Area by Coordinates Calculator
How It Works: Area Calculation Formula
This calculator uses the Shoelace Formula (also known as Gauss's area formula) to calculate the area of a polygon given its vertex coordinates.
The formula for a polygon with vertices (x₁,y₁), (x₂,y₂), ..., (xₙ,yₙ) is:
Area = ½ × |Σ(xᵢyᵢ₊₁) - Σ(yᵢxᵢ₊₁)|
Where the summation is from i=1 to n, and the last vertex (xₙ₊₁,yₙ₊₁) is the same as the first vertex (x₁,y₁) to close the polygon.
The perimeter is calculated by summing the distances between consecutive points:
Perimeter = Σ √[(xᵢ₊₁ - xᵢ)² + (yᵢ₊₁ - yᵢ)²]
The centroid (geometric center) is calculated as:
Cₓ = (1/(6×Area)) × Σ(xᵢ + xᵢ₊₁) × (xᵢyᵢ₊₁ - xᵢ₊₁yᵢ)
Cᵧ = (1/(6×Area)) × Σ(yᵢ + yᵢ₊₁) × (xᵢyᵢ₊₁ - xᵢ₊₁yᵢ)
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