To convert degrees into radians, you just need to memorize a few easy steps.
First, take the number of degrees you wish to convert. Multiply this number by π radians/180 degrees. By eliminating some redundant units and then simplifying things a bit, you'll have your answer.
Suppose you've got a metal bar that's been bent at a 120 degree angle. How can we express this in terms of radians?
To find out, we'll write our equation like so:
120° x (π radians/180°)
Notice the pair of degree symbols shown above. Those will cancel each other out, ensuring our final answer will be in radians. We are now left with:
120 x (π radians/180)
Do the multiplication and you get 120π/180 radians. But we’re not quite done yet. Now we’ve got to simplify our fraction if possible. We need to identify the highest whole number that can be divided exactly into both the denominator (180) and the non-π portion of the numerator (120). Spoiler alert: In our case, the magic number is 60.
If you actually divide 120π and 180 by 60, you get 2π/3 radians.
So, there we go: 120° is equal to 2π/3 radians.
Going from radians to degrees is a similar procedure. Only in this case, we'd take the starting amount of radians and multiply it by (180°/π).
π/3 radians x (180°/π) = 60 degrees
To convert from radians to degrees: multiply by 180, divide by π
To convert from degrees to radians: multiply by π, divide by 180