I am install wood base boards and have a newer home with rounded corners, is there a standard measurement for the center piece of the round, with 22 1/2* cuts

Wow they didn't install the square base pieces there may be an after piece try trimtex.com

Bullnose Corners

Could try this place for piece wood trim

Squarzit
This could wok if you want to do drywall work

Sorry it doesn't really answer your question but they are options every corner may be slightly different best idea would be to do small test corner

If u use vinyl trim, it can be heated and formed to curve.

If using wood will have to back cut,wet and form around curve. Back cut would be within 3/16'' of face and about 3/8 ''apart.

Chuck

Try cellular PVC moldings. They are flexible and can be heated to bend further

I mitre the long pieces of baseboard at 22.5 degrees, and then cut a very short piece with 22.5 degrees at each side to fit in between. It's a pretty good approximation of a round corner.

If you're painting them, use a filler to fill in the small gaps.