Gee, Ben, you worked too hard!
Having had a 15' Intex Donut as soon as you said it looked to be too big to be 12' I said to myself "that's because it's a 15' pool"
Then I figured the panels are clearly 4' panels...there are 12 of them...48' circumference, divided by PI is...15' 4"...

I'm just lazy!