How to Calculate the Square Feet of Land for Irregular Lots

The area of an irregular polygon is calculated mathematically if the coordinates of all its vertices are known.
••• geisha réalisée avec les 7 pièces d'un tangram image by Unclesam from Fotolia.com

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.

Obtain X-Y Coordinates

    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.

    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).

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

Hand Method

    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.

    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.

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

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

    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.

Spreadsheet Method

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

    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

    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.

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

    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.

    Things You'll Need

    • GPS unit
    • Spreadsheet program (optional)

    Tips

    • To convert square meters to acres, multiply A by 0.000247105381.

    Warnings

    • Depending on the accuracy of your GPS unit, you may wish to make several methods at each vertex of the lot and average the coordinates.

Related Articles

How do I Find UTM Coordinates From a Street Address?
How to Calculate a Point Load
How to Convert My GPA From a 12-Point Scale to a 4-Point...
How to Calculate Your YTD GPA
How to Find Out My GPA Score at Home
How to Calculate the Square Meters in a Triangle
How to Calculate an Area in Square Meters
How to Convert 55 X 40 X 20 CM to Inches
How to Find the Slope in a Circle
How to Find the Area of a Parallelogram With Vertices
How to Calculate Acreage From Perimeter
How to Calculate the Acreage of a Triangle
How to Solve Slope-Intercept Form
How to Calculate Cubic Feet of a Cylinder
How to Calculate the Volume of Water to Fill a Rectangular...
How to Calculate a Circular Area
How to Find Linear Equations
How to Calculate the Perimeter of Quadrilaterals
How to Calculate a Semivariogram
How to Find the Circumference of a Circle