Question about adding water

I brewed a 3gal batch of a blonde wheat this Saturday. Well, Actually the pre-boil was 3 1/2 gallons, post boil came out to 2 1/2. I hit my OG of 1.051, racked to primary, pitched yeast and it's fermenting away. But I started thinking yesterday that I really wanted 3 gallons. Is it too late to add a half gallon of water? Is there a way to calculate an adjusted OG if I do add an additional half gallon?

If you hit your recipe OG, you don't want to add additional water. You will literally water down your beer. Remember for your next batch that you need to either add additional grain or otherwise up your efficiency to hit your OG and your desired volume, but if I were you, I'd care more about the beer tasting as the recipe intended, in which case hitting the proper OG is way way way more important than hitting some arbitrary volume.

Good call. I'd really like to have more quantity, but what would be the point of having more, less quality beer. I suppose I'll just keep it as is.

If you want to add the volume, the calculation is as follows. Your current quantity of fermentables is 2.5 gal * 51 points = 127.5 gal*points. If you add 0.5 gal of water with no fermentables, you'll have (127.5 gal*points)/3 gal = 42.5 points. That is, a SG of 1.0425 (or about 1.043). If that's ok, go ahead.

If you really want to top up and don't want to sacrifice gravity, you could add enough DME or LME to the water to match the OG and add that instead. Just give it a 15 minute boil, cool it, and pour it in. I'd just let it ride though.

Thanks Zeg, the calculation makes sense. I'll have to remember that for future reference. I'm actually planning on making this a blueberry wheat, so with the addition of fruit/sugar purée I had planned on the ABV being higher with that second round of fermentation, so a 1.043 wouldn't be terrible. But I think I'll just let it ride too. The reason I wanted to do more is because I'm sure I'll lose about a half gallon to trub, and coming out with just two gallons of finished beer sounds kind of sad.