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
Related tools
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
- 1Draw or enter the shape: Click on the canvas to place each corner in order, or switch to text mode and enter one x, y pair per line.
- 2Adjust the points: Drag a point to move it, and use undo and redo to fix mistakes.
- 3Set the scale: Type how far one grid unit is and choose feet, meters, yards, kilometers or miles.
- 4Choose the output unit: Select square feet, square meters, acres, hectares, square yards, square kilometers or square miles.
- 5Read the area: See the area, perimeter and every unit conversion, and export the result as CSV, JSON, text or an image.
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 surveyor's formula for the area of a polygon from its corners: Area = ½ × |Σ(xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|. It works for any simple polygon, convex or concave, as long as the corners are listed in order around the edge.
How do I get real-world area?
Set the scale to the distance one grid unit represents. A 10 × 10 square with 1 unit = 1 ft is 100 sq ft (9.29 m²); with 1 unit = 1 m it is 100 m² (1,076 sq ft).
Can I use GPS coordinates?
Not as latitude and longitude, because degrees are not a length. Convert the points to a projected grid in meters or feet first, such as UTM or a State Plane or national grid, then enter those x, y values.
What if the edges cross?
A self-crossing shape gives a wrong area, because parts of it cancel out. List the corners in order, clockwise or counterclockwise, so no edges cross.
What is snap to grid?
When it is on, points you place snap to the nearest grid intersection, which makes clean shapes easier to draw.
Related Tools
Survey Area Calculator
Calculate surveyed land area.
Triangle Land Area Calculator
Calculate triangular plot area.
Trapezoid Land Calculator
Calculate trapezoid land area.
Boundary Length Calculator
Calculate boundary perimeter.
Plot Division Calculator
Divide land into equal plots.
Map Scale Calculator
Convert map scale to real distance.
Land Price Calculator
Calculate total land cost based on rate.
Land Area Calculator (Square Feet)
Calculate land area in square feet from length and width, with feet, meter and yard inputs.
Land Area Calculator (Square Meter)
Convert and calculate land area in square meters.
Soil Volume Calculator
Calculate soil excavation volume.
Earth Filling Calculator
Estimate fill material needed.
Excavation Cost Calculator
Estimate digging cost.