When I was driving home from work today I noticed a for sale sign for a plot of land that said “+ or – 2.9 Acres.” It had me wondering how they came to that number. Im sure lots of plots of land for sale are sold in squares, but I live in a very old state so property lines must be all over the place.
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You hire a land surveyor. You should always get a survey done before you buy land or build anything permanent on your land.
Surveyors. It’s their job to figure out such things. They’ll review property lines, make sure they’re accurate, and from there it’s trivial to calculate the area of the property
Property lines can be all over the place. It’s the job of a surveyor to figure them out, mark them, measure them, and plot them. Once plotted, the drafting software can calculate the area of that plot. It used to be a manual process to draw the plot on paper and using geometry to estimate the area.
A surveyor performs a boundary survey, depending on the terrain and coverage, will generally traverse the lot and locate the corners(though these days it seems more prevalent to use gnss than traverse with a total station). Once they have verified the prop lines and corners these days they will toss the file into civil3d, Autocad, Carlson or whatever drafting software and it’ll comp the acreage for them. There is alot more leading up to “just surveying the lot” but this is a very diluted explanation
One method is to use the [surveyor’s formula](https://en.wikipedia.org/wiki/Shoelace_formula). This requires representing the plot boundary as a polygon (shape made of straight lines) and knowing the coordinates of the vertices (corners).
This formula doesn’t take the curvature of the earth into account so it would become less accurate for larger shapes. The simplest way around this is to first convert the coordinates to an equal-area map projection.
Another issue is that some surveying boundaries contain circular arcs instead of straight lines. One way to deal with this is to first replace each arc with a straight line joining its end-points and then use the surveyor’s formula. Afterwards you can add or subtract the area between the line and the arc which can be calculated using a different formula.
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