The Scandinavian Beer Calculator
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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*(SGE-SGA)^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 = 4.00-0.65*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:
  1. Enter “Calculator” to delete any previous input.
  2. Enter figures for ER% (4.56) and A%mas (3.45) respectively in the column called “Calc No.1”.
  3. Enter the volume of beer (1234 hl) in the same column.
  4. Enter figures for ER% in water (0) and A%mas in water (0) respectively in the column called “Calc No.2”
  5. Specify that the volume of water in “Calc No.2” is variable.
  6. Specify in the column called “Target for blending” that the target is A%mas = 2.99
  7. Enter “Calculation” to initiate the calculation program.
  8. Wait for a reply. It may take some seconds.
  9. 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

  1. Goldiner, F., Klemann, H., Block and Kämpf, W., ‘Rohrzucker-, Alkohol-, Stammwürze- und Korrektionstafel’, Institut fur Gärungsgewerbe, Berlin, 65 Seestrasse, 1977
  2. Organisation Internationale de Metrologie Legale. International (OIML).
    Recommendation No. 22, ‘Alcoholometry and International Alcoholometric Tables’, 1973
  3. Nielsen, H., Aastrup, S., ‘Improving Tabarié’s Formula’, Scandinavian Brewer’s Review, Vol 61, No.4, 2004, p 30-34
  4. European Brewery Convention. Analytica-EBC, Third Edition, 1977. Method 9.4 ‘Original, Real and Apparent Extract of Beer’
  5. Method of Analysis of the American Society of Brewing Chemists, Method BEER-6B (issued 1992). Am. Soc. Brewing Chemists, St. Paul, MN, USA
  6. European Brewery Convention. Analytica-EBC, Third Edition, 1977. Method 9.2.1 ‘Alcohol in Beer by Distillation’.
  7. Nielsen, H., Andersen, C.B., ’Alcohol by Volume’, Scandinavian Brewer’s Review, Vol 61, No.5, 2004, p 46-50
  8. Rosendal, I., Schmidt, F., J. Inst. Brew., 1987, Vol. 93, 373-377, European Brewery Convention. ‘The Alcohol Table for Beer Analysis and Polynomials for Alcohol and Extract’.
  9. Nielsen, H., Erdal, K., ‘The Degree of Fermentation’, Scandinavian Brewer’s Review, Vol 62, No.3, 2005, p 34-39
----End of instructions.----