What is the method for converting radians to degrees?

Question

I run into this occasionally and always forget how to do it.

One of those things that pop up ever so often.

Also, what's the formula to convert angles expressed in radians to degrees and back again?

Answer 1

radians = degrees * (pi/180)

degrees = radians * (180/pi)

As for implementation, the main question is how precise you want to be about the value of pi. There is some related discussion here

Answer 2

a complete circle in radians is 2*pi. A complete circle in degrees is 360. To go from degrees to radians, it's (d/360) * 2*pi, or d*pi/180.

Answer 3

x rads in degrees - > x*180/pi
x degrees in rads -> x*pi/180

I guess if you wanted to make a function for this [in PHP]:

function convert($type, $num) {
    if ($type == "rads") {
          $result = $num*180/pi();
        }

    if ($type == "degs") {
          $result = $num*pi()/180;
        }

    return $result;
  }

Yes, that could probably be written better.

Answer 4

In javascript you can do it this way

radians = degrees * (Math.PI/180);

degrees = radians * (180/Math.PI);

Answer 5

This works well enough for me :)

// deg2rad * degrees = radians
#define deg2rad (3.14159265/180.0)
// rad2deg * radians = degrees
#define rad2deg (180/3.14159265)

Answer 6

180 degrees = PI * radians

Answer 7

360 degrees is 2*PI radians

You can find the conversion formulas at: http://en.wikipedia.org/wiki/Radian#Conversion_between_radians_and_degrees.

Answer 8

360 degrees = 2*pi radians

That means deg2rad(x) = x*pi/180 and rad2deg(x) = 180x/pi;

Answer 9

pi Radians = 180 degrees

So 1 degree = pi/180 radians

or 1 radian = 180/pi degrees

Answer 10

For double in c# this might be helpful:

        public static double Conv_DegreesToRadians(this double degrees)
        {
            //return degrees * (Math.PI / 180d);
            return degrees * 0.017453292519943295d;
        }
        public static double Conv_RadiansToDegrees(this double radians)
        {
            //return radians * (180d / Math.PI);
            return radians * 57.295779513082323d;
        }

Answer 11

radians = (degrees/360) * 2 * pi