If you are an extract/partial-mash brewer, you may have wondered how to account for the high gravity worts that you'll be boiling. You know that it must be higher than your target OG for 5 gallons, but how much higher is it? This figure is especially helpful when targeting a specific level of hop bitterness in your finished beer. By knowing the proper OG, you can hop appropriately and make beers that are closer to what you originally intended.
Let's say you intend to brew five gallons of an American Pale Ale with an original gravity of 1.050. According to Ray Daniels' Designing Great Beers, you would need about 6.6 pounds of LME to achieve this gravity.
Daniels notes that the extract potential of 1 lb. of liquid extract in 1 gallon of water yields between and OG of 1.037 - 1.039.
If we take the average (1.038) and express it in Gravity Units (GUs), we can calculate the following way:
First multiply 50 (target GUs) by 5 gallons. The total gravity units that we're shooting for will be 50 x 5 = 250 GUs.
Then divide the total GUs by the GU potential of the extract. 250/38 = ~6.6.
There you are. ~6.6 pounds is how much you'll need to get an OG of 1.050 in five gallons.
If doing a full-wort boil, you could calculate the hopping rate using 1.050 as your OG. But if all of your fermentables are in three gallons, the gravity of your wort will be higher. Subsequently, hop utilization will go down and you won't be able to extract as much iso-alpha acid from your hops. Since an APA is a fairly bitter beer, you're going to want to adjust your hopping rates to get the desired amount of bitterness.
We can use the following formula to determine what the OG of a given volume would be like assuming it will be 1.050 at 5 gallons. This formula is also courtesy of Daniels.
[GU(beg.) x Volume(beg.) ] / Volume(end) = GU(end) 
For example - (60 x 6) / 5 = 72
This formula is helpful for doing things the other way around, that is, figuring out OGs after evaporation. However, we want to solve for GU(beg.), not GU(end). After all, we already know what GU(end) will be...1.050!
In order to go the other way, we use this formula:
[GU(end) x Volume(end)] / Volume(beg.) = GU(beg.) So...
[50 x 5] / 3 = 83.3 - We can round to 83. That is, the OG of your wort is 1.083.
As you can see, that's a big difference in OG of the wort you're boiling!
 Daniels, Ray Designing Great Beers (Brewers Publications, 2000) pg. 31 - Table 5.1
 Daniels, Ray Designing Great Beers (Brewers Publications, 2000) pg. 36