Actually no. This is 38.08 TCW... Total Carat Weight. . . The carat weight of all the individual diamonds added together. Since there are a total of about 12,638 diamonds, each diamond in the ring weighs about 3/1000 of a carat. There’s a little over 7.5 grams of diamonds in that ring. . . But each diamond isn’t worth that much. . . And likely has very little faceting.
As for the size of a 38 carat diamond solitaire, you’d be wrong on it’s diameter if it were a round diamond. You are forgetting the squared cube law. A 3 carat diamond is only about ⅜” (9.1mm) in diameter. I have a really large round diamond... 121 carats and because of that squared cube law, it’s only 1 ⅛” (28.575mm) in diameter. I was thinking about buying a 255 carat diamond, thinking it would really be spectacular, but to my surprise, again due to that squared cube law, it was only 1 ¼” (31.75mm) in diameter, only ⅛” (~3mm) larger, but more than twice as massive. You could hardly notice the difference. Both were black diamonds. . .

My 16.5 carat black diamond solitaire ring is slightly under ⅝” (16mm) in diameter. . .

I’d estimate a 38 carat solitaire round diamond, less than one-third the carat weight of that 121 carat black diamond of mine, depending on depth of the pavilion, would likely be less than ¾” (19mm) in diameter... again, due to the pesky squared cube law. The famous Hope Diamond in the Smithsonian, weighing 45.52 carats, measures just 1” × 7/8” × 15/32” (25.6mm × 21.78mm × 12mm)... a fairly shallow pavilion compared to most round diamonds, which somewhat reduces it’s weight.
PS: I’m still trying to figure out what to do with a 121 carat diamond. I’ve thought about a cane topper, gear shift knob, and even a club. It’s too deep for a pendant or bracelet for hanging properly....and at 24 grams, it’s damned heavy for either purpose.