
User’s Instruction
The Scandinavian Beer Calculator
This Beer Calculator is an integrated part of the educational program for the
international students at The Scandinavian School of Brewing in Copenhagen (www.brewingschool.dk)
The Beer Calculator is a software program allowing calculation of a composition
of beer or wine based upon only 2 inputs, e.g. OE%P = 12.34 and A%vol = 3.45
. Abbreviations like OE%P will later be explained separately.
The beer analysis is calculated from only 2 specific gravities measured for the
beer (e.g. SGBeer and SGA).
For a batch of beer the volume (hl) may be entered, and the composition will
be calculated in kg beer, kg Alcohol etc.
Further the values for colour and bitterness could be entered for a batch of
beer. Use any units!
For 2 or more batches of beer the composition of the mixture will be calculated
as well in % as in kg. The colour and the bitterness of the mixture will be calculated
as well.
A “Blend to Target” facility allows for calculation of the volume
of one batch of beer to give a wanted result in the mixture.
The Beer Calculator allows for correction of any figure entered.
The Beer Calculator allows for simultaneous calculation of many separate batches
of beer as well as for the mixture of these. The number of separate columns can
be reduced or increased.
A Print Out facility allows for printing out the calculated figures as is or
in Excel.
The functions mentioned above will be described in more details below.
Calculation of the beer composition
When 2 figures are entered for a composition of beer, the Beer Calculator will
find the total composition of the beer by using the formulas and tables prescribed
by EBC plus some assisting formulas
A calculation could be as follows:
1.

Enter www.brewingschool.dk/calculator or www.beercalc.com
and adjust to “Full Screen”

2.

Enter figures for ER% (4.56) and A%mas (3.45) respectively in the column called “Calc No.1”

3.

Enter “Calculate” to activate the calculator.

4.

The calculator will now make the following series of calculations:

4a.

Calculate SGE and SGA by using the Sugar Table and the Alcohol (See below, Ref. 1 and 2)

4b.

Calculate SGBeer from “The improved Tabarié’s Formula” (Ref. 3) as follows:
SGBeer = SGE + SGA  1 + 0.011*(SGE  SGA) *; 0.5*(SGESGA)^2

4c.

Calculate OE%P from Balling’s Formula (Ref.4):
OE%P = (2.0665 * A%mas + ER%) * 100 / (100 + 1.0665 * A%mas)

4d.

Calculate EA% by entering SGBeer in the Sugar Table (Ref. 1).

4e.

Calculate RDF% and ADF% from the ASBC Formula and the classic formula. (Ref. 5 and 9):
RDF%(ASBC)

=

100*(OE%P  ER%) / (OE%P * (1  0.005161*ER%)),

RDF%(classic)

=

100*(OE%P  ER%) / OE%P

ADF%

=

100*(OE%P  EA%) / OE%P


4f.

Calculate A%vol from the EBC Formula (Ref. 6 and 7):
A%vol = A%mas * SGBeer/0.791

4g.

Calculate TMXD°, FRZP°, CalVal, Energy and BOD5 from the following formulas:
TMXD

=

4.000.65*ER% + 0.24 * A%mas (M. Soeltoft)

FRZP

=

0.20  0.42 * A%mas  0.04 * OE%P (M. Soeltoft)

CalVal

=

SGBeer * (7 * A%mas + 3.5 * ER%) (EBC)

Energy

=

SGBeer * (29 * A%mas + 15 * ER%) (EBC)

kgBOD5

=

0.9 * (kgAlcohol * 2.09 + kgER * 1.12)


