# 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

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

1 = 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

= 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

= 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

= -180 degrees / 1

= -180 degrees

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

= 540 degrees / 4

= 135 degrees

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