Productive ToolboxPolygon Area Calculator
Calculate the area of irregular polygon shapes using coordinates or interactive canvas plotting. Supports multiple units with real-time results.
Polygon Area Calculator
Click on the canvas to add polygon vertices, or enter coordinates manually. Drag points to adjust the shape. Area updates instantly.
Settings
Total Area
Interactive Canvas
Click to add points · Drag to move · 0 points placed
Quick Presets
What is a Polygon Area Calculator?
A Polygon Area Calculator is a geometry tool that calculates the area of any irregular polygon shape — including land plots, fields, property boundaries, and construction sites — using vertex coordinates. Unlike simple rectangle or triangle calculators, it handles any number of sides and any shape, making it ideal for real-world land measurement.
This tool uses the Shoelace Formula (also called the Surveyor's Formula), which is the standard mathematical method for computing polygon area from a list of vertex coordinates. The formula works for any simple polygon — convex or concave — with any number of vertices.
You can either click directly on the interactive canvas to place polygon points, or enter coordinates manually in text mode. The area updates in real time as you add or drag points, and results are instantly converted to square feet, square meters, acres, hectares, and more.
How to Use the Polygon Area Calculator
Canvas Mode
- 1Click anywhere on the canvas to place a vertex
- 2Continue clicking to add more points (minimum 3)
- 3Drag any point to adjust the polygon shape
- 4Use Undo/Redo to correct mistakes
- 5Set the scale (1 unit = X meters/feet) for real-world area
- 6Select your preferred output unit
- 7View the live area result and all unit conversions
Text Mode
- 1Switch to Text mode using the tab above the canvas
- 2Enter one coordinate pair per line: x, y
- 3Use decimal values for precision (e.g. 10.5, 23.7)
- 4Click Apply Coordinates to plot on canvas
- 5The polygon is auto-fitted to the canvas view
- 6Adjust scale and output unit as needed
The Shoelace Formula Explained
| Step | Operation | Example (Square 10×10) |
|---|---|---|
| 1 | List vertices in order | (0,0), (10,0), (10,10), (0,10) |
| 2 | Multiply xᵢ × yᵢ₊₁ | 0×0 + 10×10 + 10×10 + 0×0 = 200 |
| 3 | Multiply yᵢ × xᵢ₊₁ | 0×10 + 0×10 + 10×0 + 10×0 = 0 |
| 4 | Subtract and halve | ½ × |200 − 0| = 100 |
| 5 | Result | Area = 100 square units |
Example Polygon Calculations
| Shape | Vertices | Area (units²) |
|---|---|---|
| Square | (0,0)(10,0)(10,10)(0,10) | 100 |
| Rectangle | (0,0)(20,0)(20,8)(0,8) | 160 |
| Triangle | (0,0)(10,0)(5,8) | 40 |
| L-Shape | (0,0)(6,0)(6,4)(10,4)(10,10)(0,10) | 76 |
| Irregular 5-gon | (0,0)(8,3)(12,9)(5,12)(1,8) | 92.5 |
Who Uses This Calculator?
Land Surveyors
Calculate irregular plot areas from GPS or field-measured coordinates.
Farmers
Measure field and crop areas for planning, irrigation, and yield estimation.
Civil Engineers
Compute site areas for grading, drainage, and construction planning.
Architects
Calculate floor plan areas and irregular building footprints.
Property Buyers
Verify land area from survey maps before purchasing property.
Students
Learn and verify polygon area calculations for geometry coursework.
Frequently Asked Questions
What is the Shoelace formula?
The Shoelace formula (Surveyor's formula) calculates the area of any simple polygon given its vertex coordinates. The formula is: Area = ½ × |Σ(xᵢyᵢ₊₁ − yᵢxᵢ₊₁)|. It works for any polygon — convex, concave, or irregular — as long as the vertices are listed in order and the polygon does not self-intersect.
How do I get real-world area from canvas coordinates?
Use the Scale setting. If 1 canvas unit represents 5 meters, set scale to 5 and unit to 'm'. The calculator multiplies the raw canvas area by scale² to get the real-world area in square meters, then converts to your selected output unit.
Can I calculate area for a self-intersecting polygon?
The Shoelace formula gives the net signed area for self-intersecting polygons, which may not match the visual area. For accurate results, ensure your polygon vertices are listed in order (clockwise or counterclockwise) without crossing edges.
How do I enter GPS coordinates?
Switch to Text mode and enter your GPS coordinates as decimal degrees (e.g. longitude, latitude pairs). The calculator will compute the area in canvas units, which you can scale to real-world area using the scale factor.
What is snap-to-grid?
When snap-to-grid is enabled, points you place on the canvas automatically snap to the nearest grid intersection. This makes it easier to create precise shapes with clean coordinates.
Can I export the polygon coordinates?
Yes. Use the Export section to download coordinates as CSV, the full result as JSON, a text report as TXT, or a PNG image of the canvas visualization.
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