# Progressd Polygon Calculator

You can use this Progressd Polygon Calculator to calculate interior/exterior angle, inradius, circumradius, perimeter, area, and more.

How to use the calculator: Simply select the units of measurement, enter the number of sides, specify the side length of a regular polygon, and let our calculator do the rest.

Key Definitions:

1. An interior angle is the angle between the two adjacent sides of a geometrical shape.
2. An exterior angle is the angle between a side of a geometrical figure and an adjacent side that is extended outwards.
3. The circumradius of a polygon or triangle is the radius of a circumcircle. The latter is a circle that passes through all the vertices.
4. Inradius of a regular polygon is the radius of the incircle which is the largest circle that can fit inside the polygon.

Please note: In order to start carrying out calculations, the number of sides should not be less than 3. When calculating an interior or exterior angle, the answer will always be in degrees.

(≥ 3)

inches

° (≤ 180°)

°

inches

inches

inches

square inches

Polygon Name = Triangle (or Trigon)

## Formulas

This calculator uses the following formulas:

Side Length a = 2R sin(π/N) = 2r tan(π/N)

Interior Angle x = (((N-2)/N) × 180° ) [degrees]

Exterior Angle y = (360° / N) [degrees]

Circumradius R = a / 2sin(π/N) = r / cos(π/N)

Inradius r = R cos(π/N) = (1/2)a cot(π/N)

Perimeter P = Na

Area A = (1/4)Na2 cot(π/N) = Nr2 tan(π/N)

Where:

N = number of sides,

a = side length,