In my experience, Brent, there's no formula. I not only size up, but I also change out the block shape as well. The blocks I use are literally vertical sided, (no taper whatsoever), and has a wider "shoulder". That takes up more material. Depending on size and open crown shape, (i.e.), I could probably lose up to a 1/4 inch in brim width, but that wouldn't necessarily be consistent all around. I have been lucky enough, a few times, not to lose any brim width at all. But, those hats were closer to my actual size and had plenty of material to work with, as in a western with a tall crown and plenty of brim. If you're going to size up and change out the block shape that has a wider profile, make sure you have plenty of hat to work with to start off. If you can find a hat, a couple sizes smaller, that has a bigger profile, you can come up with a pretty decent looking hat after converting it.
I feel like I remember Art saying that it depends greatly on the qualities of the felt itself. (And I imagine also by inference the abilities of the hatter.)
Yes, some felts do have more stretch in them and lose less. I too have wondered if I could find a mathematics guy that could work out a formula but I don't travel in those circles. But as TJones says it depends a lot on the block shape. If I am refurbishing a vintage in order to maintain the dimensions even if not upsizing (or down) I have to use a block of close to the original blocking. Moving from a regular oval to a long oval presents problems as well. Especially if the brim is bound. Moving from regular to long will produce a dimensional brim. If it is bound then I can't trim it (which I am always loathe to do, brim width is precious!) and am stuck with the dimensional brim. Not much 1/8" or so but it is present. The difference between my absolute square shouldered block and my #51's is quite large. The square shouldered blocks take up a lot of felt. I am thinking that the answer, like so much in life, is......."it depends".
Is the hat as is tapered? I would guess that if you wanted it blocked on a square shouldered block you would lose a lot of brim. Even on a tapered #51 you are going up 5 sizes and at a conservative 1/4" loss per size you would be dangerously close to stingy territory.
Wow. That's going up a bit much with that size and with those dimensions. You're going up five sizes. Although, I have to say, that I've successfully sized up a couple of 6 5/8 to a 7 1/4, but they were no longer Westerns when I was done. I had to convert them to fedoras, and they originally had taller crowns and wider brims to start off with than the 7 1/8 you're describing. I would look for something bigger in size if I were you, no less than 7 3/8, at the least, and that's still going up three sizes to get what you want, but it can be done if you have plenty of hat to start with.
I have yet to take a hat up 5 sizes but I have done 3....(7 1/8 to 7 1/2") I did it in 3 increments out of a fear of putting too much stress on the felt all at one time. It was blocked on a #51 so it went over the 'shoulders' easily.
Sounds like a plan, my manI’m coming around to this way of thinking. I guess I’ll leave this as a 7 ⅛ and flip it. It should be easier to turn cash into a hat my size than this way too small for me western.
I did two 6 5/8 that way, both were originally Westerns. I also sized up a 6 3/4 and a couple of 6 7/8, all were Westerns. That said, they were no longer Westerns after I converted them. I sized up a lot of 7s and 7 1/8, and even downsized a couple of 7 3/8 to a 7 1/4.
I try to keep my inventory of new felts in line so stock only L & XL. I find that if I wet block them in hot hot water, lots of steam I can shrink them down in size & still make a hat for the ladies in the 6 7/8 - 7" range.
Gustin Vintage Heavyweight Sweatshirt - Natural Rainbow Nep - $119 Rugged 14oz cotton that gets better with every wear. 
Grant Stone Diesel Boot Dark Olive Chromexcel - #395 Goodyear welted, Horween Chromexcel, classic good looks. 
Himel Bros. - The Ross Mk. 1 Leather Jacket Classic D-pocket motorcycle/aviator style jacket.
I could not remember if it was a 7 or 7 1/8...so yeh, 4 sizes up. We didn't lose that much brim on it either. It was a wonderful felt to work with.
I have nighmares about it now after I reblocked a really nice vintage Stetson....not even trying to upsize it and had it tear along the sweat band stitching line. The stitches were real close together and it was if the felt was a piece of paper that had been perforated. The sucker just popped and ran along the stitch line for a good 6 inches. Luckily it was for me not a client!
I'll have to give that a try. What I do to size mine down, is also to use very hot water for wet blocking, and then put it on the smaller block. I'll take my cord and tie the felt tight against the block, using a square knot. Starting from the top, I'll take my 'pusher downer' and slide the cord to the bottom of the block. It tightens the felt nicely right up against the block. I did this Stetson with that method. It started out as a 7 3/8 Stetson Longhair Western and sized it down to a 7 1/4.
The worst case is the felt puckers a bit at the brim break. I learned from Art to wrap the felt in a wide (3 or 4") medical tensor bandage after ironing the heck out of it. That usually smooths out the puckers.
