Don't know if there is formula for converting degrees to percent, but here's a thought: Imagine a clockface with just the minute hand. When the hand makes a full circle, it has traveled 360 degrees for 100% of the circle. When the hand points to 3, it has traveled 45 degrees for 25% of the circle. The 6 is at 180 degrees and 50%. The 9 is at 270 degrees and 75%. You could break it down from there.
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Multiply the radians by 180/PI to convert to degrees.
One revolution = 360 degrees or 2pi radians
47.6925 deg = 83.24 radians.
5 radians = 286 degrees.
Scroll down to related links and use the fine calculator "Convert radians to degrees and degrees to radians".