Empirically Measuring and
Calculating Alcohol and Extract
Content in Beer with a Reasonable
Degree of Accuracy and Confidence
Michigan Craft Brewers Guild - Conference
Kalamazoo, MI -- January, 2014
Gary Spedding, Ph.D [FINAL CORRECTED VERSION]
Brewing & Distilling Analytical Services (BDAS) LLC
Objectives Today
Theory behind alcohol production & determinations/Definitions.
Simple but powerful equations to relate SG or Plato determinations in
the brewhouse to ABV and ABWt determinations. Methods to use.
Data and exercises for you - use those equations/get comfortable with.
Relationships!
Interconversions of data. New Equations.
Use base data to get carbohydrate estimates, and calorie info. On-line
tools and calculators.
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“Alcohol Measurement in Beer and
Useful Derived Data” via:
Hydrometers
Digital Density Meters [GC?]
Refractometers
2
“Background Info., Key Facts
and Definitions”
See handout for full details (Now added
below – post-seminar delivery - to allow for
an integrated set of slides)
Alcoholic Strength: A measure of the amount
of alcohol in beer. The alcohol content of a
beer typically refers to the amount of ethyl
alcohol (as opposed to higher or fusel
alcohols). The analysis of beer for alcohol
content is an important part of brewing
laboratory work for quality assurance
programs and for legal reporting purposes.
Results, however, are subject to appreciable
variation and under official methods the
analyses are time consuming and expensive.
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Specific gravity (SG) or relative density: is an intensive property of a
substance (be it solid or liquid) and is, historically, the ratio of the density
of a substance at the temperature under consideration to the density of
water at the temperature of its maximum density (4 °C). The actual
density in theory – for the purposes of most discussions with respect to
beer – is generally 20 °C/20 °C relative to water at unity though,
elsewhere in the alcohol beverage world, it is typically expressed as at 20
°C/4 °C. The complexity of the temperature associations could not be
presented in depth here - full details may be found in the literature (see
the references). An SG value is numerically equal to the density in grams
per milliliter (or Kg per liter) but is stated as a pure number (because the
division by the water’s own density value leads to a cancellation of the
units), while density is stated as mass per unit volume. Water has a
specific gravity of 1.0000 at 20°C. Base and derivative density values form
mathematical grounding in many of the formulas used in alcohol and
extract calculations. The density value 0.998201 will be seen in the
literature as pertaining to the formulas and conversions of alcohol density,
specific gravity, and alcohol by weight and volume and while understood
within this article is also not covered in any depth here.
Original Extract or Gravity: The initial SG of wort is known as the original extract
(OE) or original gravity (OG) depending upon units implied by these terms (OE is in
Plato, while OG is in numerical “gravity units” – see below and under “Plato”). OE
is an expression of sugar content - grams of sugar per 100 grams of wort. [Equivalent
to % weight/weight (w/w)]. In the brewing industry this is denoted as “degrees
Plato” (0P) and to a first degree of approximation beer responds in the same way as
the original solutions of sucrose and water used to derive the Plato scale. Brewers
often determine or record and report this using numerical specific gravity values
rather than in degrees Plato and it is this that is more correctly the OG value. OG
represents the ratio of the density of wort at 20 °C to the density of water at the same
temperature (see “Specific Gravity” above). Plato and SG values can, however, be
inter-converted using appropriate formulas as illustrated in the text (example, for
our purposes here, 12.00 °Plato is an SG of 1.04838 – actually 1.048311 at 20°C/20°C).
See Plato in this table. When reading the literature and interpreting equations it is
important for the reader to understand the differences in units applied to OE and
OG terms as this can otherwise cause some confusion as to which values to use in
the equations. OE = (RE + 2.0665 x ABW)/ (1 + 0.010665 x ABW). A fundamental
formula not covered in the text but which can be used to test derivation of formulas
and cross-check values.
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Apparent and Real Extract: Brewers measure changes in density as sugars
are consumed and converted into alcohol. Measurements are obscured (the
true gravity is “hidden”) by alcohol (of lower density than water, sugar
solutions or beer) causing “buoyancy effects” with hydrometers for
example. Thus false or apparent readings of gravity are made when
instruments measure beer (containing water, sugars and alcohol); hence
“apparent extract”. The real extract is a true(r) measure of remaining
sugars - and proteins etc., to be exact about the nature of the extract - as
determined in the absence of alcohol (removed via distillation or boiling)
or compensated for the actual alcohol content via its determination and/or
via algorithms in instrumentation. Such equations are described and
discussed in the text. When yeast has finished fermenting the brewers
wort, or the brewer terminates the fermentation, the final gravity reading is
sometimes also called the terminal gravity (this will also be in “apparent”
or “real” terms depending how measured or calculated). RE is real extract
in grams per 100 grams of beer (Plato).
