A worked example: a regular octagon's interior angle in radians
The Polygon Calculator gives a regular octagon (8 sides, side length 3) a perimeter of 24, an area of 43.455844 square units, and an interior angle of 135 degrees. Taking that 135 and feeding it into the Degree Radian Converter with the Degrees → Radians direction returns 2.3561944902 radians — the same angle, just expressed in the unit that trigonometric functions expect.
The formula: chaining the polygon formula and the degree-radian formula
The interior angle formula is (n − 2) × 180 / n, and the conversion formula is radians = degrees × π/180. For the octagon, n = 8 gives (8 − 2) × 180 / 8 = 135 degrees, and then 135 × π/180 gives the 2.3561944902 radians above. Nothing about the two formulas overlaps — the polygon formula only knows about the number of sides, and the conversion formula only knows about the degree value handed to it — but chaining their real outputs turns one calculator's answer into the other's input.
A regular dodecagon's interior angle in radians
A regular dodecagon (12 sides, side length 2) has a perimeter of 24, an area of 44.78461 square units, and an interior angle of 150 degrees. Converting 150 degrees the same way gives 2.617993878 radians. Notice the pattern: more sides means a larger interior angle in degrees, and correspondingly a larger value in radians too, since the conversion factor between the two units never changes.
Why converting a polygon's interior angle to radians matters
Placing a regular polygon's vertices in code — for a game sprite, a CAD drawing, or a chart — usually means calling trigonometric functions like sine and cosine to compute each corner's position, and those functions take radians, not degrees. Working out the interior angle by hand in degrees and then converting it is exactly the two-step process most graphics and engineering software performs automatically behind the scenes.