Originally Posted by Revvy
Every brewing software has a tool called a dillution calculator to help people figure out how much water to top off, when the miss their gravity in all grain brewing. If you plug the numbers of even an extract batch into the software you will see how this corrects itself.
It happens all the time. When you calculate your gravity of your current volume and you then use the dillution tool in beersmith to calculate the gravity after toppiing it off with the amount of water you are missing, you almost always come back to what the original gravity should be. I've topped off when necessary and the beer indeed has turned out fine.
(not directed at Revvy but the others on this thread)
The math in those calculators is actually very very simple.
gravity x volume = gravity 2 x volume 2 (expressing gravity as "gravity units". Basically 1.048 would be 48, and 1.072 would be 72).
So if you've done your boil, and you have 2.5 gallons of wort, and your gravity reads 1.090, and you want a 5 gallon batch, 90 x (2.5)=5 x (your OG). You come up with 45, or an OG of 1.045 if topped off to 5 gallons. Alternatively, if you don't care about the volume but want an OG of 1.065, it works the same way. You'd get 3.46, the volume you want to top off to in order to hit that OG.
And it works the same way for AG brewers (or anyone doing full boil, but most critical for all-grain) to scale down the volume, so you know before the boil whether or not you're going to hit your target gravity, and you can either adjust your boil time, your volume, or add more fermentables to make sure you're spot on.
I do partial boil all-grain (since my stove can't boil more than 5 gallons), and this formula makes life so much easier. No more second guessing my gravity readings.