Apparent Attenuation and Real Degree of
Fermentation: The expression of the percentage
reductions in the wort’s specific gravity caused by the
transformation of the sugars (higher specific gravity
than for water) into alcohol and carbon dioxide and
yeast biomass. Real and apparent values exist for the
reasons discussed under Apparent and Real Extract. It
is simply a measure, in percent terms, of the amount of
original extract which has been consumed or
converted. The Real degree of fermentation equation:
RDF = 206.65/ (2.0665 + RE/ABW), is a fundamental
equation also underpinning the theory behind many
equations as presented here (see also Original Extract
or Gravity).
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Plato – (see also Original Extract or Gravity). The typical
way brewers report extract in wort and beer (as weight
percent). Plato values may be obtained directly from
hydrometers calibrated in degrees Plato, by means of
specific gravity measurements as related to standard
Plato (or extract) tables and (to varying degrees of
approximation) by calculation – some equations seen in
the presentation. The Plato scale and tables are
themselves approximations for complex physicalchemical reasons but have stood the test of time for
most brewing purposes.
Alcoholic Strength: A measure of the amount of alcohol in
beer. The alcohol content of a beer typically refers to the
amount of ethyl alcohol (not higher or fusel alcohols).
Alcohol Content: Important for brewing laboratory work
for quality assurance programs and for legal/consumer
reporting purposes.
Results - subject to appreciable variation.
Official methods - analyses time consuming/expensive.
6
Specific gravity (SG)/relative density intensive property ( solid or liquid) - the ratio
of the density of a substance at the temperature
under consideration to the density of water at
the temperature of its maximum density (4 0C?).
SG value - numerically equal to the density in
grams per milliliter (or Kg per liter) STATED as a
pure number (division by water value -- density >
cancellation of the units), while density is stated
as mass per unit volume (g/mL or Kg/L).
Initial SG of wort is known as the original extract
(OE) or original gravity (OG). Expression of sugar
content - grams of sugar per 100 grams of wort.
[Equivalent to % weight/weight (w/w)].
Brewing industry - denoted as “degrees
Plato” (0P).
Plato and SG values can be interconverted using appropriate formulas.
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OG (tech. OE) often held as an indirect indicator of
alcoholic strength of a beer. A higher OG
(implying the higher the fermentable sugars)
indicates a higher potential for conversion to
alcohol.
But this DEPENDS upon how fermentable the
extract is - yeast can only consume the simple
sugars glucose, maltose and triose. E.G. If 65% (
typical) of OG is converted > simple sugars
(mashing) alcohol content, as % weight, is roughly
the OG divided by three.
1 gram of alcohol requires 2.0665 g of
fermentable extract or 2.0665/0.65 = 3.2 gram of
total extract when the real degree of
fermentation (RDF) is 65.
The gram “alcohol from fermentable sugars”
conversion? Theoretically, 1 gram fermentable sugar
will yield 0.51 gram of ethanol and 0.49 gram of
carbon dioxide. [Some sugar needed = cell growth.]
Realistically, the ethanol yield is more likely 0.46
gram, and carbon dioxide 0.44 gram from 1 g sugar.]
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>Alcohol is generated relative to the
amount of fermentable sugars in beer
wort.
>Is related to both wort specific gravity
(SG) and wort RDF (Real or “true”
degree of fermentation).
>Accepted - 1 gram of alcohol requires
2.0665 g of fermentable extract.
[As originally determined: 2.0665 g sugar
yields 1 g ethanol, 0.9565 g CO2 & 0.11 g
yeast. Note: for equations below, 0.9565g
& 0.11 g sum to 1.0665 extract NOT
converted to alcohol.]
>Above values used in published
equations to det. alcohol strength.
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“Using the above facts in formulas
and calculations of alcohol
determinations”
Solving for alcohol determination by weight
determinations – drop in wort gravity (Karl
Balling):
ABW 
(OE  RE )
(2.0665)  (1.0665 OE / 100)
> [ABW: alcohol by weight (as w/w, grams of
alcohol per 100 grams of beer). OG, original
gravity & RE real or present extract.]
10
Brewers using a hydrometer - real extract can be
approximated using OG and AE (orig. Balling):
RE, % w/w = (0.1948 x OE) + (0.8052 x AE)
(AE = apparent extract or attenuation – value
determined when alcohol present) NB: this is only an
empirical observation & applies only to
traditionally fermented beers near 65 % RDF.
The last formula (based on assumptions, mineral
content and physical chemical interactions of
solutes) is based on a relatively constant ratio:
(OE – RE)/(OE – AE) = 0.8052 +/- 0.0012
[95% confidence]
(Over range of OE 9-18 Plato and RDF 58-70%).
