Calculate the area of any polygon using its vertices coordinates with this Polygon Area from Coordinates Calculator.
xᵢ, yᵢ = coordinates of vertices in order
This is the shoelace formula for polygons.
| Vertices | Area |
|---|---|
| (0,0),(4,0),(4,3),(0,3) | 12.000000 |
| (0,0),(5,0),(5,5),(0,5) | 25.000000 |
| (0,0),(6,0),(6,2),(3,4),(0,2) | 14.000000 |
| (1,1),(3,1),(4,4),(1,3) | 5.500000 |
| (0,0),(2,0),(1,3) | 3.000000 |
1. List vertices in order (x,y).
2. Apply the shoelace formula: Area = 0.5 × | Σ (xᵢ yᵢ₊₁ - xᵢ₊₁ yᵢ) |.
3. Sum all terms, take the absolute value, then multiply by 0.5.
This Polygon Area from Coordinates Calculator automatically computes the area using up to six decimal places. Useful for geometry students, engineers, and GIS applications.
• The shoelace formula is efficient for any simple polygon.
• Polygon area calculation is essential in mapping and architecture.
• Convex and concave polygons can be calculated differently.
• Coordinates must be listed in order (clockwise or counterclockwise).
• Many computer graphics libraries use this formula internally.