What formulas and calculations exist for the home brewer?
As jsled mentioned, you can calculate just about everything to do with brewing beer from the specific heat of your mash tun to the amount of gas it takes to bring your brew kettle to boil given a specific gravity of its contents. It all depends on how much you want to know and how you brew!
Here is a site with several calculators that might help you see the possibilities of refinement and fine control that major breweries strive to achieve. http://www.brewersfriend.com/stats/
Personally, I use a piece of software called BeerSmith that gives me a lot of information that I find useful, particularly mash volumes and mash in temps, which is important in all-grain brewing in a non-HERMS mash tun.