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Substituting into the above
formula:
ABW 
0.8052  (OE  AE )
(2.0665)  (1.0665  OE / 100)
No RE immediately needed!
If SG has also been determined for beer then
alcohol by volume - ABV- can be determined w/a
correction to account for the specific gravity of the
beer:
Alcohol , % vol. 
alcohol , % by wt.  sp. gr.beer
sp. gr. ethyl alcohol @ 20C / 20C
[Where, sp. gr: specific gravity, e.g., for the beer or
pure ethanol.] [But need SG beer – later…]
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Which simplifies to:
Alcohol , % vol. 
alcohol , % by wt.  sp. gr.beer
0.791
Variant eq’ns available but alcohol should be reported
both % by weight (wt.) & by volume (vol.) to two decimal
places. For reporting purposes brewers are allowed a
tolerance of +/- 0.3% alcohol by volume. [0.7907]
Some questions we now need to address.
If using SG hydrometers how to get Plato Values? Or Plato to SG?
If you obtain Density values how do you obtain SG values and
vice versa?
Then: What can you do with those values?
Who or what is Tabarie ? ……and……
Should we care?
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Resolve an issue here (Assuming you
have Plato OE and AE {or RE} Values).
To Compute ABV as above we need the
current beer SG in gravity units!
Note: SGBeer = the Appt. Gravity!
Solve that using two equations (Lincoln
derivatives)
Now Two Equations for
Interconverting Plato and SG values.
(AE or other Plato value to SG):
SG 
P
1

P
258.6  
 227.1

 258.2
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And to Convert SG to AE (or other
Gravity units to Plato Value)
Plato Extract = [(SpG)2 (205.347) + (668.72)(SpG) – 463.37]
[cf. Goldiner –Europe/Tables.]
From above we can see we can get SG and
Plato Values interconverted
But What if you are obtaining Density
Values instead of SG’s?
Use simple density (“rho”) relationships
for water, extract and alcohol solutions
SG x 0.998201 =  and /0.998201 = SG
15
“Some other neat formulas
and manipulations”
What if we have or need the alcohol SG and the
methods used/instruments did not give us this? [Can be
done via distillation] But, Can we avoid that?
Enter Mr. Tabarie and his relationships!
SGAlc = SGBeer - SGRE +1
SGBeer = SGRE + SGAlc -1
SGRE = SGBeer - SGAlc +1
[Perfect - normal strength beers (ca. 3-7% ABV and Typical
ca.2.5-7.5 Plato Real Extract)] Keep below 10-12% ABV beers!
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Now from all above if we have the SG for the alcohol (or
its obtained via distillation and measurement) we have an
alternative approach to determining ABV and ABWt – Use
of OIML Tables! (at 20 °C) using density values.
Density values are taken to the Tables not as 0.98705
(example) values but as 987.0 as seen below.
OIML Table Vb for ABV
OIML Table Va for ABWt
Interpolation may be required between tabulated and actual density
values.
We can now use OIML (Legal Metrology) Tables to
look up ABV and ABWt at 20 °C from Density and
then convert as needed to SG. Or use AOAC/ASBC
(52.003) Tables to obtain ABV at 60 °F from SG.
Or a Quick ROT: ABV from 20 °C to 60 °F:
ABV(20 °C) x 0.9972 - 0.0069 = ABV (60 °F)
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For normal strength beers an (adequate)
equation can be used that even obviates the
need for the OIML Tables. Measure ABWt:
ABW = 517.4 x (1-SG) + 5084 x (1-SG)2 +
33503 x (1-SG)3
[note it uses SG Alcohol values not Density! Unlike OIML Tables.]
Use when beers expected less than 12% ABV
(pers. observations). Convert to ABV from
ABWt above using standard equations.
Note Caveats: Not Covered Here Today.
Another complexity to this.
If using distillations to obtain the alcohol SG.
Are you using gravimetric or volumetric distillations?
If gravimetric the SG alcohol is for weight of alcohol. Volume
values obtained from tables need to be corrected back for beer
SG.
If volumetric ( may only need volume at this point –OK ) – but
the weight of alcohol from tables needs correcting back to the
SG of the beer.
Contact us for details on this.
If using a DMA5000/Alcolyzer and you ask it to print out the
alcohol SG be aware that it is for weight of alcohol and not
volume. This complicates back-calculations.
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To see how well we could use individual
pieces of information - as obtained from
various methods - run examples to see
how well the equations might work for
us. (Close but not official of course).
Examples >>>>
“Data and Tables”
19
Anton Paar Data.
Typical Printout
From a
Digital
Density Meter/
Alcolyzer.
OIML Density /ABV/ABWt Tables – Parts of.
20
OIML Density /ABV Table – Portion of.