Subsequently to the calculation of a beer composition as described above the
related volume (hl) of the batch could be entered.
Consequently the Beer Calculator will return the masses (kg) of beer, extract
and Alcohol for the actual batch of beer.
In the same way the bitterness and the colour of each batch could be entered.
Subsequently the Beer Calculator will calculate the bitterness and the colour
of the mixture.
Calculation for blending
We will now illustrate how to calculate a blend.
1234 hl beer of the above composition (ER% = 4.56 and A%mas = 3.45) shall
be added water to lower the content of Alcohol to A%mas = 2.99.
The calculation for blending could be as follows:
 Enter “Calculator” to delete any previous input.
 Enter figures for ER% (4.56) and A%mas (3.45) respectively in the column
called “Calc No.1”.
 Enter the volume of beer (1234 hl) in the same column.
 Enter figures for ER% in water (0) and A%mas in water (0) respectively in the column called “Calc No.2”
 Specify that the volume of water in “Calc No.2” is variable.
 Specify in the column called “Target for blending” that the target is A%mas = 2.99
 Enter “Calculation” to initiate the calculation program.
 Wait for a reply. It may take some seconds.
 The Beer Calculator now replies that 192 hl water is required. Further,
it presents you for the full composition of the blend after dilution of the
beer.
Calculation of a beer analysis from three specific gravities
Even though the Beer Calculator is designed for calculation of the beer composition
on the basis of two inputs only, it can be used for the classic calculation
based upon inputs of SGE, SGA and SGBeer. This calculation is prescription
by EBC for the beer analysis.
When these three specific gravities have been analytical measured, two different
combinations of two specific gravities should be calculated separately (e.g.
SGBeer & SGA and SGBeer & SGE respectively) and the difference between
the two calculated results should be used for evaluation of the quality of
the analytical work. The difference between the figures for ER% or for A%mas
must
not differ more than 0.07 % (e.g. max. from 3.40% to 3.47%). If the deviation
is larger, the analytical results should be deleted, and the analytical work
should be redone. An average of the two analyses will be calculated by mixing
one hl of each
Print out of calculations
When choosing ‘Export to Excel”, the Beer Calculator answers by
presenting you to a spread sheet made in Excel including all figures from the
screen. This spread sheet can be copied into any other spread sheet in your
computer.
If formal filing is required, inputs could be required for “Doc. id” (Max.
eleven characters)
and “Beer sample”. These inputs should be made in the designated
cells.
Table modifications
The two Tables involved have been adjusted as follows:
The Sugar Table = “The Goldiner, Klemann, Kämpf Table” (Ref.
1).
This Table has been modified from five to seven decimals to allow for optimal
linear interpolation. Further the range has been extended from 0 – 30
g/100g to 5 to 30 g/100 g to allow for calculation of AE% in beer and wine
with high
values for RDF%.
The Alcohol Table (“The OIML Table”, Ref. 2).
This table has been modified to involve SG20°/20° instead of the Density
as specified by EBC. (Ref. 8)
The Alcohol Table is given a range from A%mas = 0 to13 g/100g. Further it has
been modified from five to seven decimals to allow for optimal linear interpolation.
Testing
The accuracy of the Beer Calculator can be checked by calculating a beer composition
from one set of values (e.g. OE%P = 12.43 and ER% = 3.45). Subsequently, any
set of two values can be extracted from the calculated composition and entered
to form an alternative calculation of the same beer composition. The consistency
of the calculated figures illustrates a part of the quality of calculation.
A beer composition calculated correctly in other ways will be confirmed by
the Beer Calculator, if the three specific gravities (SGBeer, SGE and SGA)
will fit into “The Improved Tabarié’s Formula” (Ref.
3). This fit could be checked by entering two different combinations of the
three specific gravities. Such two compositions must not differ more than 0.07
on the values for ER% or A%mas (e.g. max. from 3.40% to 3.47%). If the deviation
is larger, the analytical work has not been done correctly.
Abbreviations
hl  =  Beer Volume  In hectoliter, 1 hl=100 liter 
OE%P  =  Extract in Original Wort  In % Plato, g/100 g 
ER%  =  Real Extract  In %, g/100 g 
EA%  =  Apparent Extract  In %, g/100 g 
A%mas  =  Alcohol content by mass  In %, g/100 g 
A%vol  =  Alcohol content by volume  In %, ml/100 ml 
RDF%  =  Real Degree of Fermentation  In %, g/100 g 
ADF%  =  Apparent Degree of Fermentation  In %, g/100 g 
SGA  =  Specific Gravity of distillate  g/ml over g/ml 
SGE  =  Specific Gravity of residue  g/ml over g/ml 
SGBeer  =  Specific Gravity of Beer  g/ml over g/ml 
ENERGY  =  Nutritive Value of Beer  In kJoule/100 ml 
CALVAL  =  Calorific Value of Beer  In kCal/100 ml 
FRZPº  =  Freezing Point of Beer  In degree Celsius 
TMXDº  =  Temperature of Max. Density  In degree Celsius 
BOD5  =  Biological Oxygen Demand  In g/liter 
OEkg  =  kg of Original Extract  In kg 
ERkg  =  kg of Real Extract  In kg 
Akg  =  kg of Alcohol  In kg 
BOD5kg  =  kg of Biological Oxygen Demand  In kg 
EBC  =  European Brewery Convention  
ASBC  =  American Society of Brewing Chemists  
Bitterness  =  Any recognised unit for bitterness  
Colour  =  Any recognised unit for colour  
References
 Goldiner, F., Klemann, H., Block and Kämpf, W., ‘Rohrzucker,
Alkohol, Stammwürze und Korrektionstafel’, Institut fur Gärungsgewerbe,
Berlin, 65 Seestrasse, 1977
 Organisation Internationale de Metrologie Legale. International (OIML).
Recommendation No. 22, ‘Alcoholometry and International Alcoholometric
Tables’, 1973
 Nielsen, H., Aastrup, S., ‘Improving Tabarié’s Formula’,
Scandinavian Brewer’s Review, Vol 61, No.4, 2004, p 3034
 European Brewery Convention. AnalyticaEBC, Third Edition, 1977. Method
9.4 ‘Original, Real and Apparent Extract of Beer’
 Method of Analysis of the American Society of Brewing Chemists, Method
BEER6B (issued 1992). Am. Soc. Brewing Chemists, St. Paul, MN, USA
 European Brewery Convention. AnalyticaEBC, Third Edition, 1977. Method
9.2.1 ‘Alcohol in Beer by Distillation’.
 Nielsen, H., Andersen, C.B., ’Alcohol by Volume’, Scandinavian
Brewer’s Review, Vol 61, No.5, 2004, p 4650
 Rosendal, I., Schmidt, F., J. Inst. Brew., 1987, Vol. 93, 373377, European
Brewery Convention. ‘The Alcohol Table for Beer Analysis and Polynomials
for Alcohol and Extract’.
 Nielsen, H., Erdal, K., ‘The Degree of Fermentation’, Scandinavian
Brewer’s Review, Vol 62, No.3, 2005, p 3439
End of instructions.

