What is the method for converting radians to degrees?

161
votes

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?

12
algorithmmathtrigonometry
I don't see why people are downvoting this; some people aren't mathematically inclined. – thesmallprint
its just a matter of phrasing. I rephrased it as a programming problem instead of a math problem, and voila, it fits. – DevelopingChris
The title of this question makes no sense. "[B]uilt in method" --- built in to what? – Michael J. Barber
i am going to go ask for a method for converting Celsius to Fahrenheit and back, i keep forgetting that one too – Alex
StackOverflow is more than a forum for questions and answers. It's a place of reference. I originally put the question here as a reference question, because it's really really common. It belongs here so when someone answers "Just Google it", Google will direct you here. – Hans Sjunnesson

12 Answers

286
votes
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

10
votes

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.

9
votes

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.

4
votes

In javascript you can do it this way

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

degrees = radians * (180/Math.PI);
1
votes

This works well enough for me :)

// deg2rad * degrees = radians
#define deg2rad (3.14159265/180.0)
// rad2deg * radians = degrees
#define rad2deg (180/3.14159265)
0
votes

180 degrees = PI * radians

0
votes

360 degrees is 2*PI radians

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

0
votes

360 degrees = 2*pi radians

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

0
votes

pi Radians = 180 degrees

So 1 degree = pi/180 radians

or 1 radian = 180/pi degrees

0
votes

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;
        }
0
votes

Here is some code which extends Object with rad(deg), deg(rad) and also two more useful functions: getAngle(point1,point2) and getDistance(point1,point2) where a point needs to have a x and y property.

Object.prototype.rad = (deg) => Math.PI/180 * deg;
Object.prototype.deg = (rad) => 180/Math.PI * rad;
Object.prototype.getAngle = (point1, point2) => Math.atan2(point1.y - point2.y, point1.x - point2.x);
Object.prototype.getDistance = (point1, point2) => Math.sqrt(Math.pow(point1.x-point2.x, 2) + Math.pow(point1.y-point2.y, 2));
-1
votes
radians = (degrees/360) * 2 * pi