No Login Data Private Local Save

Polygon Area Calculator - Online Irregular Shape Tool

Calculator Educational area coordinates geometry polygon
72
0
0
0
0 Vertices Self-intersecting
Snap:
Hover over canvas to see coordinates Click to add • Drag vertices • Double-click to delete
Calculated Area
0.00
sq pixels
px = 1
1m=100px 1ft=50px 1in=96px 1yd=150px
# X (px) Y (px)
Click on canvas to add vertices
Frequently Asked Questions
How is the polygon area calculated?

This tool uses the Shoelace formula (also known as Gauss's area formula), which computes the area of a simple polygon from its vertex coordinates. The formula sums cross-products of consecutive vertex pairs: Area = ½ |Σ(xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|. It works for any simple polygon — regular, irregular, convex, or concave — as long as edges do not intersect.

What units does the calculator support?

You can set a custom scale ratio to convert pixel measurements into real-world units. Supported units include meters, feet, inches, yards, and centimeters. For example, if 100 pixels = 1 meter on your reference image, the area is displayed in square meters. You can also use a fully custom unit by selecting "custom unit."

Can I calculate the area of an irregular or concave shape?

Yes! The Shoelace formula handles concave polygons correctly. Simply place vertices around the perimeter of your shape in order. The tool automatically closes the polygon by connecting the last vertex back to the first. For best results, trace the outline consistently in one direction (clockwise or counterclockwise).

What happens if my polygon self-intersects?

If edges cross each other (a self-intersecting polygon or "bow-tie" shape), the Shoelace formula produces an algebraically signed area that may not represent the true geometric area. The tool detects self-intersections and displays a warning badge. For accurate results, rearrange vertices so no edges cross.

How do I edit or delete individual vertices?

You can drag any vertex by clicking and holding on its circular handle on the canvas. To delete a vertex, double-click it on the canvas, or use the trash icon next to its coordinates in the table. You can also manually edit X/Y values directly in the coordinate table — the canvas updates automatically.

Is this tool suitable for measuring land or floor plans?

Absolutely. If you have a scaled image (e.g., a blueprint, map, or floor plan), set the scale ratio to match the image's scale. For instance, if 1cm on the image = 50px and represents 1 meter in reality, set "50 px = 1 meter." Then trace the outline to get the real-world area in square meters, square feet, or any supported unit.

Can I save or export my polygon data?

Yes. Use the Copy button to copy all vertex coordinates as a JSON array to your clipboard, or CSV to download a comma-separated file. You can also Import coordinates by pasting a JSON array, making it easy to share, store, or reload polygon data later.

How accurate is the area calculation?

The calculation is mathematically exact for the given vertex coordinates (using double-precision floating point). Accuracy in real-world terms depends on how precisely you place vertices and how accurately you set the scale ratio. The snap-to-grid feature helps with precise vertex placement at 25-pixel intervals.

🔧 Related Tools