Area of Irregular Shape Calculator
Calculate the area and perimeter of any irregular polygon using the Shoelace formula. Enter up to 6 vertices (x,y coordinates). Find centroid, convert to acres/hectares, and apply a scale factor.
Area (square units)
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Perimeter —
Centroid X —
Centroid Y —
Extended More scenarios, charts & detailed breakdown ▾
Area
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Perimeter —
Professional Full parameters & maximum detail ▾
ft/unit
Area (sq units)
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Area (scaled ft²) —
Area (acres) —
Area (hectares) —
Perimeter —
Centroid X —
Centroid Y —
How to Use This Calculator
- Enter the x,y coordinates of each vertex of your polygon (4 points minimum).
- Enter points in order (clockwise or counter-clockwise) around the polygon.
- Results show area in square units, perimeter, and centroid location.
- Use the Professional tab to apply a scale factor and convert to acres or hectares.
Formula
Shoelace Formula: Area = |Σ(x_i × y_{i+1} − x_{i+1} × y_i)| ÷ 2
Perimeter = Σ √((x_{i+1}−x_i)² + (y_{i+1}−y_i)²)
Centroid = (Σ(x_i+x_{i+1})(x_i×y_{i+1}−x_{i+1}×y_i)) / (6A)
Example
Example: Quadrilateral with points (0,0), (4,0), (5,3), (1,3). Shoelace sum = |0×0−4×0 + 4×3−5×0 + 5×3−1×3 + 1×0−0×3| = |0+12+12+0| = 24. Area = 24÷2 = 12 sq units.
Frequently Asked Questions
- The Shoelace formula calculates the area of any polygon from its vertex coordinates: Area = |Σ(x_i × y_{i+1} − x_{i+1} × y_i)| ÷ 2. It works for any simple (non-self-intersecting) polygon, convex or concave.
- For land plots, use the survey description (metes and bounds), GIS software, or Google Maps. You can read coordinates by clicking points in Google Maps. Measure irregularly shaped rooms by dividing into rectangles and triangles.
- The centroid is the geometric center (average position) of the polygon — the point where it would balance if cut from a sheet of uniform material. For irregular shapes, it's not the same as the center of the bounding box.
- If your coordinates are from a scaled drawing or map, enter the real-world unit equivalent. For example, if 1 unit on your drawing = 5 feet, enter a scale factor of 5 to get ft² results.
- The current calculator supports 4–6 vertices. For complex shapes with more vertices, divide the shape into simpler polygons, calculate each area, then sum the results.