Enter the number of sides to compute diagonals and polygon properties
Number of Sides (n)
Result
Polygon Name
-
Total Diagonals
-
Diagonals per Vertex
-
Total Segments
-
Detailed Derivation
Diagonal Formula
Total Diagonals D = n(n - 3) / 2
Diagonals per Vertex = n - 3
Total Segments = n(n - 1) / 2
A diagonal is a line segment connecting two non-adjacent vertices of a polygon. The number of diagonals grows quadratically - more sides means many more diagonals.
⚠The formula applies to convex polygons. Concave polygons have the same count of diagonals, but some may lie outside the polygon boundary.
What Is a Polygon Diagonal?
A diagonal is any line segment connecting two non-adjacent vertices of a polygon. Triangles have no diagonals, quadrilaterals have two, and the number increases rapidly as the polygon adds more sides.
Counting Method
Each vertex connects to n-3 diagonals. Total = n(n-3)/2. Divide by 2 because each diagonal is counted from both ends.
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