How many 12/3 cables in 1/2" (trade) Greenfield?

The flexible metal conduit is only being used to "protect" the wires in the vertical drop from their run along my basement ceiling joists to the waist-level outlet boxes -- approximately 4 ft total length. The rest of the run is pure Romex (and appropriate bushings are used to protect the wire where it enters the flex conduit and where the flex conduit attaches to the 4x4 outlet box).

I'm guessing that 3/4" for two and 1" for three 12/2's. Keep in mind that the greenfield will need to be terminated at one end in a grounded metal box as all metal conduit carrying live wires needs to be grounded.

You are probably guessing one size too small. When you use an oval cable you need to calculate it as a circle the diameter of the widest dimension. They assume the cable may be twisted Since a 12/2 is about .4" across the flat side it would look like a #1 single THHN conductor in your calculation. That means one in a 1/2", one in a 3/4" and one in a 1" (table C3). You could surely get more in there if you carefully stacked and taped them but it would not be code compliant.

Cheers, Wayne

Excellent advice.