Polygon Area Calculator
Find polygon area from ordered vertices with the shoelace formula.
How the polygon area calculator works
The shoelace formula calculates the area enclosed by an ordered polygon boundary by cross-multiplying neighboring coordinates and taking half the signed sum. Its sign also reveals whether vertices were entered clockwise or counterclockwise. This calculator closes the final vertex back to the first automatically and reports absolute area, signed area, orientation, perimeter, and vertex count.
The default vertices trace a square from 0,0 to 4,0 to 4,4 to 0,4. The forward and backward diagonal products produce a signed total of 32, so half gives the verified area 16. The counterclockwise order makes that sign positive, and four sides of length four produce perimeter 16.
Reading polygon area calculator results privately
Vertices must follow the boundary in order; an arbitrary point cloud can cross itself and produce a signed algebraic area rather than the intended outer region. Do not repeat the first point because closure is automatic, although repeating it gives the same area. Coordinates may be decimal, and output uses the coordinate units squared. This polygon area calculator calculation runs entirely in your browser, so the numbers you enter never leave your device.
Frequently Asked Questions
Does vertex order affect the area?
It changes the sign but not the absolute area for a simple polygon. The sign identifies clockwise or counterclockwise order.
Can I enter a self-intersecting polygon?
The formula returns signed algebraic area, which may cancel overlapping lobes. It is not the total filled area of a self-intersecting shape.
Is the polygon area calculator private?
Yes. Its inputs and results stay in your browser. Bushe.co does not upload or store the values used in this calculation.
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