Final drive ratio is a mere claculation and equals top gear ratio times axle ratio.
To determine other ratios in whatever gear simply multiply the transmission gear of choice by the axle ratio.
Crawl ratio is similar in so far as being a mere calculation. In this case it's 1st gear ratio times transfer case ratio times axle ratio.
So tire diameter doesn't affect either - but that doesn't mean real world performance is unaffected.
An auto gives a huge benefit to real world results, particularly with crawl ratio since you can modulate throttle prior to lock up, getting the torque you need but not the speed you don't.
With 4.10's I'm assuming you have a Rubicon. That means 4:1 transfer case. The WA580 has a pretty low 1st gear, a huge advantage for the 2012's. 3.59 1st gear ratio X 4 (transfer case ratio) = 14.36, that times 4.10 (axle ratio) = 58.876. That is a fine crawl ratio with 37's.
FWIW, I run at about 15psi off road, on BFG, know for being a shorter tire for nominal diameter.
Also fwiw, final drive ratio for your Jeep: .83 x 4.10 = 3.403; and for mine: .67 x 4.88 = 3.2696, so your is geared lower on the highway...
Thanks - you didn't really directly answer what I was attempting to ask, but kinda' re-made my point in a round about way.
Let me clarify a bit -
First, I probably should have said "final/'realized' overall effective gear ratio" instead of "final drive ratio". "Final drive ratio" can be ambiguous depending on what site or forum one is on and because, as you stated, simply put FDR=Tranny ratio X axle ratio, "final drive ratio" wasn't the best choice of words on my part.
Second, my use of that term, however technically incorrect, stems from knowing that, all things being equal (ie- the calculated final drive ratio), shorter tires will give a lower 'realized/final' gear ratio than taller tires on a given vehicle.
So, with my current set-up on 35s (which I'm perfectly content with on and offroad), I am naturally concerned about having appropriate gearing when throwing on a set of 37s for dedicated off-road only use.
You touch on my point with crawl ratio. While you say ~59 is a good crawl ratio for 37s, my prior rigs have been higher (closer to having a 2012 auto with 4.88s, for example - CR of ~70).
So, given that, it got me thinking about what effect air pressure has ... lowering air pressure 'lowers' the weighted radius of the tire and, thus, the overall 'weighted' tire diameter. But, the circumference doesn't change ...
So, the point of my "logic check" was to simply verify what I was thinking; mainly, that despite running larger tires aired down (in the past I've run 37s at 8-12psi on a similarly weighted rig), ideally I'd still need to regear to hit optimal gearing off-road for that size tire because the circumference of an aired-down 37" tire is larger than a 35" tire at road pressure, despite 'weighted' diameters being the same/similar