Polygon Area from Coordinates
Use ordered vertices to find a simple polygon’s area and perimeter.
Your numbers
Area
Vertices must follow the boundary of a non-self-intersecting polygon. Self-intersections are not interpreted as filled unions.
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Formula
Use A = abs[Σ(xᵢyᵢ₊₁−xᵢ₊₁yᵢ)]/2. (xᵢ,yᵢ) are vertices in boundary order; the last vertex connects back to the first. abs means absolute value. Coordinates must use the same length unit.
Use ordered vertices to find a simple polygon’s area and perimeter.
Worked example
- Ordered x,y coordinate pairs (m)
- 0, 0 4, 0 0, 3
- Area
- 6 m²
- Perimeter
- 12 m
Scope and limitations
Vertices must follow the boundary of a non-self-intersecting polygon. Self-intersections are not interpreted as filled unions.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
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Formula version: ad48cb631a20 · Example checked: