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Calculate the Angular Sum of an N-gon

Calculator for the angular sum of a polygon or n-gon, a two-dimensional closed shape with straight lines. For every shape with n vertices and straight edges, the sum of the inner angles is equal. Best known is this from the triangle with its angular sum being always 180°. For a quadrilateral, this is 360°. The average angle is the arithmetic mean of the n-gon's angles. For a regular n-gon, it is the exact size of each angle.


Number of vertices n:
Angular sum:°
Average angle:°

Please enter for the number of vertices a natural number ≥3, angular sum and average angle will be calculated.

Formulas:
Angular sum = n * 180° − 360°
Average angle = 180° − ( 360° / n )

The average angle is at least 60° (for a triangle) and approaches 180° for large n, but is always lower.




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