Content

• To step

Degrees and radians are two units of measurement for angles. A circle can be divided into 360 °, the equivalent of 2π radians. This means that 360 °, or 2π radians, represent a "rotation" of a circle. And this means that 180 °, or 1π radians, is a semicircle. Does this sound confusing? That is not necessary at all. You can convert degrees to radians or radians to degrees very easily with a few simple steps.

To step

1. Write down the number of degrees you want to convert to radians. Let's work out some examples to really understand the concept. Here are the examples you will be working with:
   • Example 1: 120°
   • Example 2: 30°
   • Example 3: 225°
2. Multiply the number of degrees by π / 180. To understand why, you need to know that 180 degrees consists of π radians. Therefore, 1 degree is equal to (π / 180) radians. Since you already know this, you just need to multiply the number of degrees by π / 180 to convert it to radians. You can omit the degree sign, because your answer will be given in radians. This is what this will look like:
   • Example 1: 120 x π / 180
   • Example 2: 30 x π / 180
   • Example 3: 225 x π / 180
3. Calculate it. Now you can just do the calculation by multiplying the number of degrees by π / 180. Think of it like multiplying two fractions: the first fraction has degrees in the numerator and "1" in the denominator, and the second fraction has π in the numerator and 180 in the denominator.You calculate this as follows:
   • Example 1: 120 x π / 180 = 120π / 180
   • Example 2: 30 x π / 180 = 30π / 180
   • Example 3: 225 x π / 180 = 225π / 180
4. Simplify. Now you need to simplify each fraction to the smallest terms to get your final answer. Find the largest number by which both the numerator and denominator of each fraction are divisible and use it to simplify each fraction. The largest number of the first example is 60, that of the second is 30 and that of the third is 45. But you don't need to know that right away; you can try dividing the numerator and denominator by 5, 2, 3 or whatever works. This is done as follows:
   • Example 1: 120 x π / 180 = 120π / 180 ÷ 60/60 = 2 / 3π radians
   • Example 2: 30 x π / 180 = 30π / 180 ÷ 30/30 = 1 / 6π radians
   • Example 3: 225 x π / 180 = 225π / 180 ÷ 45/45 = 5 / 4π radians
5. Write down your answer. To be clear, you can write down what the initial angle value became when converting to radians. Then you are done! You can do the following:
   • Example 1: 120 ° = 2 / 3π radians
   • Example 2: 30 ° = 1 / 6π radians
   • Example 3: 225 ° = 5 / 4π radians