Polygon diagonals calculator
How many diagonals a polygon has, from its number of sides: n·(n−3)/2 — because each vertex connects to all others except itself and its two neighbours. It also names the polygon and gives the number of triangles it splits into and the sum of its interior angles.
Related tools
All Geometry tools →Need Number of diagonals, Polygon name, Triangles (n−2), Sum of interior angles? The Polygon diagonals calculator derives it from Number of sides (n) in one step. For instance, with Number of sides (n) = 6 it returns Number of diagonals = 9, Polygon name = Hexagon and Triangles (n−2) = 4.
How to use it
- Enter your values: Number of sides (n).
- Read the result instantly: Number of diagonals, Polygon name, Triangles (n−2), Sum of interior angles.
Frequently asked questions
How does the Polygon diagonals calculator work?
It takes Number of sides (n) and derives Number of diagonals, Polygon name, Triangles (n−2) and Sum of interior angles from them. The calculation is live as you type, so the result updates on every change.
Which values does the calculator ask for?
A single value: Number of sides (n). Nothing else is required — no account, no file upload.
What does a typical calculation look like?
With Number of sides (n) = 6, the calculator returns Number of diagonals = 9, Polygon name = Hexagon and Triangles (n−2) = 4. Those figures come from running this exact tool, so you can reproduce them by entering the same values.
How much does the result change with different inputs?
It moves a lot. Using Number of sides (n) = 12 instead, Number of diagonals goes from 9 to 54 — which is why it is worth testing a few scenarios rather than trusting a single figure.
What does it give for smaller values?
Scaled down to Number of sides (n) = 3, Number of diagonals comes out at 0. The relationship is worth checking at both ends before you rely on a single result.
When would I actually use this?
Homework and site work alike: how much paint a wall takes, how much water a tank holds, whether a corner is square — and, on the coordinate side, the slope between two points, the distance across a plan, the midpoint of a span.
What is the most common mistake?
Mixing units inside one shape. Entering a length in centimetres and a width in metres gives an area wrong by a factor of a hundred, and the result looks perfectly plausible.
What is the difference between the Polygon diagonals calculator and the Regular polygon calculator?
This one returns Polygon name and Triangles (n−2); the Regular polygon calculator returns Area and Perimeter. That is the whole difference — open the one whose figure you need.
Is there a tool for the next step?
Irregular polygon area calculator is the closest one after this: The area of any polygon — regular or not, convex or concave — from its corner coordinates. Enter the vertices in order and the shoelace formula returns the exact area, plus the perimeter, the centroid and whether the points run clockwise or counter-clockwise, with a drawing of the shape. Ideal for land plots and CAD sketches.
What else is worth having open alongside it?
Regular polygon area calculator and Regular polygon perimeter calculator — they come up in the same task often enough to be worth a second tab.