Converting from radians to degrees

To convert from radians to degrees, just multiply by (180 degrees) / (π radians). Let us briefly see why all we need to do is to multiply by (180 degrees) / (π radians).

Recall that the circumference of a circle is 2πr. Therefore, there are 2π radians in any circle. 

2π radians is equivalent to 360 degrees or 2π radians = 360 degrees.

Divide both sides of 2π radians = 360 degrees by 2.

2π radians / 2 = 360 degrees / 2

π radians = 180 degrees

Now divide both sides of π radians = 180 degrees by π radians.

π radians / π radians = 180 degrees / π radians

1 = 180 degrees / π radians

1 radian = 180 degrees / π radians

Since 1 radian is equal to 180 degrees / π radians, we can just multiply any amount greater than 1 radian by 180 degrees / π radians to get the answer in degrees.

60 degrees or π/3 radians

A few examples showing how to convert radians to degrees


Example #1: Convert (π/3) radians to degrees

(π / 3) radians  = (π radians / 3) × 180 degrees / π radians

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

                        = 180 degrees / 3

                        = 60 degrees

Notice that since π radians is on top and at the bottom, we can cancel it.

The figure above shows 60 degrees or π/3 radians.

If you were converting (-π/3) radians to degrees, the answer would be -60 degrees.

Example #2: Convert (π/2) radians to degrees

(π / 2) radians  = (π radians / 2) × 180 degrees / π radians

                        = (π radians × 180 degrees) / 2 × π radians

                        = 180 degrees / 2

                        = 90 degrees

If you were converting (-π/2) radians to degrees, the answer would be -90 degrees.

Example #3: Convert (-π) radians to degrees

First, notice that (-π) radians = (-π / 1) radians

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

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

                          = -180 degrees / 1

                          = -180 degrees

Example #4: Convert (3π/4) radians to degrees

(3π / 4) radians  = (3π radians / 4) × 180 degrees / π radians

                          = (3π radians × 180 degrees) / 4 × π radians

                          = (540 degrees × π radians) / 4 × π radians

                          = 540 degrees / 4

                          = 135 degrees

Recent Articles

  1. Mean of a Discrete Random Variable

    Jul 20, 21 10:08 AM

    Learn to calculate the mean of a discrete random variable with this easy to follow lesson

    Read More

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.