Polygon Area Visualizer — Shoelace Formula
Animated polygon area with the shoelace formula — sums signed triangle areas with step controls. Runs in your browser.
Pseudocode
Press Run to animate the algorithm.
Time · Space
How to use
- 1 Press Run to compute the polygon’s area with the shoelace formula.
- 2 Watch each triangle fanned from the first vertex add to the running total.
- 3 Use Shuffle for a new random polygon, or step through one triangle at a time.
- 4 The final value is the polygon’s area in square units.
Why use this tool
- See the shoelace (Gauss’s area) formula build the area triangle by triangle.
- Understand how signed cross products combine into the total area.
- Works for any simple polygon — convex or concave — in O(n).
- Runs entirely in your browser. No signup, no uploads.
Frequently asked questions
What is the shoelace formula?
A formula for the area of a simple polygon from its vertex coordinates: sum the cross products of consecutive vertices and halve the absolute value. It is named for the criss-cross multiplication pattern.
What is the time complexity?
O(n) — a single pass over the polygon’s n vertices, with O(1) extra space.
Does it work for concave polygons?
Yes, as long as the polygon is simple (its edges do not cross). The signed triangle areas correctly cancel for concave regions.
Why divide by two?
Each cross product equals twice the signed area of the triangle it represents, so the total sum is twice the polygon’s area.
What is Polygon Area Visualizer (Shoelace)?
A Polygon Area Visualizer animates the shoelace (Gauss) formula: it fans triangles from the first vertex and sums their signed cross-product areas to compute the area of any simple polygon in O(n) time.
Polygon Area Visualizer (Shoelace) is a free algorithm utility by Zerethon Tools. Animated polygon area with the shoelace formula — sums signed triangle areas with step controls. Runs in your browser. Runs entirely in the browser — no signup, no upload.
- Category
- Algorithm
- Pricing
- Free
- Privacy
- Browser-based
- Signup
- Not required
Privacy
Your data never leaves your browser unless explicitly stated. Polygon Area Visualizer (Shoelace) runs entirely client-side — no server upload, no logging, no tracking of your input.
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