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Irregular Polygon Area and Perimeter Calculator — result sheet
Calculate the area and boundary length of a simple irregular polygon from ordered Cartesian vertices.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Area=|Σ(xᵢyᵢ₊₁−xᵢ₊₁yᵢ)|/2; perimeter=Σ√((Δx)²+(Δy)²), including the closing edge.
The shoelace sum handles an ordered polygon boundary, while the perimeter adds the straight distance between each consecutive vertex and the closing pair.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Ordered vertices — Enter x,y pairs separated by semicolons, in boundary order.
Worked example
| Input | Value |
|---|---|
| Ordered vertices | 0,0; 6,0; 7,4; 3,6; 0,3 |
Area =31.5; perimeter≈21.8379 coordinate units.
Assumptions and limits
- Vertices are finite Cartesian coordinates listed around one simple non-self-intersecting boundary.
- At least three distinct vertices are required; the polygon is implicitly closed.
- Geographic projection, self-intersection repair, holes, and survey uncertainty are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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