

Convert Radians to DegreesFormula to convert radians to degrees and backformula convert radians to degrees  formula convert degrees to radians animated demonstration of a radian  s = rθ  images
Just as we can measure a football field in yards or feetwe can measure a circle in degrees (like the good old days) or in radians (welcome to the big leagues!) Think about what the word radian sounds like...well, it sounds like 'radius', right? It turns out that a radian has a close relationship to the radius of a circle
Demonstration of Radian of CircleThe video below is an animation of 1 radian. Notice how the length of 1 radius stretches out to a portion of the circle. That portion is 1 radian of the circle. There is a simple formula to convert radians to degrees. 1Π radian = 180. Therefore you can easily convert from one unit of measure to the other Degrees to radiansThe general formula for converting from degrees to radians is to simply multiply the number of degree by Π /180° Example 1:
Convert 200° into radian measure: $ 200 ^{\circ} \cdot \frac{\pi }{ 180 ^{\circ}} \\ = \frac{10\pi}{ 9} \text{ radians } = \text{3.49 radians } $ Example 2:
Convert 120° into radian measure: $ 120 ^{\circ} \cdot \frac{\pi }{ 180} = \frac{2\pi}{ 3}\text{ radians }= \text{2.09 radians } $ Radians to degreesThe general formula for converting from radians to degrees to simply multiply the number of degree by 180°/(Π) Example 1:
Convert $$ \frac{4}{9} \pi \text{ radians} $$ to degrees $ \frac{4\pi}{9} \cdot \frac{180 ^{\circ} }{\pi} \\ = \frac{4\pi \cdot 180 ^{\circ} \cdot}{9\pi} =\frac{720 ^{\circ} \pi \cdot}{9\pi} \\ \frac{720 ^{\circ} \cancel{ \color{Red} \pi} \cdot}{9\cancel{ \color{Red} \pi}} \\ = 80 ^{\circ} $ Example 2
Convert 1.4 radians into degrees: $ 1.4 \cdot \frac{180 ^{\circ} }{\pi} \\ =\frac{252 ^{\circ} }{\pi} \approx 80.2^{\circ} $
" Is there any difference between 5 radians and $$ 5\pi \text{ radians }$$? "
Practice Converting Degrees between Radians
Problem 1) What is the radian measure of 60°?
Use the formula to convert degrees to radians and multiply the degrees by $$ \frac{\pi}{180}$$. Problem 2) What is the degree measure of an arc whose measure is $$ \frac{2\pi}{3} \text{ radians} $$?
Use the formula to convert radian to degrees and multiply the radian measure by $$ \frac{180}{\pi}$$. Problem 3) What is the degree measure of an arc whose measure is $$ \frac{7\pi}{12} \text{ radians} $$?
Problem 4) What is the degree measure of an angle whose measure is 14 radians?
Further Reading
