Where do you live?
Go to the menu and click on Profile.
Then, you can fill in your town & state or part of the state--I have Central IL on mine.
Back to your question:
If you have a really secured yard in a suburban area, you MIGHT be able to just have chicken wire. OR, if your birds are in a barn with a good guard dog, you might get away with it.
Unfortunately EVERYBODY
LOVES CHICKEN!!
Many predators can rip apart chicken wire.
I LOVE having my birds in the old unused dog chain link fencing. We haven't had any bears here since, I think, Abe Lincoln was riding the circuit!, so it keeps them pretty safe.
My neighbor and others on the forum have suggested that you bury hardware cloth 3-4 inches deep on the outside perimeter. Predators that dig---like dogs!!!---dig to the wire and then, give up, even if they try several places.
Somebody on the forum was thinking about using hardware cloth AND putting down 12 x 12 pavers. I Liked that idea, especially because they've heavy and hard for a predator to move aside.
DEFINITELY, check out the "Coop Designs" link. When you click on the pic you'll get the BYC webpage (usually) and specifics about size and materials. I got SO MUCH 'food for thought' this last winter 'cause I spent time reading on this site. That should help you with the size of your run.
hope this helps and WELCOME to BYC and chicken addicts!!