Alcohol By Volume Calculator Updated - Brewer's Friend
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# Alcohol By Volume Calculator Updated

Thursday, June 16th, 2011

The Brewer’s Friend ABV Calculator was just updated to include not one, but now two formulas for calculating ABV.  There are two popular formulas out there for calculating ABV.  You can pick the one you prefer for use in your brewing notes.   If you don’t like math, or don’t care that much, just stick with the basic formula. If you are super into math, and want to use the advanced formula (which is supposedly more accurate for high gravity beers), then the alternate equation is now there for you.

Standard Formula:

Most brewing sites use this basic formula:

ABV = (og – fg) * 131.25

This equation was created before the computer age.  It is easy to do by hand, and over time became the accepted formula for home brewers!

Variations on this equation which report within tenths of each other come from The Joy of Homebrewing Method by Charlie Papazian, Bee Lee’s Method, Beer Advocate Method. Some variations use 131 instead of 131.25. The resulting difference is pretty minor.

Alternate Formula:

A more complex equation which attempts to provide greater accuracy at higher gravities is:

ABV =(76.08 * (og-fg) / (1.775-og)) * (fg / 0.794)

The alternate equation reports a higher ABV for higher gravity beers. This equation is just a different take on it. Scientists rarely agree when it comes to equations. There will probably be another equation for ABV down the road.

The complex formula, and variations on it come from Ritchie Products Ltd, (Zymurgy, Summer 1995, vol. 18, no. 2) -Michael L. Hall’s article Brew by the Numbers: Add Up What’s in Your Beer, and Designing Great Beers by Daniels.

Why don’t calculators all agree?

1. The relationship between the change in gravity, and the change in ABV is not linear. All these equations are approximations.
2. Some calculators round internally as they go. The Brewer’s Friend calculator rounds only at the very end, which means significant digits are kept along the way (making it more true to the equation).
3. Other online calculators should be close to one of the two equations reported by the Brewer’s Friend ABV Calculator. If not, they are doing their own thing which warrants inquiry.

What equation should I use?

Your home brewing friends probably use the basic equation. If you don’t like math, go with the basic equation.

If you are a really tech heavy brewer, and want to brew a lot of high gravity beers, or prefer Daniels over Papazian, use the advanced equation.

Either way, they are close for beers below 6% ABV.   The difference does get larger as the gravity increases.   For a brew with OG 1.092, and an FG of 1.021, the standard equation reports an ABV of 9.32%, while the alternate equation reports 10.17%, that’s a difference of 0.85%.  At that alcohol level, after a few beers, maybe it doesn’t matter so much… hehe ;)

Prost!

Legal Disclaimer: The Brewer’s Friend ABV calculator is for entertainment purposes and should not be used for professional brewing. No warranty or guarantee of accuracy is provided on the information provided by this calculator.

1. ## 9 Responses to “Alcohol By Volume Calculator Updated”

2. Please oh, please stop using archaic homebrew formulas for any brewing purposes.

Unless you are simply a homebrewer.

Read professional works on this topic. Bamforth’s Brewing Materials Book or the ASBC Journal for pros please.

By Gary on May 17, 2021

3. Hi, the basic formula is the same as in winemaking, is the alternate formula applicable to winemaking too or does it deviate?
Cheers
Sergio

By Sergio Muelle on Jul 18, 2021

4. Although I would like to agree with Gary, the ASBC methods are not easy to follow without proper lab equipment. Specifically for measuring alcohol, which requires weighing distillate to generate a curve on which you can use refractometer gravity readings. And even then, it confuses me quite a bit. I’m slow with math, so I appreciate calculators like this, even though I know it’s less than ideal.

By Spencer on Nov 23, 2021

5. I found the article by M. Hall referenced above at this link: https://www.homebrewersassociation.org/attachments/0000/2497/Math_in_Mash_SummerZym95.pdf

I was able to derive the “Alternate Formula” above from the equations in the article. This “Alternate Formula” is an approximation based on some simplifications. For example, it contains a simplified equation for converting SG (Specific Gravity) to E (Extract in degrees Plato): E in deg. Plato = 1000*(SG-1)/4. It also contains a simplification for the calculation of the Real Extract (RE) value (in deg. Plato) by assuming an OE (Original Extract in degrees Plato) of 12.5 (which corresponds to an Original Gravity (OG) of about 1.050).

I calculated tables of % Alcohol By Volume (ABV) for OGs from 1.030 to 1.110 and Final Gravities (FGs) from 0.990 to 1.050 using both the “Alternate Formula” (i.e., Equations 17 and 18 in Hall’s article) and with the “most accurate equations” in Hall’s article (i.e., Eqs. 7, 10, 16, and 18). These two tables agreed pretty well (-0.1 to +0.1 % ABV over most of the range of gravities. However, neither of these tables matched well with Table 2 in Hall’s article “TABLE 2: ALCOHOL PERCENT BY WEIGHT (USING MOST ACCURATE EQUATIONS”. Using the values in Hall’s Table 2 (in % ABW) and converting to % ABV there was a significant difference in the values (up to -1.5 % ABV lower than the values I calculated using the “Alternate Formula” and the “most accurate equations” in Hall’s article).

