The circumference of any circle is just the distance around it.A circle has 360 degrees all the way around.Or as summarized by Teacher’s Choice, one radian is the angle of an arc created by wrapping the radius of a circle around its circumference. Okay, so radian is an angle with vertex at the center of a circle that intercepts an arc on the circle equal in length to the radius of the circle. Radians! If we convert degrees into radian measure, then we are allowed to treat trigonometric functions as functions with domains of real numbers rather than angles! What is a radian? Therefore to convert a certain number of degrees in to radians, multiply the number of degrees by PI /180 (for example, 90 90 × PI /180 radians PI /2). But, if we wanted to do any mathematical computation then we have to convert it to a useful number, which means we have to convert it to its decimal form of 0.5. If I said, we have used up 50% of our storage space, we all have a clear picture. In fact, as Purple Math explains, a degree is not a number we can do most mathematical computations with. Conversion Formula Let's take a closer look at the conversion formula so that you can do these conversions yourself with a calculator or with an old-fashioned pencil and paper. Well, the problem with only working with degree measure is that it limits our ability to apply angles to other functions because we’re stuck with values between 0 and 360. There are 57.2957795130823 degrees in a radian. Haven’t you heard the phrase, “he turned a 180” or “make a 360”? Most trig applications deal with degrees – in fact, our brains naturally tend to think in terms of degrees too. 1 degrees (deg) is equal to 0.017453292519943295 radians (rad).