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But you've already closed the seam on the tube no? If so, you just need the finished circumference of the tube. If that is 28" it should give a disc diameter of 8.91". If you then sew a half inch seam all the way around, the finished disc when you turn it right way around should be pretty much an inch less than that in diameter.
Black_Rainbow_Project
moocher
I found an online converter that gives me a diameter of 9.2" including seam. Will see how that goes tomorrow. Starting from the base makes more sense, I'll try that next time.