What are the dimensions of the panels you're looking at? Then I can tell you if 8ft, you'll need 20 if 10ft, you'll need 16 if 12ft, you'll need 13 This is not including the gate... if the gate is a different dimension, then it'll be a bit different.

found this on a site that sells panels - they have different sizes listed for 30/40/50/60 & 70 foot round pens 50'13-12ft 1-4x8 walk thru gate

Depends on the length of the panels. Circumference = diameter x pi So if you want a diameter of 50 ft you take 50 x 3.14159 = 157 (approx) feet. So then just divide that by the length of your panels for the number needed. You'll need 20 if they're 8ft long. 26 if they're 6ft.

round pen panels I think the smallest most people use is like 40 foot, but you need like 60 feet for heavy work I think. Don't quote me on that.All I know is 22 feet aint that big.