How Do We Convert Between Radians and Degrees?

Converting between radians and degrees is actually pretty simple.

 RADIANS : One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.

To Convert From DEGREES to RADIANS :
      You can use the simple Formula :   π 
                                                            180
This is accurate because since 360° = 2 π 
To find the amount of radians is 90°, we can use this ratio : 90   =  radians
                                                                                           360          2 π    
So you simply have to multiply degrees by 2π and divide by 360. This simplified is π over 180.
Lets use :  105°

You multiply 105 by  π  and get 7π because you simplify 105 π
                              180             12                                    180

To convert from RADIANS to DEGREES: 

      You use the formula:  180  
                                            π 

Lets take 2π  for example, 

You set up the formula to look like this: 

2π *180      The two pi's cancel out and you are left with 360°.
      π

See how simple ? Now Try it Yourself : 

Convert to Radians using:  60° 




Convert to Degrees using :  5 π
                                           12