What coordinate format should I use?

Enter one pair per line, separated by a comma: "x, y" or "latitude, longitude". The order of coordinates within each pair should be consistent throughout.

Does the polygon need to be closed?

No. The tool automatically connects the last point back to the first point to close the polygon before computing the area.

What is the Shoelace formula?

The Shoelace (or Gauss) formula computes the area of a simple (non-self-intersecting) polygon from its vertex coordinates. It sums cross-products of consecutive vertex pairs and halves the absolute value.

How accurate is the geographic area conversion?

The geographic approximation treats 1 degree of latitude as ~111.32 km and adjusts longitude by the cosine of the mean latitude. It is suitable for small regions but not for continental-scale polygons.

Does this handle self-intersecting polygons?

The Shoelace formula only gives correct results for simple (non-self-intersecting) polygons. Self-intersecting polygons will produce an incorrect area.

What is the minimum number of points needed?

A polygon requires at least 3 points (vertices) to have a non-zero area.

Area By Coordinates

Name: Area By Coordinates
Availability: InStock
Author: Nham Vu

Enter a list of coordinate pairs (x/y or lat/lon) and instantly get the polygon area using the Shoelace formula.

Coordinates

One pair per line — "x, y" or "lat, lon"

Coordinate mode

Planar unit label

Result

Enter coordinates and press Calculate

Polygon Preview

Preview updates after calculating

Summary

Enter a list of coordinate pairs (x/y or lat/lon) and instantly get the polygon area using the Shoelace formula.

How it works

Enter one coordinate pair per line in the format "x, y" or "lat, lon".
The tool parses each pair and builds a polygon vertex list.
The Shoelace (Gauss) formula computes the signed area and returns the absolute value.
For geographic coordinates, the result is shown in both square degrees and approximate square kilometers.
The polygon preview updates live as you type, showing the shape on a canvas.

Use cases

Estimate the area of a parcel of land from surveyed corner coordinates.
Calculate the footprint area of a building or site from its corner points.
Verify polygon areas when working with GIS data outside a full GIS tool.
Quickly convert a list of GPS waypoints into an area estimate.
Compute area of an irregular shape drawn on a grid.
Check survey or CAD data for plausibility before importing.

Frequently Asked Questions

Last updated: 2026-06-24 · Reviewed by Nham Vu