What ABV equation do YOU use?

[markbrannan]

Just wondering how everyone calculates their ABV in their brews.

To date, I have seen 2 different versions, and have done a purely mathematical derivation - which is different to the other two. I'm willing to send people my derivation (in pdf format) if they wish to check my working, or are just interested in how its done. PM me - only a basic knowledge of maths is needed.

These look a little ugly because they're typed inline, but they're fairly easy to understand.

***In all of these cases, OG and FG are taken without a decimal place. i.e. a reading of 1.040 would be taken as 1040.***

Coopers: ABV = (OG - FG) / 7.46
First Steps In Winemaking by C.J.Berry (and other books): ABV = (OG - FG) / 7.36
My own mathematical derivation: ABV = (OG - FG) / 8.01

The question is, who is right?

I'd like to think it is myself, but when I e-mailed Coopers about this, they said that they couldn't fault my maths, but their equation is derived empirically (i.e. by doing many fermentations and checking the ABV with an instrument) rather than purely mathematically, and gave me a couple of reaons for the discrepancies.

However, it could be a conspiracy (for those of you who like that sort of thing) - as my derivation gives lower ABVs than the other two. Maybe some kind of marketing ploy by the homebrewing industry to keep us drinking lower ABV products? Or to make us think that we are getting a bit more ABV for our money? Who knows...

[kay-jay]

hi

i use total gravity drop x 0.129 which if i recall correctly is what customs use for calculating duty!

kj

[adm]

hi

i use total gravity drop x 0.129 which if i recall correctly is what customs use for calculating duty!

kj

Which would work out to be (OG-FG)/7.75

Which kind of splits the difference between Mark's number and the others.....

[WallyBrew]

Here's a set of figures obtained from a brew

O.G. 1045.69
P.G. 1005.32
S.G. 992.51
E.G. 1012.71
alcohol % vol 5.25
apparent attenuation 88.4
real attenuation 72.2

(for P.G. substitute F.G. and S.G. is the gravity of the distillate)

If you go to this site : http://hbd.org/cgi-bin/recipator/brew/widgets/ac.html and enter the appropriate figures it will agree closely with the given alcohol content

For the OG-PG= 40.37 the excise figure to multiply this by is 0.130 and this gives 5.24

The alcohol % by vol given is obtained from the laboratory alcohol table (published by the NPL I think)

Whereas Marks gives 5.04

So in this case it tends to indicate that, as expected, the HM Revenue & Customs factor is correct

[Garth]

Just wondering how everyone calculates their ABV in their brews.

I generally drink 6 pints of it then decide in the morning, using this equation :- how much head hurts = ABV.

I believe the Customs and Excise is supposed to be pretty spot on.

[boingy]

Equation? What are you on about? Just stuff it into some brewing software and be happy

Actually, in my case I never bother working it out, because it doesn't really matter to me.

[Blackaddler]

hi

i use total gravity drop x 0.129 which if i recall correctly is what customs use for calculating duty!

kj

The HMRC formula for the calculation is:

(OG - PG) x f = a% ABV

f being the HMRC fudge factor...see here

[markbrannan]

Here's a set of figures obtained from a brew

O.G. 1045.69
P.G. 1005.32
S.G. 992.51
E.G. 1012.71
alcohol % vol 5.25
apparent attenuation 88.4
real attenuation 72.2

Where PG is the final gravity.

I question why you quote your hydrometer readings to 2 decimal places, but that's another thing entirely.
Using these figures:

Coopers: ABV = 5.4
First Steps In Winemaking by C.J.Berry (and other books): ABV = 5.5
My own mathematical derivation: ABV = 5.0
"HM Revenue" formula: ABV = 5.2

Seems HM Revenue is closest, with Coopers formula second and mine a close third (damn!). I'm glad that mine gets a look in, at least.

But when I say "closest", I mean closest to the value for the ABV that you have given - which was calculated by a widget on a website (dubious?).
However, I wonder which formula gives the best approximation to the actual alcohol content. Is there a cheap and easy way to do this?

Again, there could be a conspiracy - as if HM Revenue taxes on the basis of (OG - FG)/7.75, but the actual alcohol content is (OG - FG)/8.01, then we're being swindled.

