Computing area from a metes-and-bounds description
The area stated in a description should match the area of the figure its calls describe. Computing it yourself is a quick check on both the calls and the stated acreage.
From calls to coordinates
Start at the point of beginning with any convenient coordinates, such as 0, 0. Each course adds its latitude to the northing and its departure to the easting, which gives coordinates for every corner. The closure guide shows how to compute latitudes and departures.
The coordinate (shoelace) method
With corner coordinates (E₁, N₁), (E₂, N₂), … (Eₙ, Nₙ) taken in order around the tract, the area is:
Area = ½ × | Σ (Eᵢ × Nᵢ₊₁ − Eᵢ₊₁ × Nᵢ) |
with the last corner wrapping around to the first. The name comes from the criss-cross pattern of the multiplication when the coordinates are written in two columns. The sign of the sum tells you which way the description runs: positive for counterclockwise and negative for clockwise.
Adding the curves
The shoelace formula treats every curve as its chord. To correct for that, add or subtract the circular segment between each chord and its arc:
Segment area = R² ÷ 2 × (Δ − sin Δ), with Δ in radians
Whether a segment adds or subtracts depends on which way it bulges. A segment that bulges outward from the tract adds area, and one that bulges inward subtracts it. For a description that runs clockwise, that means curves to the right add and curves to the left subtract.
Square feet to acres
One acre is 43,560 square feet, so divide square feet by 43,560. A tract of 59,014 square feet is 1.355 acres.
When the description doesn't close
If the description misses its point of beginning, the computed area is for the figure closed straight back to the POB. A small misclosure barely changes the area, but a blunder can change it a lot. Fix the closure first, then compare the area with the stated acreage.