I have a few questions regarding Tinseth's and Rager's equations. First of all, I tend to brew three gallon batches of partial mash brews. I usually mash in about 1 gallon of water and add a half gallon when I rinse the grains before I bring the water to a boil. Before I start my hops, I add in the malt extract, which is usually liquid. After the boil I add the wort to 1.5 gallons of cool water and top it off if I am below the three gallon mark.
Now, when I look at the Formulas mentioned above, I notice they both ask for the wort gravity and wort volume, but I am not sure if this means the wort before I bring it up to three gallons (i.e., the boiling wort) or the after I have brought it up to three gallons. Furthermore, I don't know how to estimate gravity given a particular grain bill (specialty grains and malt extract) and an assumed efficiency level. I have used beer tools in the past and it was able to estimate the O.G. and boiling wort gravity. So, does anyone know what formulas these programs use to do this?
Summary. I want to know if
1) I use the final wort volume of just the boiling wort volume in my calculations and
2) how to estimate the specific gravity of either the boiling wort or final wort given an arbitrary grain bill.