Work out area by coordinates instantly with clear inputs, formula shown and shareable results.
The shoelace or surveyor's formula computes the area of any simple polygon from its vertex coordinates: sum the cross products of consecutive points, halve the absolute value. It is exact for straight boundaries regardless of shape or convexity, which is why it underpins every cadastral area calculation and GIS polygon measurement.
Shoelace formula
Area = 0.5 x |sum of (xi yi+1 - xi+1 yi)| over all vertices, closing back to the first
Area = 0.5 x |sum of (xi yi+1 - xi+1 yi)| over all vertices, closing back to the first. The shoelace or surveyor's formula computes the area of any simple polygon from its vertex coordinates: sum the cross products of consecutive points, halve the absolute value.
The direction determines the sign, which is why the absolute value is taken. The points must be in sequence around the boundary though: listing them out of order gives a self-intersecting polygon and a meaningless area.
This calculator takes 2 inputs: Boundary coordinates as easting,northing pairs, Scale factor applied to coordinates. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.