WaterBear,
In the formulas I've posted, the round to square is the
accurate one since it was derived from the ASHRAE formula.
Since you're the one in need of a shorcut, you can verify
the accuracy of the formula for all cases. I repeat, I can
vouch for the accuracy on round to square cases only. The
formulas for the rectangular duct was derived using an equal
area method using the area of the square duct equivalent of
the round duct. I've not tested the conversion formulas and
the accuracy might be questionable. Sorry for the confusion,
as I was hoping that you'll be able to see through the formulas.