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Polygon Area Perimeter Calculator - Calculate Area Online

Free polygon calculator: calculate area, perimeter, and centroid of any polygon. Draw on map, import GeoJSON/WKT, get results in multiple units instantly.

What is a Polygon Calculator?

A polygon calculator is a GIS tool that computes geometric properties of polygons including area, perimeter, centroid (center point), and bounding box. This tool supports both manual input (GeoJSON/WKT) and interactive drawing on a map.

Polygon calculations are essential in surveying, land management, urban planning, agriculture, environmental studies, and geographic analysis. Accurate measurements help in property valuation, resource management, and spatial planning.

Key features:

  • Area Calculation: Compute polygon area in various units (m², km², acres, hectares)
  • Perimeter Calculation: Measure boundary length in meters, kilometers, miles, or feet
  • Centroid: Find the geometric center of the polygon
  • Interactive Drawing: Draw polygons directly on the map
  • Multiple Formats: Support for GeoJSON and WKT input formats

How to Calculate Polygon Area

There are two methods to calculate polygon area:

  • Manual Input: Paste GeoJSON or WKT polygon coordinates
  • Interactive Drawing: Click on map to draw polygon vertices

The calculator uses geodesic calculations to account for Earth's curvature, providing accurate measurements for large polygons. For smaller areas, the tool automatically adjusts for local coordinate systems.

Area calculation formula depends on the coordinate system. For geographic coordinates (latitude/longitude), the tool uses spherical geometry formulas. For projected coordinates, it uses planar geometry.

Understanding Polygon Perimeter

Perimeter is the total length of the polygon boundary. It's calculated by summing the distances between consecutive vertices along the polygon edge.

For geographic polygons (lat/lon coordinates), the tool uses the Haversine formula to calculate geodesic distances, accounting for Earth's spherical shape. This ensures accuracy for large-scale measurements.

Common Use Cases

Polygon calculations are used in various fields:

  • Land Surveying: Measure property boundaries and land parcels
  • Agriculture: Calculate field sizes for crop planning and yield estimation
  • Urban Planning: Analyze zoning areas and development sites
  • Environmental Studies: Measure forest coverage, water bodies, and protected areas
  • Real Estate: Calculate property sizes for listings and valuations
  • Construction: Estimate material quantities based on area measurements

Area and Perimeter Units

The calculator supports multiple units for flexibility:

Area units:

  • Square Meters (m²): Standard metric unit
  • Square Kilometers (km²): For large areas like cities or parks
  • Hectares (ha): Common in agriculture (1 ha = 10,000 m²)
  • Acres: Common in US/UK (1 acre = 4,047 m²)
  • Square Miles (mi²): For very large areas

Distance units: meters, kilometers, miles, and feet are available for perimeter measurements.

What is Centroid?

The centroid (also called geometric center or barycenter) is the arithmetic mean position of all points in the polygon. It represents the balance point where the polygon would be perfectly balanced if made of uniform material.

Note: For concave or complex polygons, the centroid might fall outside the polygon boundary. The centroid is different from the center of the bounding box, which is simply the midpoint of the extent.

Frequently Asked Questions

The Shoelace formula, named for the criss-cross pattern of its computation and credited to Carl Friedrich Gauss in 1795 (and independently to Albrecht Meister in 1769), computes the signed area of any simple polygon directly from its vertex coordinates without triangulation. The formula is A = ½ |Σ (xᵢ · yᵢ₊₁ − xᵢ₊₁ · yᵢ)|. It runs in O(n) time, handles convex and concave shapes uniformly, and returns a negative value if vertices are wound clockwise (positive for counter-clockwise) — which is how GIS systems detect ring orientation. The unsigned absolute value gives the area regardless of winding. The formula assumes planar Cartesian coordinates, so for geographic lat/lon you must project first (UTM, Albers, Lambert) to avoid the distortion from treating degrees as flat units.

A self-intersecting (complex) polygon — like a bowtie or figure-eight — violates the simple-polygon assumption of the Shoelace formula and returns a meaningless "net" area where some regions cancel out. Robust implementations test for edge intersections in O(n log n) with the Bentley–Ottmann sweep-line algorithm and either flag the polygon as invalid, decompose it into simple sub-polygons, or return an error. GeoJSON RFC 7946 explicitly disallows self-intersection. PostGIS provides ST_IsValid and ST_MakeValid to detect and repair these cases. If your area result looks far too small for the visible polygon, suspect a self-intersection — plot the vertices in order and look for crossing edges. Our geojson-validator-repair tool can identify and fix these geometry errors.

