Find the exact geometric center or centroid point of any polygon with our free online calculator. Simply input the X and Y coordinates of each vertex, and instantly get the centroid's coordinates. Ideal for engineering, design, and mathematical applications.
Formula:
For a polygon with n vertices (x1, y1), (x2, y2), ..., (xn, yn), the centroid coordinates (Cx, Cy) are calculated as follows:
First, calculate the signed area (A) of the polygon:
A = 0.5 × ∑ (xiyi+1 - xi+1yi) for i = 1 to n (with (xn+1, yn+1) = (x1, y1))
Then, the centroid coordinates are:
Cx = (1 / 6A) × ∑ (xi + xi+1)(xiyi+1 - xi+1yi)
Cy = (1 / 6A) × ∑ (yi + yi+1)(xiyi+1 - xi+1yi)
Where:
- xi, yi: Coordinates of the i-th vertex.
- xi+1, yi+1: Coordinates of the next vertex (for the last vertex, this refers to the first vertex).
- A: Signed area of the polygon.