# 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?

• Pardon me for being sill but what is og and fg stand for??
– user2969
Dec 30, 2012 at 17:02
• OG = Original Gravity. FG = Final Gravity
– Doug
Nov 22, 2013 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, 2013 at 11:21
• Hi Rich, can you explain these numbers? I know OG and FG but what do the rest represent? Jun 12, 2016 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. Jun 13, 2016 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.

• 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. Dec 14, 2010 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. Dec 14, 2010 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. Sep 11, 2013 at 15:50
• I also have seen (og-fg)*132 but the "real" number is between 131 and 132 so 131 point something... Aug 25, 2017 at 18:33
• If I'm going to devote 7 hours of my day to making 5 gallons of beer, It doesn't seem like too much more of a hassle to spend an extra 30 seconds calculating what is effectively performance data for that process. Sep 8, 2018 at 19:28

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!

• 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. Dec 16, 2010 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.

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

• 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. Dec 14, 2010 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. Dec 14, 2010 at 10:54
• The Plato formula in common use here (also found in Fix) is abv=(og-fg)/(2.0665-0.010665xog) Sep 12, 2018 at 2:28
• What the heck is a degree Plato? Jun 25, 2019 at 0:39

I believe that the answer is to use as a multiplying factor .13125, ie OG 1040 minus FG 1009, gives 31 degrees drop, so multiply by .13125 = 4.06875, just tack a % sign on the end of it and you have it! I believe that this figure is what Brewers Friend use in their calc', Graham Wheeler used .131, I have also seen .1293 as a multiplying factor, I agree with the above writers, it is not linear and is only approximate between 4% and 6% beers.40 years ago I wrote to 4 breweries North South East and West in this country, Two of them said multiply by .128, and the other two said divide by 7.78. !! So there you go. Take your pick. But I think that .13 is best, if you know your 13 times table, - Cheers all. Nick.

• The inverse of 7.78 is 0.129. Jun 25, 2019 at 0:43
• Could someone tell me where the factor 0.13125 comes from? Nov 5, 2021 at 14:15

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.

• If you're going to divide by 10 after, why don't you simply do (og - fg) * .11? :-) Dec 30, 2011 at 18:55
• This formula is not accurate enough. Multiply by 131 is more precise (as specified by Brandon). Aug 25, 2017 at 18:29

Another dead easy way for assessing the alcohol content of a beer, is to simply divide the OG radicle by 10, and then add .1 after the decimal point, ie 1040 would become 4.0, plus .1 = 4.1% This does not work on beers that have a large amount of higher than average fermentability malts or sugars in them, nor will it work for the 'thicker beers that have malts with a lower percentage fermentability. This is why I choose to calculate on the points of gravity drop, and use .13 as a multiplying factor. Cheers all Nick.