The convex hull is the smallest convex polygon that contains all given points — like stretching a rubber band around them. Andrew's monotone chain or the Graham scan computes it in O(n log n). A concave (or "alpha") hull tracks the true outline more tightly, allowing inward dents to form: this is what you want for outlining a city from its building footprints, or a coastline from sample points. Alpha shapes, introduced by Edelsbrunner in 1983, use a parameter α that controls how aggressive the inward concavity becomes — small α gives a tight outline approaching the original points, large α approaches the convex hull. For most real-world boundary estimation, alpha = 1/(average nearest-neighbor distance) is a good starting point. Convex hull is simpler and uniquely defined; concave hulls require tuning.

For a polygon treated as a uniform-density 2D shape, the centroid equals the center of mass and is computed as the area-weighted average of the centroids of its constituent triangles (or directly via the extended Shoelace centroid formula). For a non-uniform distribution — say a population-weighted "center" of a country — you instead compute Σ(xᵢ · wᵢ) / Σwᵢ over discrete sample points with weights wᵢ. The US Census Bureau publishes a "mean center of US population" each decade computed this way; it has moved steadily west and slightly south since 1790. The geometric centroid of the polygon and the population centroid can differ by hundreds of kilometers — Alaska's geometric centroid is far from where most Alaskans live.

A polygon with holes is encoded in GeoJSON as multiple linear rings: the first ring is the outer boundary (counter-clockwise per RFC 7946), and each subsequent ring is an inner hole (clockwise). The total area is the outer ring's Shoelace area minus the sum of the inner rings' areas. For perimeter, you sum the outer boundary length plus all inner boundary lengths (because they are physical boundaries of the region). The centroid of a polygon with holes uses the weighted-area formula with inner rings contributing negatively. South Africa with the Lesotho exclave, Italy with the Vatican and San Marino, and any lake-on-island-in-lake topology require this multi-ring encoding. Make sure your input data respects the ring-orientation convention or compute it and flip if needed.

The classic point-in-polygon test is ray casting: draw a horizontal ray from the test point to +∞ and count how many polygon edges it crosses. Odd count means inside, even means outside. This works for any simple polygon, convex or concave, in O(n) per query. Edge cases — ray passing exactly through a vertex, or along an edge — must be handled with consistent rules (e.g., count an edge only if it crosses below the test point) to avoid double-counting or missing. The winding-number algorithm is an alternative that counts how many times the polygon's boundary winds around the test point and is more robust for self-intersecting polygons. For high-throughput queries, pre-index with an R-tree (Shapely's STRtree, PostGIS GiST index) to skip polygons whose bounding box does not contain the point.

Douglas–Peucker (1973) reduces the number of vertices in a polyline or polygon while keeping its overall shape within a tolerance ε. It works recursively: find the vertex farthest from the line between the start and end points; if its distance exceeds ε, keep it and recurse on the two halves; otherwise drop all intermediate vertices. The result is the polyline approximation with the fewest vertices that stays within ε of the original. It is the algorithm behind Shapely's simplify(tolerance), PostGIS ST_Simplify, and Mapshaper's default. It is fast but does not preserve topology — adjacent polygons may simplify to overlap or develop gaps. For topology-preserving simplification (essential for political boundaries), use Visvalingam–Whyatt or the topology-aware modes in TopoJSON / Mapshaper.

GPS-derived polygons typically suffer from positional noise (±3 m for consumer GPS, ±0.5 m for SBAS-corrected, sub-cm for RTK) which adds zig-zag jitter to what should be straight edges. A long straight fence sampled every 1 meter with ±3 m noise has a measured perimeter much longer than the true length because every wiggle adds path. The fix is post-processing: simplify the polygon with Douglas–Peucker at a tolerance matched to your GPS error (e.g., 5 m), or apply a Kalman filter or moving-average smoother to the raw track first. Survey-grade GPS or differential corrections collapse this problem. For walking-surveyed boundaries, also account for the surveyor not walking exactly on the boundary — corner snapping and inset can introduce systematic perimeter inflation.
Polygon Area Perimeter Calculator - Calculate Area Online — Free polygon calculator: calculate area, perimeter, and centroid of any polygon. Draw on map, import GeoJSON/WKT, get re
Polygon Area Perimeter Calculator - Calculate Area Online
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