Math
Regular polygon area
Calculate area and perimeter of a regular polygon.
Calculators / Math / Polygon diagonal count
Polygon diagonal count calculator
Count the diagonals of a simple polygon from its number of vertices.
On this page
Total diagonals20diagonals
Diagonals from one vertex5diagonals
Calculator controls
How to calculate
Count the diagonals of a simple polygon from its number of vertices.
Total diagonals =
n*(n-3)/2 diagonalsDiagonals from one vertex =
n-3 diagonalsWorked example
- Number of vertices: 8
- Total diagonals: 20 diagonals
- Diagonals from one vertex: 5 diagonals
Assumptions and limits
Vertices must be distinct and the polygon must be simple. Each unordered pair of nonadjacent vertices counts once; crossing locations are not counted.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Count the diagonals of a simple polygon from its number of vertices. Subtract the two neighbours and the selected vertex, then divide the total pair count by two.
When this tool is useful
Subtract the two neighbours and the selected vertex, then divide the total pair count by two.
Understanding your inputs
| Input | Example |
|---|---|
Number of vertices n | 8 |
Frequently asked questions
Which assumptions matter for this result?
Vertices must be distinct and the polygon must be simple. Each unordered pair of nonadjacent vertices counts once; crossing locations are not counted.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.