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In making the assumption that given the final gravity and physical weight of beer (or any liquid for that matter), that you can find the total quantity, what is the calculation necessary for determining the total quantity of beer in either pounds or kilograms when the gravity of the beer is known within 2 gravity points gravity accuracy (determined by a hydrometer) and one pound weight accuracy (using a digital scale)?

Also, what impact will CO2 from carbonation have on this calculation?

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If you know the gravity and physical weight of the beer, then you can work out the quantity (volume) like this:

V = W / SG

where 

V is the volume in liters
W is the weight of the beer in kilos
SG is the specific gravity, e.g. 1.040

For this to be accurate, you have to be weighing just beer - the trub and yeast should not be present.

US Gallon = 3785ml

Imperial Gallon = 4546ml

To convert to US gallons volume and pounds weight, the formula is almost the same:

(lb in grams)/(UsGal in ml) => scaling facator

454 / 3785 => 0.11995 => 0.12 (2 d.p.)

V(USgal) = (0.12) * W(lb) / SG

Accuracy With a SG of +/- 0.002 and a weight +/- 1lb, the resulting accuracy is 

= 0.12 * 1 / 1.002
= +/- 0.12 USgallons

Effects of CO2

The effects of dissolved CO2 is to increase the weight of the beer by the weight of the CO2 without increasing the beer volume.

Since the CO2 is completely dissolved it adds to the SG of the beer. You don't need to worry about this, since it also adds to the total weight, hence the volume calculation is still correct.

However, if measuring with a hydrometer, you may need to be mindful of the CO2 bubbles, which can affect the reading.

If you take a SG reading with CO2, and then again without, you can see how much the CO2 weighs, and compare this with predicted results.

The density of CO2 is 1.82 kg/m3 @ 18.3°C/65°F. The density of water is 1000kg/m3. The SG of 1 volume of dissolved CO2 is then

SG_1_vol_CO2 = 1.82/1000
             = 0.0018 SG

So, for the typical beer, 2.4 volumes of CO2 adds

= 1.82 * 2.4 / 1000
= 0.004 SG

So, we would expect the beer with 2.4 volumes of CO2 to have a SG that is 0.004 larger than the degassed beer.

You can use this to compare gassed and degassed beer samples to confirm if the hydrometer is affected by the CO2 bubbles or not. A refractometer is not affected.

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  • Oh, wow! Well written! Thanks for the thorough explanation!
    – Scott
    Commented Jun 5, 2013 at 15:16
  • You had, indeed. You know, I think your point about the dissolved CO2 being part of the weight is worth emphasising. Any and all substances within the beer affect both density and volume, ergo the total weight. One should remember, though, that to mathematically add the densities together is wrong. If one were to have a volume of two substances mixed together, one with a density of say 5.0 and another of say 6.5, the resultant substance has a density somewhere between the two values, not a density of 11.5.
    – iWeasel
    Commented Jun 5, 2013 at 15:18
  • The fact the the CO2 is dissolved doesn't affect the final volume, since the weight is also factored into the SG reading. (Assuming you're using a current SG reading and not the FG of the beer before carbonation.)
    – mdma
    Commented Jun 5, 2013 at 16:10
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I am curious to know why you would need to work backwards to the volume. Having said that, and from my rudimentary mathematics:

weight/(FG x 1000) = m3

So, multiplying by 1000 to give litres would cancel the 1000 divisor to leave:

weight/FG = litres.

Example: You have beer weighing 55kg and its FG is 1.005.

55/(1.005 x 1000) = 55/1005 = 0.054m3 or 55/1.005 = 54 litres.

As for the CO2, would this not be so negligable that one could ignore it?

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  • The reason for doing this is because I thought the most inaccurate measurement of the three variables mentioned was the volume, as my scales used measure in half gallons (buckets). Come to find out though, even a 2 gravity point error in a hydrometer reading can drastically throw off the amount by around a quarter gallon, which is quite a variation in homebrewing, enough to be noticeable on my equipment at least. Maybe a (sanitized) measuring stick is the better answer....
    – Scott
    Commented Jun 5, 2013 at 15:38

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