Nonagon Calculator
Calculate nonagon properties
Frequently Asked Questions
What is a nonagon?
A nonagon is a polygon with 9 sides and 9 angles. A regular nonagon has all sides equal and all interior angles equal to 140°. The sum of interior angles is (9-2) × 180° = 1,260°.
How do I calculate the area of a regular nonagon?
Area = (9/4) × s² × cot(π/9), where s is the side length. For a nonagon with side length 5: Area = (9/4) × 25 × 2.7475 = 154.55 square units. The calculator also accepts the apothem or circumradius as input.
What is the apothem of a nonagon?
The apothem is the distance from the center to the midpoint of a side. For a regular nonagon: apothem = s / (2 × tan(π/9)). It is also the radius of the inscribed circle. Area can be calculated as (perimeter × apothem) / 2.
How many diagonals does a nonagon have?
A nonagon has n(n-3)/2 = 9(9-3)/2 = 27 diagonals. These diagonals create 126 intersection points inside the nonagon when no three diagonals meet at a single point.
Can a nonagon tile a plane?
Regular nonagons cannot tile a plane by themselves because 140° does not divide evenly into 360°. However, nonagons can form semi-regular tilings when combined with other polygons, such as triangles.