How to Convert Radians to Degrees

Step-by-Step Guide

1. 1

   Step 1: Know that π radians is equal to 180 degrees.

   Before you begin the conversion process, you have to know that π radians = 180°, which is equivalent to going halfway around a circle.
   
   This is important because you'll be using 180/π as a conversion metric.
   
   This is because 1π radians is equal to 180/π degrees.
2. 2

   Step 2: Multiply the radians by 180/π to convert to degrees.

   It's that simple.
   
   Let's say you're working with π/12 radians.
   
   Then, you've got to multiply it by 180/π and simplify when necessary.
   
   Here's how you do it: π/12 x 180/π = 180π/12π ÷ 12π/12π = 15° π/12 radians = 15° , If you really want to get the hang of it, then try converting from radians to degrees with a few more examples.
   
   Here are some other problems you can do:
   Example 1: 1/3π radians = π/3 x 180/π = 180π/3π ÷ 3π/3π = 60° Example 2: 7/4π radians = 7π/4 x 180/π = 1260π/4π ÷ 4π/4π = 315° Example 3: 1/2π radians = π /2 x 180/π = 180π /2π ÷ 2π/2π = 90° , If you say 2π radians or 2 radians, you are not using the same terms.
   
   As you know, 2π radians is equal to 360 degrees, but if you're working with 2 radians, then if you want to convert it to degrees, you will have to calculate 2 x 180/π.
   
   You will get 360/π, or
   114.5°.
   
   This is a different answer because, if you're not working with π radians, the π does not cancel out in the equation and results in a different value.
3. 3

   Step 3: Practice with a few examples.

4. 4

   Step 4: Remember that there's a difference between "radians" and "π radians."

Detailed Guide

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