When you are first introduced to angles, you typically refer to them in terms of “degrees.” Chances are, you know what a 45° angle looks like. Also, by the time you reach middle-school, you know that a triangle has 180°. It’s easy, cut and dry, black and white. However, most of the scientific geniuses of modern time opt to use radians to measure an angle.

Now the question that may come to mind is – why radians? Degrees are pretty easy, right?

Back in the dark ages, the first mathematicians determined a degree’s size based on the divisions of a full circle. Degrees are the same thing as a slice (1/360) of a circle. While there is no real reason as to why a circle has 360°, it is something you must accept and move on from.

Regardless of the reason, 360 is a great number. This is because it is easily divided (evenly) by many other numbers – 180, 120, 90, 72, 60, 45, 40, 36, 30, 24, 18, 15, 12, 10, 9, 8, 6, 5, 4, 3, and 2. The earliest measures of distance and time relied on having easy and convenient numbers to work with.

Unfortunately, the radian isn’t as easy and nice since it isn’t a whole number. Some believe that radians were originally developed to provide mathematicians with a method to relate the measure of an angle to the size or radius of a circle.

Radians are much larger than degrees. Circles have 2π radians, which is just a little over six radians. A single radian is approximately 1/6 of a circle or just over 57°.

The biggest advantage offered by radians is that they are the natural measure for dividing a circle. If you take the radius of a given circle and bend it into an arc that lies on the circumference, you would need just over six of them to go completely around the circle. This is a fact that is true for ALL circles.

If you are given degrees and want to convert it to radians, there is a simple formula to use: