12-2 UF with a 'big' dimension of 0.463 results in a calculated area (pretending it is now circular with a diameter of 0.463 inch) 0.463^2 x pi/4 = 0.1684 in^2
A single chunk of 12-2 UF would then meet the Chapter 9 Table 4 fill values in Rigid Schedule 40 PVC at the 2-conductor 31% fill-ratio with 1" (nominal) conduit.
But "cable" is supposed to be counted as 'one conductor' for fill area calculations. So that puts the single chunk of 12-2 UF in the 1-wire/conductor 53% column, so 3/4 inch rigid PVC Sch 40 or Sch 80 meets that requirement. Not that I would really like to pull 50+ ft of UF 12-2 through some 3/4 inch plastic conduit.
But running two chunks of 12-2 UF in the rigid PVC conduit then triggers an ampacity 'adjustment' down to 80% (2 current-carry conductors per cable x 2 = 4 current-carrying conductors), as well as increasing the calculated cable cross-sectional area up to 2x the previous number or 0.3367 in^2, which then pushes up the required conduit size up to (now using the two wire column) 1-1/4 Sch 80 or Sch 40 rigid PVC.
Of course, all this won't matter if the AHJ doesn't allow UF inside plastic conduit, or doesn't like the burial depth you are putting any of this in, or whatever else they don't like.