived coordinates.

The centroid is the geometric center of mass of the polygon — the point where the shape would balance on a pin if cut from uniform cardboard. For convex shapes (squares, regular hexagons, the contiguous USA outline) the centroid lies inside. For concave or non-simply-connected shapes — a crescent, a doughnut, the state of Florida if you include its panhandle — the centroid can fall outside the polygon boundary. That is mathematically correct, not a bug. If you need a guaranteed interior point for labeling, use a "point on surface" algorithm (Turf.js pointOnFeature, PostGIS ST_PointOnSurface) instead of the centroid. Centroid is computed here using the planar Shoelace centroid formula on the projected coordinates, then unprojected.

It should match almost exactly: 1 acre = 4046.8564224 m² = 0.40468564 ha. If your numbers diverge by more than 0.001 ha you are probably comparing two definitions of the acre. The international (US/UK statutory) acre is the standard, but the US survey acre, defined for legal land surveys from 1893 to 2022, is larger by 12.7 parts per million — about 0.013 m² on a 1-acre parcel, but 0.13 m² on a 10-acre parcel, which can be enough to trigger a deed discrepancy. The NIST retired the US survey foot in 2022, so all new US surveys should use the international foot/acre. For agricultural use the difference is irrelevant; for cadastral work, confirm which definition your jurisdiction requires.

The vertex list you paste can be exported manually as a GeoJSON Polygon feature: wrap the coordinates in {"type":"Polygon","coordinates":[[[lon,lat],...]]} — note that GeoJSON requires longitude first, latitude second, the opposite of how most humans write coordinates. The first and last coordinate must be identical to close the ring. Use our wkt-geojson-converter to translate to WKT POLYGON syntax for PostGIS or Spatialite, or our kml-gpx-geojson-converter to produce a .kml file that opens directly in Google Earth. ESRI shapefiles require a binary format with three associated files (.shp, .shx, .dbf) — convert your GeoJSON with GDAL/ogr2ogr or QGIS for that workflow.

Switch to Planar mode whenever your coordinates are already projected onto a flat grid — UTM easting/northing, US State Plane, a national grid, or a local site datum staked by total station or RTK GPS. In that mode the tool runs the exact planar Shoelace formula on the same grid the survey was computed in, so the area matches the legal/deed value to the millimeter and you avoid the lossy step of unprojecting grid coordinates back to lat/lon. Choose meters, the international foot (0.3048 m) or the US survey foot (1200/3937 m) for input; feet input adds a ft² area readout alongside m², hectares and acres. Two survey rules to remember: (1) Ring closure — list each vertex once, walking the boundary in order; the polygon closes automatically by joining the last vertex back to the first, so do NOT repeat the opening point. (2) Winding order — the tool reports a signed area so you can confirm orientation. A positive sign is counter-clockwise (CCW), negative is clockwise (CW). Area uses the absolute value, so a reversed ring still gives the correct magnitude, but GeoJSON RFC 7946 expects exterior rings CCW and interior holes CW, so check the sign before exporting. For Geographic mode, keep using WGS84 lat/lon.
Area & Perimeter Calculator - Calculate Polygon Size — Geodesic polygon area calculator: WGS84 lat/lon or planar survey X/Y. Land parcel area, perimeter, Shoelace centroid in
Area & Perimeter Calculator - Calculate Polygon Size
See also
Geography & Mapping ToolsGEOGRAPHY & MAPPING TOOLS21
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