Calculadora de Área de Terreno Irregular
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
A = |Σ(xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)| / 2 (Shoelace 4 pontos)
About this calculator
This calculator determines the area of an irregular plot of land with four vertices using the Gauss formula, also known as the Shoelace formula. The method involves entering the coordinates (x, y) of each vertex in order (clockwise or counterclockwise) and applying the formula A = |Σ(xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)| / 2. The result is given in square meters, assuming coordinates are in meters.
To use the tool, input the coordinates of the four points that define the plot. The order of points must follow the perimeter without crossing edges. The calculator automatically performs the sum of cross products and divides by 2, providing the exact area. It is useful for non-rectangular plots, such as corner lots or rural areas.
Common use cases include property valuation, construction projects, land subdivisions, and land regularization. For example, when buying a lot with an atypical shape, the calculator helps verify the area stated in the deed. It is also used by surveyors and civil engineers for quick measurements.
Important precautions: coordinates must be accurate, preferably obtained via GPS or topographic survey. The order of vertices must be consistent (clockwise or counterclockwise) to avoid sign errors. The formula assumes the plot is a simple polygon without self-intersections. For plots with more than 4 sides, the formula must be adapted for additional points.
Frequently asked questions
Do I need to enter the coordinates in a specific order?
Yes, enter the vertices in order around the perimeter, either clockwise or counterclockwise, without skipping or crossing edges.
Does the calculator work for plots with more than 4 sides?
No, this version is for 4 vertices. For more sides, use a calculator that accepts N points.
What happens if I reverse the order of points?
The area will be the same, but the sign of the sum may flip. The absolute value corrects it, so the final result is correct.
Can I use measurements in feet or other units?
The calculator assumes coordinates are in meters. If using feet, the result will be in square feet; convert afterward.
Is the formula accurate for curved plots?
No, the Shoelace formula works only for polygons with straight sides. For curves, approximate with many points.