How to convert  from degrees to radians

To convert from degrees to radians, just multiply by (π  radians) / (180 degrees). The math is shown below.

Convert degrees to radians

Did you understand the example above clearly? Did you not understand it at all? Do you need to see more examples? Do you need to know why we multiplied by (π  radians) / (180 degrees)?  Just keep reading please!

More examples showing how to convert from degrees to radians

Example #1: Convert 30 degrees to radians

30 degrees    = 30 degrees × π radians / 180 degrees

                      = (30 degrees / 1× (π radians / 180 degrees)

                      = (30 degrees × π radians) / 1 × 180 degrees

                      = (30 π radians) / 180 

                      = π radians / 6

Notice that since degrees is on top and at the bottom, we can cancel it. Notice also that we divided both the numerator and denominator of (30 π radians) / 180 by 30 to simplify it.

Example #2: Convert -90 degrees to radians

-90 degrees    = -90 degrees × π radians / 180 degrees

                      = (-90 degrees / 1× (π radians / 180 degrees)

                      = (-90 degrees × π radians) / 1 × 180 degrees

                      = (-90 π radians) / 180 

                      = -π radians / 2

Example #3: Convert 120 degrees to radians

120 degrees    = 120 degrees × π radians / 180 degrees

                        = (120 degrees / 1× (π radians / 180 degrees)

                        = (120 degrees × π radians) / 1 × 180 degrees

                        = (120 π radians) / 180 

                        = 2π radians / 3

Why did we multiply by (π  radians) / (180 degrees) when converting from degrees to radians?

We know that 360 degrees = 2π radians

Just divide both sides of the equation 360 degrees = 2π radians by 2.

(360 degrees)/2 = (2π radians)/2

180 degrees = π radians

Now let ? represent the amount in degrees that you would like to convert to radians and x the converted amount in radians. You can set up first an "if-then" sentence.

"If" 180  degrees equal  π radians,

"then" ?  is equal to x .

Then, you can pull out all the numbers in red and put them in a table in the same order they are listed above.

180 degrees π radians
? x

The proportion is 180 degrees / ? = π radians / x

After cross multiplication, we get 180 degrees × x = ? × π radians

x = (? × π radians) / 180 degrees

x = ? × (π radians / 180 degrees)

Therefore, if ? is the amount in degrees, to convert from degrees to radians, just multiply by (π radians / 180 degrees)

Recent Articles

  1. Introduction to Physics

    Nov 18, 20 01:20 PM

    Top-notch introduction to physics. One stop resource to a deep understanding of important concepts in physics

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

                                 Follow me on Pinterest

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.