Irregular Shape Area Calculator
Calculate area and perimeter for irregular polygons from coordinate points.
Table of Contents
How to Use
- Choose how many vertices (3–6) describe your shape
- Enter each point's x and y coordinates
- Optionally add a unit label (e.g., m, ft)
- Calculate to see area, perimeter, and orientation
Shoelace formula
The shoelace (Gauss area) formula computes polygon area from ordered vertices: area = 1/2 · |Σ(x_i y_{i+1} − x_{i+1} y_i)|. It works for any simple polygon when points are listed in order.
- Keep vertices ordered around the shape
- Avoid self-intersections for reliable results
- Use the same unit for all coordinates
Understanding orientation
The sign of the shoelace sum reveals orientation: positive for counter-clockwise ordering, negative for clockwise. Collinear or repeated points can lead to zero area.
Frequently Asked Questions
- What if my points are out of order?
- The formula assumes vertices are listed around the boundary. If points are unordered, the area can be incorrect—sort them around the shape or trace them in order.
- Can I mix units for coordinates?
- No. Use the same unit for all coordinates. The area is reported in squared units, and the perimeter in linear units.
- How many points can I use?
- This tool supports 3 to 6 vertices. For more complex outlines, break the shape into sections or export points from a CAD or GIS tool.