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Advanced Polygon Calculator
You can use this Advanced 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:
- An interior angle is the angle between the two adjacent sides of a geometrical shape.
- An exterior angle is the angle between a side of a geometrical figure and an adjacent side that is extended outwards.
- The circumradius of a polygon or triangle is the radius of a circumcircle. The latter is a circle that passes through all the vertices.
- 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.
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,
r = inradius,
R = circumradius,
P = perimeter,
A = area,
x = interior angle,
y = exterior angle,
π = 3.141592654.
