How To Calculate The Square Feet Of Land For Irregular Lots

Calculating the area of square or rectangular lots is a simple matter of multiplying the length times the width. A simple shape such as an "L" or a "T" that could be broken into smaller rectangles is slightly more difficult, but the smaller rectangles' areas are added together.

Calculating the area of a lot with many small sides that do not meet at right angles is not so simple. The area can be calculated with a general equation, however. This equation requires the coordinates (X-Y pairs) of each point along the edge of the polygon.

Step 1

Capture the X-Y coordinates of each point along the lot's perimeter. Walk the lot line with a GPS unit, pausing at each bend in the lot line to set a waypoint. Make certain that your GPS unit is capturing the UTM coordinates, which are X and Y measurements.

Step 2

Transfer the coordinates to a text file or to two columns on a spreadsheet. Verify which column is X coordinates (usually 6 digits) and which is Y coordinates (usually 7 digits).

Step 3

Close the line by repeating the first point in the line at the end of the list.

Step 1

Begin with the first point in the file. Multiply the X value of this point by the Y value of the next point, and subtract the value of the X value of the next point times the Y value of this point. This is the formula S = (Xi * Yi+1) – (Xi+1 * Yi). Record the result, S.

Step 2

Move to the next point in the list. Repeat the calculation: multiply the X value of this point times the Y value of the next point, and subtract the product of the X value of the next point multiplied by the Y value of this point. Record the result, S.

Step 3

Continue moving through the list of points until you have calculated the value of S for the next-to-last point.

Step 4

Sum all values of S and divide the total by 2. This is A, the area of the lot.

Step 5

Convert the area of the lot to square feet. Because UTM coordinates are in meters, the value of A is in square meters. To convert square meters to square feet, multiply A by 10.7639104.

Step 1

List the X coordinates in column A and the Y coordinates in column B.

Step 2

Type the following formula in cell C1: =(A1_B2)-(A2_B1) and press enter. The spreadsheet automatically calculates the value of S for the first point

Step 3

Copy the formula in C1 to the bottom of the list, less one row. Doing so calculates the value of S for each vertex of the lot's perimeter.

Step 4

Sum the list of values in column C and divide by 2. The result is A, the area of the lot.

Step 5

Convert the area of the lot to square feet. Because UTM coordinates are in meters, A is in square meters. To convert square meters to square feet, multiply A by 10.7639104.