Calculating Alcohol by Volume

I've got a formula for calculating ABV (alcohol by volume) from several different sources on the Internet:

``````((76.08*(OG-FG)/(1.775-OG))*(FG/0.794))
``````

It works just great, but it's not the easiest one to remember. Are there any other formulas out there?

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Pardon me for being sill but what is og and fg stand for?? – user2969 Dec 30 '12 at 17:02
OG = Original Gravity. FG = Final Gravity – Doug Nov 22 '13 at 11:15
To elaborate... Original Gravity is the hydrometer reading before the yeast is pitched (i.e. before the fermentation begins). Final Gravity is the hydrometer reading after fermentation is complete, or at any other stage during fermentation so you can keep track of how your fermentation is progressing. An example of Original Gravity might be 1.036, and Final Gravity might be 1.010. Given these values the ABV (according to the above equation) would be 3.4% – Doug Nov 22 '13 at 11:21
Hi Rich, can you explain these numbers? I know OG and FG but what do the rest represent? – kristian nissen Jun 12 at 17:56
@kristiannissen I think they're just constants. I don't have any explanation for what they actually are, just that [the internet says] they yield an accurate ABV. – Rich Armstrong Jun 13 at 13:26

If you're looking for a quick, easy calculation, you can use:

ABV = (OG - FG)/.75
(and then multiply by 100 to get a percentage)

or

ABV = (OG - FG)*131

However, it's not a linear relationship, so there's a fair bit of error in both of those estimations but they'll get you within a half a percentage point of the actual value.

If you are concerned about accuracy, you'll need a messier formula, like the one you gave. Balling and DeClerk have good methods. There are also online calculators, like the one at Rooftop Brew. Or you could put one into a spreadsheet, and just enter your OG and FG there.

Again, if you want a simple formula, expect error.

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Agree with the fact that it isn't a linear relationship. Beyond the simple case of a simple sugar solution fermenting into ethanol it get real complex. Remember, there are a lot of other things in beer that can affect both gravity and refraction. Unless you have a real need for it, use the simple (OG-FG)*131. Its good enough for homebrew. – thebeav Dec 14 '10 at 0:46
While it does suffice to use these formulas, serious homebrewers might want to be more accurate, especially if they've gone to the trouble to take accurate measurements. Other additives, like proteins, hop matter, and even dissolved CO2, don't significantly change hydrometer readings, so there really aren't many variables. Thus, accurate hydrometer readings, paired with precise formulas, yield accurate results. – Brandon Dec 14 '10 at 2:17
The Simple formulas work best for 'average' beers, between 4 and 6 percent. The simple formula underestimates ABV for high gravity beers and overestimates low gravity beers. – Wyrmwood Sep 11 '13 at 15:50

I used Maple to plot the expression in your question as a two dimensional surface using the range of values you suggested. The plot looks rather flat in that region, so I chose the midpoint of your intervals (OG=1.065, FG=1.015) and computed the tangent plane to the surface at that point. (The tangent plane is the best linear approximation to the surface at that point.) Here's what I got:

Linear Approximation

ABV = -17.1225210+146.6266588*OG-130.2323766*FG

If you're looking for an easier to remember formula, then you can go with

Simplified Linear Approximation:

ABV = 147*OG - 130*FG -17

With this simplified linear approximation, the computed ABV differs from your original formula by no more than 0.78 on the interval you specified.

This is fairly easy to remember since 147-17=130. What luck!

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Love the approach! The 0.78 difference is a bit steep, though. I get better results subtracting higher than 17. 147*OG - 130*FG - 53/3 is about as good as my method. – Rich Armstrong Dec 16 '10 at 14:19

I spent some time this weekend dusting off my algebra. (Do not tell my high school algebra teacher that algebra was useful!)

I tested this formula against the original for a range of typical brewing OG's (1.035 - 1.095) and FG's (1.002 - 1.028). I found that it didn't stray from the above calculation by more than 0.06% ABV. Considering the variables involved in reading a hydrometer, this is definitely close enough for me. Rather than using SG in the form of `1.040` and `1.008`, it uses whole numbers like `40` and `8`.

``````( (OG-FG)*(832+OG)*(832+FG) )/5500000
``````

It's not quite back-of-the-envelope, but I can use only a calculator to get a good ABV number. It's only two constants to remember (and I can remember the latter as "five, five, five zeroes"). Would love to hear any simplifications or alternatives.

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In terms of an approximation that you can do in your head, take the difference in degrees Plato and divide by 2. It'll get you within a few 10ths of the ABV.

~ABV = (OG(°P) - FG(°P)) / 2

Edit: this approximation gets less accurate for stronger beers

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At first I was really impressed that this formula was so simple, but then I decided to check the accuracy. On a 2D plot, it differs from Balling's method by about 10% error in standard beer range, and up to 15% for strong beers. – Brandon Dec 14 '10 at 2:05
Yeah, it's definitely just an approximation (answer edited to emphasise this). I use brewing software for working out actual ABV, but this is good for getting a ball-park figure if you don't have a calculator handy. Using the plot that you generated, you could probably come up with a good correction factor to apply for better accuracy. – tallie Dec 14 '10 at 10:54

I generally use (og - fg) * 1.10. It's not spot on accurate, but you'll get a good idea. Don't forget to divide by 10 after.

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If you're going to divide by 10 after, why don't you simply do (og - fg) * .11? :-) – Jeff Roe Dec 30 '11 at 18:55