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Calculating gearing is quite straightforward, if easier with an online app. (or a spread sheet).
Divide the engine rpm by the particular ratio (the taller gears will be multiplying engine rpm as you are dividing by a number <1) and then divide by the final drive (always a reduction).
That will give the wheel rpm - which is nominal with an auto. transmission. Multiply by the tire circumference to give a distance (in inches) covered per minute. By 60 gives distance per hour and then convert inches to miles for MPH.
It's nominal with an auto. trans. because the torque converter slips, varying with engine torque/load, when it is not locked up. That effectively lowers the gearing. That is why auto. trans. are geared "taller" - numerically lower - than manual trans. and can use fewer gear ratios. Swapping in the different ratio trans. may not be the only option if different TC are available.
I don't know how you would find out (easily) what the exact characteristics of the TC are, particularly because they also depend on the torque and load it is subject to. Size is one indication; physically smaller are usually "looser" i.e. slip more at a given load. The stall speed - measured with the driven wheels held stationary - of a TC might be found in shop manuals though.
TC clutch lock up is usually determined based on road speed and engine load, either directly from a MAP sensor or derived within the ECU from engine air flow and rpm. If the road speed sensor is "downstream" of the final drive, that will remain the same with altered gearing. With taller gearing the engine load will be higher - good, in terms of getting the TCC to lock - and rpm lower - may not be so good, depending - for a given road speed. Really high engine load will also cause the TCC to unlock.
To calculate "ideal" gearing with some precision you really want a full BSFC map. For some more insight, find any BSFC map that has the lines of constant power on it (like the VW one). Pick an arbitrary - but typical - power output (from measured engine MAP or TPS %). Then see what effect your new rpm will have by running along the constant power line to the new rpm and reading off the lower(?) BSFC.
A couple of other things to consider. The trans. shift points will be determined from engine load, engine rpm and road speed. The different installation (and wheel circumference?) may affect those. If the trans. is shifted electronically you may have issues with compatibility with the PCM or need an associated stand alone trans. control module.
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