OIML Density /ABWt Table – Portion of.
21
AOAC Alcohol Table
“Example Calculations
and Exercises”
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Test Calculations – I
Exercises
Assuming you can carefully obtain the OG and the AE for
beer using hydrometers. Then taking the AE (and OG)
equation you can prove (use the Anton Paar Data) the ABWt,
then the ABV values (in the example) Anton Paar Printout.
Other calculations can follow (see below).
Test Calculations – II
Exercises
Supposing you can obtain accurate SG or Density
measurements (Maybe hand held digital units) of from SG
hydrometers you can now calculate from these values the OG,
AE, and (if de-alcolyzed or distilled beer) the RE in Plato.
Hand calculate (Excel sheet?) from the “AE to SG” Equations
the SG for the beer, the OG and the Real Extract from the
Anton Paar data. (You are given the SG sample = the AE!). If
Density readings convert to SG as shown above.
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Test Calculations –II (cont..) Exercises
Have SG for beer 1.00961 (AE).
OG 10.71 (Calc. as SG = 1.04298)
RE 4.06 (Calc. as SG = 1.01592)
AE 2.46 (Calc. as SG = 1.00959 - NB: very close to
1.00961 from the A-Paar printout.)
How to get the Alcohol SG? – Try Tabarie!
[SGAlc = SGBeer – SGRE +1] = 1.00961 – 1.01592 + 1
= 0.99369.
Convert to Density (to use OIML Tables) = 0.99190
(or 991.9 for Tables).
Test Calculations –II (cont..) Exercises
Now we have the SG for Alcohol – Use OIML and
AOAC Tables to Determine ABV’s and ABWt. {or
alt. eq if below ca. 12% ABV.}
[SGAlc = 0.99369 to Density {0.99369*0998201} =
0.99190 (or 991.9) From the OIML Tables (next) –
we obtain 4.38% ABV @ 20 °C (close to 4.35% APaar Data) and 3.48% ABWt (a little off but quite
good?). ERROR HERE (See next slides)
[Using the AOAC (60 °F) Tables (data not shown
here) gives us 4.33% ABV (@ 60 °F) – About right
for this 20 °C ABV figure! Typically 0.02% higher
@ 20 °C!]
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Addendum (Correcting an Error!)
Last slide: From the OIML Table we
obtained 4.38% ABV @ 20 °C (and stated
close to 4.35% A-Paar Data) and 3.48%
ABWt (a little off but quite good?).
But (Go back to Caveat slide):The ABWt value of 3.48% is derived from
an SGalc that represents the value as if in
pure “alcohol/water mixture”, So…
We need to correct the ABWt
value here, accounting for the
SG of the beer itself.
From earlier:-
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Correcting ABWt from (“water/alc
soln.”) to SG of the beer.
Alcohol , % wt 
corr
ABWt 
alcohol , % by wt.  Alc. SG
Beer or sample SG
3.48%  0.99369
 3.425%
1.00959
Much closer (using the calculated Beer SG) to the Anton
Paar Value. 3.42 or 3.43% (rounded) vs. the AP – 3.41%
ABWt! Even better overall for us using such calculations!
Now we have determined all the relevant
data and can confirm its closeness to the
original AP printout data for this beer
sample.
This correction for the ABWt completes the
basic data and reminds us that the SG for
ABV and ABWt (from Tabarie derivation in
this example set) gives us the correct ABV
(just like for a volumetric distillation – for
explanations not fully covered in the
seminar) but a value for ABWt that needs to
be back-corrected to account for the beer SG.
26
OIML Density /ABV/ABWt/ For Exercise
II
Calculations and Exercises: Conclusion
Armed w the set of equations and tables defined
above - if you can obtain either Plato Extract Values or
SG Values for Original Extract (Gravity) and Terminal
(Apparent) Extract Gravity – as well as Real Extract (by
computation or by de-alcoholyzing/distilling a beer
sample) via use of hydrometers or simple digital
density meters - you can get quite close to true alcohol
results for beer.
Remember to get a final official check for any legal
needs though!
BUT WAIT … THERE IS more…
27
“Introducing the Scandinavian
Beer Calculator”
28
Finally: Try plugging some values including
those from the Anton Paar data shown here into
the Scandinavian Beer Calculator and see how
that works for you.
Hopefully this gives you a good start to dealing with
brewery and brewing lab calculations with benefit to
you, legal authorities and your consumers!
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Suite 202, Lexington, KY 40504.
Tel: 859-278-2533.
www.alcbevtesting.com
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NOTE: THIS TALK FORMED THE BASIS FOR A PAPER
WHICH IS FREE ON-LINE IN THE INAUGURAL
(RESURRECTED) ISSUE OF THE BREWERS DIGEST.
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