# Formula for make up water / gravity change

If I were to put 3.5 gallons of 1.060 wort into a carboy, and use 0.5 gallons of water to top off to 4 gallons: - What could I project that gravity would be? - Anyone have a good formula, even if just a rough calc?

Basically I'm stuck using my 20 qt pot, and I think the most liquid i could fit without boilover would be 4-4.25 gallons. I typially have around a .75 gallon/hour boil off...so ending around 3.5.

Thanks!

There are plenty of online dilution calculators, but if you want a formula, the below was taken from Mechanics of No Sparge Brewing:

The Dilution Formula (reference Ray Daniels, Designing Great Beers)

Most of the dilution/gravity calculations found in this write up are based on a simple formula that states:

Beg Volume * Beg Gravity=End Volume * End Gravity

(The Gravity numbers are Gravity Points, i.e. 1.060 OG=60 gravity pts, 1.045=45 gravity pts.)

By algebraically re-arranging this formula, we can find any element in the formula, as in:

Beg Volume=End Volume * End Gravity / Beg Gravity

Beg Gravity=End Volume * End Gravity / Beg Volume

End Gravity=Beg Volume * Beg Gravity / End Volume

End Volume=Beg Volume * Beg Gravity / End Gravity

End Gravity = 3.5 * 60 / 4 = 52.5

So about 1.053, which agrees with Beersmith's calculator.

• Thanks, Joefish. Exactly what I needed. The few beginner level books i've got don't cover this. – dsidab81 Feb 7 '12 at 22:04
• Cheers! You may want to consider using brewing software. I use Beersmith, which comes with plenty of calculators and tools to help you figure this sort of thing out. – JoeFish Feb 8 '12 at 13:57

You can work it out by using gravity points.

The final gravity is your current gravity (in points) x original volume / new volume.

Gravity points is the gravity, but without the leading 1.

For example, .060 (original gravity) x 3.5 (original volume) / 4 (new volume) = .0525, or a specific gravity of 1.0525.

So your final gravity after topping up to 4 gallons would be 1.053 (rounding up.)

• Thanks for the answer also...i accepted the first response but I gave you some credit too! – dsidab81 Feb 7 '12 at 22:37
• Thanks, an no worries, JoeFish's answer was a good one! Good luck with the brew. – mdma Feb 7 '12 at 22:48

The calculation is pretty simple, I think.

(Original Point of Gravity) * (boil volume / total volume) = (new points of gravity)

60 * (3.5/4) = 52.5

Predicted SG after dilution, therefore is 1.0525

You should also be aware that with partial boils, your hop utilization will be lower than if you were boiling all the wort. See Palmer's How to Brew.