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Area By Coordinates Calculator

Work out area by coordinates instantly with clear inputs, formula shown and shareable results.

About Area By Coordinates Calculator

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.

Formula

Shoelace formula

Area = 0.5 x |sum of (xi yi+1 - xi+1 yi)| over all vertices, closing back to the first

Worked example

With the default values below, Area By Coordinates Calculator returns Enclosed area of 1,200.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Boundary coordinates as easting,northing pairs
0,0; 40,0; 40,30; 0,30
Scale factor applied to coordinatesminimum 0
1

Results

Enclosed area
1,200.0000 m²
Area in hectares
0.120000 ha
Boundary points used
4
Perimeter
140.0000 m

Step by step

  1. 1Values used
  2. 2Shoelace formula
  3. 3Enclosed area= 1,200.0000 m²
  4. 4Area in hectares= 0.120000 ha
  5. 5Boundary points used= 4
  6. 6Perimeter= 140.0000 m

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Area By Coordinates figure worked out?

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.

Does the order of points matter?

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.

What values do I need to enter?

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.

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