I am running 4 matic on my s class. I know when I had my bmw x drive I was running F 20x9 R 20x10.5. I want to run 22’s on my s class. What’s the most concave I can go so the tires are running the same diameter? Thank you

 

Tires are given size ratings that allow one to calculate their dimensions: 235/35ZR18 for example.
235 is the width of the contact patch on the road in mm
35 is the aspect ratio in mm
18 is the wheel rim diameter in inches
Z means capable of speeds in excess of 149 MPH
R means radial

Rolling diameter = aspect ratio * width * 2 / 25.4 + rim

So you have an arithmetic problem of changing wheels size from 20 to 22.
You probably want a similar tire width, so we are left solving for aspect ratio.

If your W222 has 20" tires, it probably came with 245/40ZR20 tires

So we have::
245*0.40*2/25.4+20 = 245*x*2/25.4+22
Solve for x:
245*0.40*2/25.4 = 245*x*2/25.4+2
245*0.40 = 245*x + 2*25.4/2
0.40 = x + 2*25.4/2/245
x = 0.40 - 2*25.4/2/245
x = 0.40 - 0.10367
x = 0.29663 which rounds to 0.30
So you want 245/30ZR22

Now don't you wish you paid attention in school?