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).

60 degrees or π/3 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.

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. Factoring trinomials of the form x^2 + bx + c

    Jul 03, 20 09:51 AM

    factoring trinomials (ax^2 + bx + c ) when a is equal to 1 is the goal of this lesson.

    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.