Ok, the formula for length of arc in radians is:
s = r@
where s is the arc length, r is the radius, and @ is supposed to be the symbol theta, which is measured in radians.
the formula for arc length in degrees is
s = @/360 * 2pi*r
we won't need both formulas, one is enough. let's use the radian formula since its simpler.
s = r@
=> @ = s/r
if s=7, r = 3
@ = 7/3 radians
now to convert from radians to degrees, we multiply by 180/pi
so @ = 7/3 * 180/pi = 420/pi degrees
but how many did we make? we can use either the radians or degrees to find out
Using degrees, Revs = (420/pi)/360 = 7/6pi revs = 0.371 revs
Using radians, Revs = (7/3)/2pi = 7/6pi revs = 0.371 revs