Irregular Polygon Area Calculator

Find the area of a polygon from up to five vertex coordinates (shoelace formula).

Area 12

Formula: Shoelace: A = ½|Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|

Step-by-step with your numbers:
1. Values used:
2. x₁ = 0
3. y₁ = 0
4. x₂ = 4
5. y₂ = 0
6. x₃ = 4
7. y₃ = 3
8. x₄ = 0
9. y₄ = 3
10. x₅ (optional) = 0
11. y₅ (optional) = 0
12.
13. Area = 12
Did we solve your problem today?

The shoelace formula finds the area of any simple polygon from its vertex coordinates.

The math behind it

List the vertices in order; cross-multiply consecutive coordinates and sum, then halve the absolute value. Leave the 5th vertex at (0, 0) for a quadrilateral.

Worked example

A 4×3 rectangle's vertices give area 12.

FAQ

Does vertex order matter?

List them in order around the polygon (clockwise or counter-clockwise); the absolute value handles the direction.