📐 Irregular Polygon Area Calculator
Calculate area of any polygon using shoelace formula
Vertices (Points)
How to Use This Calculator
Enter Vertices
Input coordinates (x, y) of each vertex of the polygon. Enter at least 3 points. Add more points as needed.
Click Calculate
Press "Calculate Area" to find the polygon's area using the shoelace formula.
View Result
See the calculated area displayed in square units.
Formula
Shoelace Formula: Area = ½ |Σ(xᵢyᵢ₊₁ - xᵢ₊₁yᵢ)|
where (xᵢ, yᵢ) are vertices in order, wrapping around
Example: Triangle with vertices (0,0), (4,0), (2,3)
Area = ½ |(0×0 + 4×3 + 2×0) - (0×4 + 0×2 + 3×0)|
= ½ |12 - 0| = 6 square units
About Irregular Polygon Area Calculator
The Irregular Polygon Area Calculator uses the shoelace formula (Gauss's area formula) to calculate the area of any polygon given its vertices. It works for any polygon, regular or irregular, convex or concave.
When to Use This Calculator
- Geometry: Calculate areas of irregular shapes
- Land Surveying: Find area of plots with irregular boundaries
- Architecture: Calculate floor areas of irregular rooms
- Engineering: Measure areas in design and construction
- Mathematics: Practice shoelace formula applications
Frequently Asked Questions
What is the shoelace formula?
The shoelace formula (Gauss's area formula) calculates polygon area from vertex coordinates: Area = ½ |Σ(xᵢyᵢ₊₁ - xᵢ₊₁yᵢ)|. Vertices must be in order, clockwise or counterclockwise.
Does point order matter?
Yes! Vertices must be in order around the polygon. The absolute value in the formula ensures positive area regardless of orientation.
Can I use this for concave polygons?
Yes! The shoelace formula works for both convex and concave polygons. For concave polygons, the formula accounts for the "negative area" of indented regions.