50 Amp Pedastal/Nr. 4 AWG

Number of conductors AWG into a certain size raceway:

Is there an online reference now for underground wire vs conduit diameter?

50a terminals can take 3 awg wires easily so no problems there with 4 awg.
Go for it.

Cut off a small piece and check the lug fit on both ends before proceeding.

How are you going to terminate #4 onto the 50 amp recept. terminals? You probably need to splice #4 to a smaller gauge at the recept. to make it work. If so, the splices will be physically large and require a large junction box adjacent to the 50 amp recept. Same at your panel. I think you'll need split lugs to do this. Before you use the #4 you might want to price out the lugs and junction boxes vs buying some new wire.

Absolutely no reason not to use the #4 wire, except as above and also as noted by another poster above, the insulation jacket on the wire must be code approved for the location and application.

sgip2000 wrote:
If undergound, wire needs to be THWN rated to meet code requirements.

More precisely, if in conduit it needs to be wet location listed and if not it needs to be listed for direct burial. THWN is most commonly what would be used in conduit in this situation, but it's not the only permitted option.

If undergound, wire needs to be THWN rated to meet code requirements.

Already paid for is good:

Sounds good to me. As long as you understand how and wire it correctly for an RV 30 feet is nothing.