Although, is the calculating the ABV not upto the brewery, then HMRC taxes them upon their value?
I know that the printed value of the ABV of a drink is only allowed to be within +/- 1%

Does anyone go to the hassle of chemically finding out the ABV of their brews? Even once in a while? Do the results match up with your expectations? What equation do YOU use?

[adm]

Again, there could be a conspiracy - as if HM Revenue taxes on the basis of (OG - FG)/7.75, but the actual alcohol content is (OG - FG)/8.01, then we're being swindled.

Well.....to me, as soon as I read the words "HM Revenue", my brain automatically substitutes the words "Robbing Bastards"....so I'd dare say that yes, there could very well be a conspiracy - or at least something not 100% in the brewer's favour....

[WallyBrew]

Here's a set of figures obtained from a brew

O.G. 1045.69
P.G. 1005.32
S.G. 992.51
E.G. 1012.71
alcohol % vol 5.25
apparent attenuation 88.4
real attenuation 72.2

Where PG is the final gravity.

I question why you quote your hydrometer readings to 2 decimal places, but that's another thing entirely.
Using these figures:

Coopers: ABV = 5.4
First Steps In Winemaking by C.J.Berry (and other books): ABV = 5.5
My own mathematical derivation: ABV = 5.0
"HM Revenue" formula: ABV = 5.2

Seems HM Revenue is closest, with Coopers formula second and mine a close third (damn!). I'm glad that mine gets a look in, at least.

But when I say "closest", I mean closest to the value for the ABV that you have given - which was calculated by a widget on a website (dubious?).
However, I wonder which formula gives the best approximation to the actual alcohol content. Is there a cheap and easy way to do this?

Again, there could be a conspiracy - as if HM Revenue taxes on the basis of (OG - FG)/7.75, but the actual alcohol content is (OG - FG)/8.01, then we're being swindled.

Although, is the calculating the ABV not upto the brewery, then HMRC taxes them upon their value?
I know that the printed value of the ABV of a drink is only allowed to be within +/- 1%

Does anyone go to the hassle of chemically finding out the ABV of their brews? Even once in a while? Do the results match up with your expectations? What equation do YOU use?

I think you may have misunderstood my post.

Your last sentence: Does anyone go to the hassle of chemically finding out the ABV of their brews? Even once in a while? Do the results match up with your expectations?

The post relates to the determination of the original gravity of one of my beers by the official method.

The readings are not hydrometer readings they are determined using a density bottle and a 4 decimal place balance hence the weighings are of the order 50.0000g area or 1 part in 500,000.

The alcohol content as I stated is derived from the spirit gravity and a set of official tables and not from a "widget"

The widget given just happens to be one that calculates the alcohol very close to what would be an official figure and if it were displayed to 2 dp it may well agree entirely with my figure.

[mysterio]

I sit down at my desk with a 500ml bottle and drink it as quickly as possible and just the ABV by how much of a buzz I get.

[markbrannan]

After reading over my derivation, and using a more accurate value for the density of ethanol, my derivation becomes: (OG - FG) / 7.9 - making it closer than Coopers - YEEUUUUSSSSS!!!

[Graham]

There are a few pitfalls when attempting to calculate ABV from first principles. The first is that a certain amount of sugar is consumed by yeast metabolism and growth, which does not get turned into alcohol. The second is that the weight of sugar in solution versus specific gravity is not a linear function. Twice the specific gravity does not mean twice the sugar; plot out S.G versus Plato to see the non-linearity. It is probably this non-linearity that the steps in the Excise table compensate for. The third is that the type of sugar makes a difference; wort is mostly disaccharides, but with a disaccharide the total weight of the alcohol and carbon dioxide produced is 5.3% higher than the weight of sugar consumed, because a molecule of water is taken up by the inversion (which also reduces the volume as well). Get all those taken into account and you should be spot on. Simples.

Much easier to use the Excise table and it will, sort of, match commercial standards.

[CrownCap]

...a molecule of water is taken up by the inversion (which also reduces the volume as well)...

Hmmm, bit OT, but I guess that explains why the post fermentation volume always seems lower? Can't be down to evaporation in an essentially closed fermenter, though I guess the expired CO2 also accounts for some loss of mass.

[Hawkinspm]

I use 7.38 for my guesstimate, I was given it by a brewer in a local micro, seems to be in the same ballpark so works for me.