The first known ouroboros design was found in the Enigmatic Book of the Netherworld in the tomb of Tutankhamen dating to about the 14th century BC. This design is completely smooth as opposed to the typical designs one finds that have scales. It's a US ring size 10, which is 0.779 inches or 19.8 mm inside diameter. It's also available in a US size 9.
Other sizes can be can be fabricated, just let me know what size you want it in by using the contact designer button on the right.