I think this is an exercise in futility.
I think the circumference of the tire doesn't change enough to matter. I really doubt that it "grows" like a dragster tire, and even with a flat spot where it contacts the ground, I think the circumference stays essentially the same.
A 225/40 18 tire should have a diameter in the 25" range.
(225 X.40 X 2 divided by 25.4 + 18 = 25.086")
25.086 X 3.1416 = 78.80" circumference.
Jack a tire off the ground and measure the circumference and see how close it is.
Just my opinion,