Calculating Alcohol by Volume

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.

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.

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

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!

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 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.

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.