How is the number of diagonals in a polygon calculated?

Diagonals = n(n−3)/2, where n is the number of sides.

Why does a triangle have zero diagonals?

Every pair of vertices in a triangle is already connected by a side, leaving no interior diagonal connections possible.

How does diagonal count grow with more sides?

It grows quadratically — adding more sides increases the diagonal count much faster than the side count itself.

Polygon Diagonals Calculator - CalculatorLabs.net

Polygon Diagonals Calculator

Every polygon — a triangle, hexagon, or any straight-sided shape — has a predictable number of diagonals (lines connecting non-adjacent corners) and interior angles that add up to a fixed total.

Number of Sides (n)

Instant Result

Number of Diagonals -

Sum of Interior Angles -

Each Interior Angle -

Each Exterior Angle -

What Is a Regular Polygon Diagonals & Angles Calculator?

Every polygon — a triangle, hexagon, or any straight-sided shape — has a predictable number of diagonals (lines connecting non-adjacent corners) and interior angles that add up to a fixed total. This calculator works out the diagonal count, angle sum, and each interior and exterior angle for any regular polygon just from its number of sides.

How to Use This Regular Polygon Diagonals & Angles Calculator

Count the number of sides (n) of the polygon.
Enter that whole number into the field above.
Click Calculate to get the number of diagonals, the total interior angle sum, and each individual angle.

Formula

Number of Diagonals = n(n − 3) / 2
Sum of Interior Angles = (n − 2) × 180°
Each Interior Angle (regular) = (n − 2) × 180° / n
Each Exterior Angle = 360° / n

Worked Example

A regular heptagon (7 sides): Diagonals = 7(4)/2 = 14. Sum of Interior Angles = 5 × 180° = 900°. Each Interior Angle = 900°/7 ≈ 128.57°. Each Exterior Angle = 360°/7 ≈ 51.43°.