The closest I came to recreating Hall’s Table 2 was by replacing the OE in the denominator of Hall’s equation #16 with the RE. This gave me % ABV values very close to the % ABV values calculated from in Hall’s Table 2. Since Hall’s Eq. 16 for % ABW comes from the work of Balling done many years ago and has been in use for a long time, I do not believe it is incorrect and therefore it suggests that the values in Table 2 of Hall’s article are incorrect (but the equations in the article are correct). The fact that the % ABV tables I calculated from the “Alternate Formula” and from Hall’s “most accurate equations” agree also suggest that the equations in the article are correct but the values in Table 2 of the article are not. M. Hall is/was a computational physicist at Los Alamos National Laboratory. I would very much trust his research and that the equations in the article are correct. However, anyone can fat finger a wrong entry into a spreadsheet cell equation and get a table of incorrect values that gets quickly pasted into an article. Also, the “Alternate Formula” has been used for many years for many of the online brewing calculators so I would tend to believe it is correct.

Has anyone seen any actual empirical data (% ABV versus OG and FG from experiments) that would validate the “Alternate Formula” for % ABV ( i.e., ABV =(76.08 * (OG-FG) / (1.775-OG)) * (FG / 0.794) ) ?

By Ron on Nov 19, 2023

6. My previous comment stated that I could not match the % ABW values in Hall’s Table 2 using Hall’s Eqs. 7, 10, and 16. I have now found the problem with my calculations. I fat fingered a coefficient in Eq, 16 into my spreadsheet incorrectly. I had the value as 0.01665 instead of the correct value of 0.010665 ! My calculations using Hall’s “most accurate equations” now give me identical values to those found in his Table 2.

This poses a new question. Why does Hall’s simplified equation for % ABV (the “Alternate Formula” above) give much higher values for % ABV than the values from his “most accurate equations” for high OG cases? I believe it is caused by using the very simplified equation for converting SG to E (i.e. E = 1000*(SG-1)/4 where E is in deg. Plato) to derive the simplified % ABV equation (i.e., the Alternate Formula). For example, the simplified SG to E equation gives an E value of 22.5 P at an OG of 1.090 while Hall’s more accurate method for this conversion give an E value of 21.5 P. The result from the simplified equation is over 4% higher than the accurate method’s result. This error is carries into the simplified Alternate Formula to produce % ABV values that are overly high for high OG cases. For example, the Alternate Formula produces a % ABV of 10.65 for an OG = 1.090 and FG = 1.015 while Hall’s “most accurate equations” gives a value of 9.93 % ABV. The Alternate Formula (Hall’s simplified equation) result is 0.72 % ABV higher than the accurate method, an error of over +7 %.

So if the Alternate Formula produces overly high values for high OG brews (significantly higher than Hall’s accurate method), why is it in use? It does produce fairly accurate % ABV values for OGs under 1.065. Do brewers doing high OG brews (OGs over 1.065) just like the “incorrectly” higher % ABV the Alternate Formula produces or is there empirical data that shows the Alternate Formula (Hall’s simplified method) is valid?

By Ron on Nov 20, 2023

7. I disagree with the statement that precedes the Alternate Formula equation shown above => “A more complex equation which attempts to provide greater accuracy at higher gravities is:”

In Dr. Hall’s article he clearly states:

‘If you’re not interested in extreme accuracy, then the simple formulas are probably adequate. This is especially true of beers with original gravities less than 1.070, because the two formulas diverge significantly for high specific gravities. You might want to go through all the complicated calculations for a barleywine or a mead …”

You can find a copy of Dr. Hall’s article at:
https://www.homebrewersassociation.org/attachments/0000/2497/Math_in_Mash_SummerZym95.pdf

By Ron on Nov 21, 2023

8. I agree with the above. The second formula is only accurate near OG 1.050, and the first formula works just as well for a quick estimate. You should provide the full calculation using the Balling formulas instead, it’s pretty straightforward.

1. Measure extracts OE and AE in Plato or convert from gravity readings using accurate tables or formulas.

2. Compute
q = 0.22 + 0.001 OE
RE = (q OE + AE) / (1 + q)
A%w = (OE – RE) / (2.0665 – 0.010665 OE)
A%v = A%w / 0.794

This is easy to implement in a calculator so I see no reason to introduce errors by arbitrary oversimplification.

By Fredrik on Mar 6, 2024

9. Sorry the last formula should read A%v = A%w FG / 0.794. It’s all in the article linked above.

By Fredrik on Mar 6, 2024