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. 45-45-90 Triangle

    May 01, 23 07:00 AM

    45-45-90 triangle
    What is a 45-45-90 triangle? Definition, proof, area, and easy to follow real-world examples.

    Read More

  2. Theoretical Probability - Definition, Explanation, and Examples

    Apr 24, 23 07:02 AM

    Theoretical probability versus experimental probability
    Learn how to compute the likelihood or probability of an event using the theoretical probability formula.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes