I'm building kitchen cabinets and stuck on the design aspect. The problem I'm having trouble with is the back corner in L shape corner cabinets (See first photo). How do you size the diagonal back?

It doesn't have to be very big, its only purpose is to clear any drywall mud causing the corner to bulge. Hopefully your corner is square, or you will have fun with the install. We generally do blind corners as they are easier to install and build, unless our customer is set on a comer cab like this one.

You size the back corner to get it through the door that you will be using to get cabinets into the kitchen. I also make my corner cabinets 23.5" deep so I don't have to worry about out of square corners. The cabinet being a triangle is very stable on the floor and a couple shims to attach it to the wall keeps it put.

The guys have given you some excellent advice,
I like to make my corner cabinets a little smaller like Leo said, the lowers sit on the base and when fastened to the other cabinets won’t go anywhere. The upper cabinets we will put a 4 inch wide x 1/2 inch thick cleat top and bottom, we stop the cleat about 6 inches from the corner to avoid the drywall mud in the corners, you can go with a 1/4 thick cleat if you prefer.
I always check the corner for square when site measuring as it is easy to cut the top and bottom on the cnc to match the corners if there has been movement or the corner is way out of square. I find most new construction is fairly good, some older houses nothing is square or plumb.

Are you trying to figure out the actual size? Or what to base the size of the clip on?

Note it is 12" deep so this is a wall cab , no need for the clip to get through door, it's for corner square only, make it as small or large as you want .

I make mine square in the back corner, 45 degree was a pain. The end panels are standard depth with the back set in, 3/4" on the base cabinets and 1/4" on the upper cabinets. This is far enough so sheet rock mud in the corner has never been an issue. All use all 3/4" material so it can be comformat screwed together.

I was working on a several high end houses many years ago. They had a really smart architect doing the design work. He absolutely hated lower corner cabinets. He thought lazy susans were stupid. When you do the math they are expensive for what you get. He had us leave the corner empty.

We have always done upper corners in two cabinets. You keep one shy of the corner, so there are no issues with the drywall. The frame covers half of the cabinet and you ply the other half. I think they look better and are more functional. We are more or less a face frame only shop. Beaded & Inset exclusively.

Adam, that's how I feel about corner bases. I usually just kill the corners. The left over space around a lazy Susan pretty much adds up to a dead corner. So why buy the extra cabinet and accessory.

I have that conversation every single time somebody asks for one

Totally agree with Adam and Karl. I remember reading this a few years ago:
https://www.popularwoodworking.com/woodworking-blogs/quit-worshiping-at-the-church
-of-inside-corners/

It doesn't include the modern Rev-a-Shelf update to the half-round lazy Susan (or the even fancier pull out / pull over options), but even in a small kitchen it's rarely worth the "extra" space.

A lot of the cubic footage is still wasted around the specialty hardware in corner cabinets plus I find even with the highest end stuff, it's still a pain in the butt to access them. Drawers on either side of the corner make much more sense to me. Glad to hear I'm not alone.

I have given up trying to educate the customer that a lazy susan is a waste of space. After all, I just fell off the turnip truck last week.

What I have figured out is they are the easiest and fastest way to turn a corner. Sometimes I will put shelves instead of a turn table however the hardware is simpler, 4 screws top, four screws bottom. The holes are drilled off the CNC.

Ever since I stopped using the doors spin with the LZsue hardware life has been simple.

If it's the math that you're after:
It's A squared (AxA or 6x6=36)
Plus B squared (BxB or 6x6=36)
Equals C squared (72)
Then hit the square root button (check mark) on your calculator to get 8.4853.

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