Content

• Steps
• Advice
• What you need

Radians and degrees are both units of measure of angle. As you know, a circle has 2π radians, equivalent to 360 °; both of these values ​​represent the "once going around" the circle. So 1π of radians represents 180 ° on a circle, which makes 180 / π the perfect converter from radians to degrees. To convert radians to degrees, simply multiply the radian value by 180 / π. If you want to know how to calculate and understand the concept in it, read the article below.

Steps

1. 

   Understand that 1π of the radians equals 180 degrees. Before starting the transition, you must know π radians = 180 °, which is equivalent to a half circle. This is important because you will be using 180 / π as the converter. That's because 1 radian is equal to 180 / π degrees.

2. 

   
   
   Multiply radians by 180 / π to get your measurements in degrees. Just that simple! Let's say you have π / 12 radians. To convert it to degrees, you must multiply it by 180 / π and reduce it as needed. Here's how:
   • π / 12 x 180 / π =
   • 180π/12π ÷ 12π/12π =
   • 15°
   • π / 12 radians = 15 °

3. 

   
   
   Practice with a few examples. If you want to be more proficient, you have to practice converting from radians to degrees for more examples. Here are some exercises 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 °
   • Listing 3: 1 / 2π radians = π / 2 x 180 / π = 180π / 2π ÷ 2π / 2π = 90 °

4. 

   
   
   Remember that "radians" are different from "π radians". 2π radians and 2 radians are completely different. As you know, 2π radians equals 360 degrees but if you have 2 radians, then you want to convert it to degrees then you will have to do the 2 x 180 / π calculation. You should get 360 / π or 114.5 °. Here's another answer, because if you don't work with π radians then π will not cancel out in the equation, thus leading to a different value. advertisement

Advice

• When multiplying, let the integer pi follow radians because the symbol is not a decimal, so you will easily cancel it out during the calculation.
• Many graphing calculators have functions for converting units, or you can download a program to convert. Ask your teacher if your calculator has that function.

What you need

• Ballpoint pen or pencil
• Paper
• Laptop