There is no special unit related to the distance around a circle. It's a distance, a length measurement.
Pick what fits. Millimeters, inches, yards, kilometers....
It's possible to describe it in degrees too, referring to the width of an angle as seen from the center.
Rarely used outside fairly specialized navigation purposes.
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It was never confirmed. The degree was created as a unit equal to one three hundred sixtieth of the way around a circle
Since the radius of the unit circle is 1, the circumference is 2 x pi.
A 'unit cube'. Just like a circle with radius 1 and center at (0,0) is a 'unit circle'.
If x2 + y2 = 1, then the point (x,y) is a point on the unit circle.
Pi over 12 on a radian unit circle is a little more than a quarter of the circle. Radian units are an alternative to degrees.