math - Translating radians to degrees

I noticed that translating radians to degrees and vice versa is like translating a percentage to a whole number and vice versa. For example, to get 60 percent of 345 you do the following

60 * 345/100

to convert 60 degrees to radians you do

60 * 3.14/180

There is a pattern there BUT... we use 100 to compare percentages to a number. So, why do we use 180 degrees instead of 360 degrees to compare degrees to radians?

%100 percent = a whole number
360 degrees represents a whole circle

using 180 degrees is like using 50% instead of 100%

I hope I am making some sense. Can anyone answer? Thanks