ENGINEERING – URVEYING & GEOMATIC CALCULATOR
Area By Coordinates
A precise tool.
What is the Area By Coordinates & How does it work?
The shoelace (or Gauss) formula provides a quick way to compute the area of a simple polygon when the vertex coordinates are known. By traversing the vertices in order, the cross‑product of successive coordinate pairs captures the signed area contribution of each edge. Because the formula sums the products of x‑coordinates with the next y‑coordinate and subtracts the opposite products, the result is twice the geometric area. Taking the absolute value and halving yields the true area, regardless of whether the vertices are listed clockwise or counter‑clockwise. In practice the method is ideal for surveying and GIS applications where field‑collected coordinate sets define land parcels, road alignments, or construction sites. The calculation can be performed instantly in a web widget once the coordinate list is supplied.
A = frac{1}{2}left|sum_{i=1}^{n} (x_i y_{i+1} – x_{i+1} y_i)right|
n = number of vertices
Parameters
Result
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Frequently Asked Questions
How do I use the shoelace formula to calculate the area?
List the coordinates in order, multiply each x-coordinate by the next y-coordinate and vice versa, sum the products, take the absolute value, and divide by two.
What is the shoelace formula used for?
The shoelace formula is used to calculate the area of a simple polygon when the vertex coordinates are known.
Can I use this formula for any type of polygon?
Yes, you can use the shoelace formula for any simple polygon (non-intersecting sides).
Why is it called the 'shoelace' formula?
It's called the shoelace formula because of the way you multiply and subtract the coordinates, similar to tying a shoelace.
How does the order of vertices affect the result?
The order of vertices matters as it affects the direction of traversal. Ensure they are listed in either clockwise or counterclockwise order.
What if I have a complex polygon with intersecting sides?
The shoelace formula does not work for complex polygons with intersecting sides; you would need to break it into simpler shapes first.
Can this formula be used in 3D space?
No, the shoelace formula is designed for 2D polygons. For 3D shapes, different methods are required.
Results are for informational purposes only and do not constitute professional advice.