Calculator Inputs
Diagonal Growth Chart
This chart compares total diagonals and interior angle sums across the selected polygon range.
Formula Used
Diagonals: d = n(n - 3) / 2
This formula counts line segments joining non-adjacent vertices in a polygon with n vertices.
Interior angle sum: (n - 2) × 180
Each interior angle for a regular polygon: ((n - 2) × 180) / n
Each exterior angle for a regular polygon: 360 / n
Total vertex connections: n(n - 1) / 2. Subtract sides to isolate diagonals.
How to Use This Calculator
- Enter the number of polygon vertices.
- Optionally set a start, end, and step range.
- Click Calculate Now to generate metrics.
- Review diagonals, angles, and segment counts above the form.
- Use the chart to compare diagonal growth visually.
- Download your result summary as CSV or PDF.
Example Data Table
| Vertices | Sides | Diagonals | Interior Sum (°) | Each Interior (°) | Each Exterior (°) | Total Connections | Triangles |
|---|---|---|---|---|---|---|---|
| 3 | 3 | 0 | 180.00 | 60.00 | 120.00 | 3 | 1 |
| 4 | 4 | 2 | 360.00 | 90.00 | 90.00 | 6 | 2 |
| 5 | 5 | 5 | 540.00 | 108.00 | 72.00 | 10 | 3 |
| 6 | 6 | 9 | 720.00 | 120.00 | 60.00 | 15 | 4 |
| 7 | 7 | 14 | 900.00 | 128.57 | 51.43 | 21 | 5 |
| 8 | 8 | 20 | 1,080.00 | 135.00 | 45.00 | 28 | 6 |
| 9 | 9 | 27 | 1,260.00 | 140.00 | 40.00 | 36 | 7 |
| 10 | 10 | 35 | 1,440.00 | 144.00 | 36.00 | 45 | 8 |
| 11 | 11 | 44 | 1,620.00 | 147.27 | 32.73 | 55 | 9 |
| 12 | 12 | 54 | 1,800.00 | 150.00 | 30.00 | 66 | 10 |
Frequently Asked Questions
1. What is a polygon diagonal?
A polygon diagonal is a line segment connecting two non-adjacent vertices. It is different from a side because it passes through the interior of the polygon.
2. Why must a polygon have at least three vertices?
Three vertices are the minimum needed to form a closed shape. With fewer than three points, a true polygon cannot exist.
3. How is the diagonal formula derived?
Every vertex connects to all others except itself and two adjacent vertices. Counting those valid connections for all vertices and dividing by two avoids double counting.
4. Does this calculator work for irregular polygons?
The diagonal count depends only on the number of vertices, so it works for any simple polygon. Angle values shown per vertex assume a regular polygon.
5. What happens when the number of vertices grows?
Diagonal counts rise quickly as vertices increase. The relationship is quadratic, which is why the chart becomes steeper for larger polygons.
6. What is the difference between sides and diagonals?
Sides connect adjacent vertices and define the outer boundary. Diagonals connect non-adjacent vertices and lie inside the shape.
7. Can I export the calculation results?
Yes. This page includes CSV and PDF export buttons so you can save the visible table and result summary for reference or reporting.
8. What polygons are common examples for this tool?
Common classroom examples include triangles, quadrilaterals, pentagons, hexagons, octagons, and decagons. These make it easy to verify patterns manually.