Evaluation of The Method:  Comparing Estimated and Measured %ABV

©  James M. Gossett (March 31, 2012)                Questions/Comments?    Description: escription: http://www.ithacoin.com/brewing/stoichiometry_files/image002.gif



     Stoichiometry of Ethanol Production From Maltose

     Contribution of Ethanol to Apparent Brix

     Measurement of %ABV Using Brix Refractometry

     Derivation of Calculator Equations

     Evaluation of The Method: Comparing Estimated and Measured %ABV  

My refractometer-based method for estimating %ABV from pre- and post-fermenation Brix was evaluated using a dataset of 12 beers.  Results were compared to experimentally measured %ABV data.   Note that most of my brewing is of fairly high-gravity beers – Northern Ale, Double IPA (DIPA), Honey Malt Ale, Belgian Tripel;  consequently, the dataset is skewed towards the high end of %ABV.  There is also one apple cider among the set.  Two of the samples (DIPA-1a and 1b) were actually of the same beer, sampled months apart.




Figure 1 presents comparison of Brix-estimated vs. measured %ABV.



Figure 1.  Comparison of Brix-based modeled vs. measured %ABV for a dataset of 12 brews.


The summary statistics are:  mean difference = 0.1 %ABV; sample standard deviation of the difference (n=12) = Ī0.4 %ABV.    Thus, one can reasonably expect to estimate %ABV, for home-brewing purposes, with the Brix-based calculator.  Commercial brewers would likely feel the need for more accuracy.


The mean difference and sample standard deviation of the difference reflect some combination of imprecision and inaccuracy – in both the model-based estimates and in the experimental measures of %ABV.  We are comparing the model-based estimates to imperfect measures of “actual %ABV.”  As reported earlier, the standard deviation of the method used here for measuring alcohol content is Ī 0.2 %ABV.  And imprecision in reading the Brix scale affects model estimates of %ABV, just as it does experimental measures of %ABV:  the refractometer cannot be read more precisely than to Ī 0.1 Brix.   That sort of imprecision in reading the Brix scale propagates to an imprecision in model-estimated alcohol values of about 0.1% ABV.    Putting these sources together, it’s not hard to understand why imprecision in the difference between Brix-estimated model and measured alcohols would be as high as Ī 0.4% ABV.



Residual Real Extract


Figure 2 presents Brix-based calculator estimates of residual Real Extract (Pf) versus “measured” values.



Figure 2.    Comparison of Brix-based modeled vs. “measured” residual real extract.


What I am referring to as “measured” residual RE is not quite that.  It’s not based on specific analysis of carbohydrates, via HPLC or some wet-chemical technique (e.g. anthrone reagent).  As presented elsewhere, it is based on Brix measurement (Bf aft boil/reconst) of the beer after boiling off 75-80% of its volume (to remove EtOH) and replacing it with distilled water.  If we assume that the factor of 1.04 between initial Brix (Bi) and initial extract (Pi) in pre-fermented wort represents non-carbohydrate constituents that contributed to initial Brix; and that these remain after fermentation; then


         residual RE “meas” = Bf aft boil/reconst – (Bi –Bi/1.04)*(OG/SGf aft boil/reconst)



The factor (Bi –Bi/1.04) represents the grams of non-carbohydrate contribution to original Brix (Bi) and the ratio (OG/SGf aft boil/reconst) corrects for the difference in specific gravity between original, pre-fermentation wort (when the Bi measurement was made) and the specific gravity of the post-fermentation beer after boil/reconstitution (when the Bf aft boil/reconst measurement was made).  It is necessary because the reference on which weight% is based has changed.  The same mass of nonfermentable carbohydrates in 100 g of original wort at (for example) SG = 1.050 will contribute a greater extent of weight% to a post-fermentation beer, after boil/reconstitution, with (for example) SG =1.010.


The model-estimated residual RE compares reasonably well with the “measured” residual RE.


Final Brix, After Boiling/Restoration


For those who would prefer to model the final Brix measured on the post-fermentation beer, after boiling off 75-80% of its volume and restoring with distilled water, I present Figure 3.





Figure 3.  Comparison of Brix-based modeled vs. measured residual Brix (after boiling/reconstitution).



Comparison With Hydrometer-Based Methods of %ABV Estimation


There are many hydrometer-based methods to estimate %ABV in finished beers.   I chose only four of them for comparison to my Brix-based method. 


Standard SG-Drop Method

From the FermCalc website



“…Described on pages 79-80 of First Steps in Winemaking by C. J. J. Berry (1987). It estimates the alcohol content by dividing the drop in specific gravity by the constant 0.00736,” or:

av = (sgi - sgf) / 0.00736


av = alcohol content, % by volume
sgi = initial specific gravity
sgf = final specific gravity




From Dave Miller (The Complete Handbook of Homebrewing, 1988, Storey Communications.  Miller uses the same formula as the Standard, SG-Drop Method above, except the factor in denominator is 0.0075.


Duncan and Acton

From the FermCalc website


“This method is described on pages 64-66 of Progressive Winemaking by Peter Duncan and Bryan Acton (1967).” 

av = 1000(sgi - sgf) / [7.75 - 3.75(sgi - 1.007)]




Gives %ABW


ABW = 76.08(OG-FG)/(1.775-OG)


which I then converted to %ABV by %ABV = %ABW*FG/0.794, where 0.794 is the density of EtOH at 15ŻC.


I used each of the four hydrometer-based methods to estimate %ABV in the 12 finished beers.  Because my FG hydrometer measurements were made on finished, bottle-conditioned beer, I added 0.0036 to OG (pre-fermentation) hydrometer measurements to include the effects of 5 oz/gal bottling sugar.


Figure 4 presents the results, with both my Brix-based, model predictions and measured %ABV shown for comparison.



Figure 4.  Comparison of Brix-based method and four hydrometer-based methods with measured %ABV,


If the measured %ABV values are to be believed, the Brix-based method appears at least as accurate as any of the hydrometer-based methods.


The data are presented in an alternative way in Figure 5.



Figure 5.  Scatter plot of estimated vs. measured


The four, hydrometer-based methods tend to over-estimate %ABV.  As presented earlier, the mean error (from measured %ABV) of the Brix-based method was +0.1 %ABV, with sample standard deviation (n=12) of Ī0.4 %ABV.


It is, of course, up to prospective users whether this level of accuracy and precision is sufficient for their needs.  However, consider that similar analysis of most hydrometer-based methods is not readily available.

                                  Derivation of Calculator Equations