SR G36 barrel change help (Newbie)

[biggs111]

hi, not long got into the sport and i wanna upgrade the barrel from standard 6.05 to 6.01, been looking through the madbull stuff but i dont actually know what one it is i need? in the book it says that the inner barrel is 247mm but ive taken it apart and thats not what it measures at? also do i need to change the hop up if i buy a new barrel or would the one that comes with the gun work with a new barrel?

any help would be great!

thanks