Polygon Diagonals Calculator

Work out polygon diagonals instantly with clear inputs, formula shown and shareable results.

About Polygon Diagonals Calculator

From each of the n vertices you can draw a diagonal to every vertex except itself and its two neighbours, giving n(n − 3) endpoints. Each diagonal is counted twice, hence n(n − 3)/2.

Formula

Number of diagonals

D = n(n − 3) / 2

Worked example

With the default values below, Polygon Diagonals Calculator returns Total diagonals of 54. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number of sidesaccepts 3–10,000: 12
Count diagonals from this many verticesminimum 1: 2

Results

Total diagonals: 54
Diagonals from each vertex: 9
Triangles when triangulated: 10
Diagonals drawn from the chosen vertices: 18

Step by step

1Values used
2Number of diagonals
3Total diagonals= 54
4Diagonals from each vertex= 9
5Triangles when triangulated= 10
6Diagonals drawn from the chosen vertices= 18

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does a triangle have no diagonals?

n(n − 3)/2 = 3 × 0 / 2 = 0; every pair of vertices is already joined by a side.

How many diagonals does a hexagon have?

6 × 3 / 2 = 9.