Land Area Calculator

Deeds describe a plot in one of two ways. Either they list the corners as coordinates, or they walk you round the boundary leg by leg, giving a compass bearing and a length for each side. This Land Area Calculator takes either and returns the enclosed area.

Nothing here needs a regular shape. Five-sided plots, six-sided plots and plots where no two sides match all work the same way, because the maths underneath cares only about where the corners sit.

Worked Example: A Five-Corner Plot in Metres

Load Sample opens on corner coordinates: 0 | 0, 40 | 0, 40 | 25, 18 | 32, 0 | 25. That plot is a 40 by 25 rectangle with one corner cut back and another pushed out, and it comes to:

• 1,140 m² exactly, with a perimeter of 132.40 m
• 0.2817 acres, or 0.1140 hectares, or 12,270.86 ft²
• 17.0423 katha and 0.8521 bigha, on the 720 ft² katha the tiles name

Press it again and the same job arrives as a traverse instead: 90 | 40, 0 | 25, 270 | 40, 180 | 25, four legs that close back on the start and enclose 1,000 m².

How It Calculates an Irregular Boundary

The shoelace formula, which surveyors have used since long before computers: cross-multiply each corner with the next one round the boundary, add the lot up and halve it. A bearing-and-distance list is turned into coordinates first, stepping east by distance × sin(bearing) and north by distance × cos(bearing), then fed through the same sum. Order matters and direction does not, so listing corners clockwise and anticlockwise give the same answer, but hopping back and forth across the plot gives a crossed outline and an area smaller than the ground really holds.

Precision, Closure and Local Units

A traverse almost never closes perfectly on the ground, so the tool reports the gap and expresses it as a closure ratio: the sample traverse lands exactly on its start, while a survey that misses by 0.30 m over 450 m of walking reads 1 in 1,500. Anything looser than 1 in 5,000 is flagged amber rather than green. Areas are shown to four decimals, which for katha means you can see a quarter of a square metre move. Katha and bigha are the Bangladesh definitions and both shift by region, so the tile labels state what they assume rather than leaving you to guess. A row that is not two numbers is refused with “Row 2: write a corner as two numbers separated by a pipe, like 40 | 25.”