You're probably not going to find "an equation" as to the components you mention to the size of the cooling capacity.
IF you want to stay with 12v, you can check out Sunfrost ( Google them ) fridge specs, as they are the ones most off grid folks use.....just be prepared for sticker shock.
The other way to go is what tinknal mentions.....using a standard, energy star rated small chest freezer AS a fridge using an external thermostat. Buddy of mine and I did some experimentation with a 7cuft freezer and found you can run it on 200watt/hrs/day. That means a typical 100 watt solar panel with sun 5 hrs/day would run this for 2.5 days without sun.
The external thermostat you use is:
http://kegman.net/9025.html
You will also need an inverter capable of STARTING the motor on the freezer....meaning you will need a decent 1,000w inverter with 1,500w or so surge.....something like this:
INVERTER
Throw in a brand new 7-8cuft energy star rated freezer for 300 bucks or so, and you have a super efficient fridge for 600 bucks.
The batteries/panel(s), etc are pretty much the same whether you go 12v or invert it to 120AC.....and with the inverter, you have some more power options available to you.