Polygon Diagonals and Angles Calculator
Enter the number of sides of a polygon to count its diagonals and find the sum of interior angles, each interior angle of a regular polygon, and the exterior angle.
How to count polygon diagonals
- Enter the number of sides, a whole number of at least 3.
- Read the number of diagonals instantly.
- See the interior angle sum, each interior angle and the exterior angle.
Examples
Hexagon (6 sides)
sides = 6
diagonals = 9, angle sum = 720, interior angle = 120, exterior angle = 60
Pentagon (5 sides)
sides = 5
diagonals = 5, angle sum = 540, interior angle = 108, exterior angle = 72
Frequently asked questions
What is the formula for the number of diagonals in a polygon?
The number of diagonals equals the number of sides times the number of sides minus three, divided by two. A hexagon has six times three over two, which is nine.
Why does a triangle have no diagonals?
A diagonal connects two non adjacent corners. In a triangle every pair of corners is already joined by a side, so there are zero diagonals.
What is the sum of the interior angles?
The interior angles add up to the number of sides minus two, times 180 degrees. A pentagon gives three times 180, which is 540 degrees.
How big is each interior angle?
In a regular polygon every interior angle is equal, so it is the angle sum divided by the number of sides. A regular hexagon has 720 over 6, which is 120 degrees.
What is the exterior angle?
The exterior angles of any convex polygon always add to 360 degrees, so each one in a regular polygon is 360 divided by the number of sides.
Related tools
Regular Polygon Calculator
Find the area, perimeter, interior and exterior angles, apothem and circumradius of a regular polygon from its side count and side length. Free and instant.
Polygon Area Calculator
Find the area of a regular polygon from its sides and side length, or any polygon from its vertex coordinates with the shoelace formula. Free and instant.
Hexagon Calculator
Calculate the area, perimeter, apothem and diagonals of a regular hexagon from its side length. Exact formulas give precise results. Free and private.
Triangle Area Calculator
Find the area of a triangle from base and height, three sides (Heron's formula) or two sides and an angle (SAS). Free, accurate and instant.
Annulus Area Calculator
Calculate the area of an annulus, the ring between two concentric circles, from its outer and inner radius. Returns both circumferences and width too. Free.
Area Calculator
Find the area of a circle, square, rectangle, triangle, trapezoid, parallelogram, ellipse, sector or rhombus. Free and runs in your browser.