Wanted to enlighten all of you, especially those of you who took the time to criticize a product you know nothing about, and educate you about the analysis that goes into determining alcohol percentage, calories, ABW, etc. in beer. Oh, and if you can't do math, which those posters who took the time to criticize my grammar and punctuation errors probably can't, don't bother reading this. Enjoy!
Also, there are various references listed below that you may want to read over if you really want to debate this issue...
1. Specific Gravity & Plato Scale
A solution's specific gravity (SG) is its density (g/ml) relative to water, and is easily measured with a hydrometer or other suitable instrument. Wort (unfermented beer) has a specific gravity greater than water due to the presence of sugars. Beer has a specific gravity less than wort because some of the sugars have been fermented into alcohol. Professional brewers often use the Plato (°P) scale, instead of specific gravity, as a metric for the sugar levels in wort and beer. The Plato of a solution is equivalent to its percent by weight of sucrose and has dimension of (g equiv. sucrose)/(100 g solution). Thus, a 1% sucrose solution is a 1 °P solution. For the same weight of other sugars, the Plato of a solution is slightly different. The relationship between Plato and specific gravity is nonlinear.
Jan DeClerck [A Textbook of Brewing, 1957, reprinted by the Siebel Institute External in 1994] gives a least squares fit for conversion from specific gravity to Plato at 20 °C. DeClerk's equation is used for all subsequent calculations below since it deviates from the values given by the ASBC ["Table 1" in: American Society of Brewing Chemists, 1992, Methods of Analysis of the ASBC. American Society of Brewing Chemists.] by less than 0.04% °P from SG 1.010 to 1.083:
(1) °P = (-463.37) + (668.72 × SG) - (205.35 × SG2)
Example: The specific gravity of a wort is 1.070 and that of the resulting beer is 1.015 at 20 °C. What are the densities on the Plato scale?
According to eq. 1
°P[initial] = °Pi = (-463.37) + (668.72 × 1.070) - (205.35 × 1.0702) = 17.06
°P[final] = °Pf = (-463.37) + (668.72 × 1.015) - (205.35 × 1.0152) = 3.82
2. Real Extract
Ethanol has a density of 0.79 g/ml at 20 °C, so its presence in beer, along with the loss of sugars due to fermentation, also reduces the specific gravity of beer relative to wort. The "Real Extract" (RE, in °P) is a measure of the sugars which are fermented and accounts for the density lowering effects of alcohol. The Real Extract is calculated from the initial and final densities (in °P) and an old empirically derived formula from Karl Balling [see Homebrew Digest 880-9]:
(2) RE = (0.1808 × °Pi) + (0.8192 × °Pf)
Example: The specific gravity of a wort is 1.070 and that of the resulting beer is 1.015 (measured at 20 °C). What is the Real Extract?
According to eq. 2
RE = (0.1808 × 17.06) + (0.8192 × 3.82) = 6.21 °P
Attenuation is a measure of the degree to which sugar in wort has been fermented into alcohol in beer. Ceteris paribus, a sweet beer has more residual sugar and lower attenuation. Hydrometer measurements of the specific gravity before fermentation and after fermentation are used to determine attenuation. However, the residual sugars are not in a solution of pure water; rather they are in solution with water and ethanol, which has a density of 0.79 g/ml. Thus, many brewers give a number which must be called the "Apparent Attenuation" (AA):
(3a) AA = 1 - [°Pf / °Pi]
The "Real Attenuation" (RA) can be calculated from the RE (see eq. 2) and the initial density, °Pi:
(3b) RA = 1 - [RE / °Pi]
Example: The original gravity of a wort is 1.070 and the final gravity of the resulting beer is 1.015. What is its apparent attenuation and real attenuation?
According to eq. 3a
AA = 1 - (3.82 °P / 17.06 °P) = 0.776
According to eq. 3b
RA = 1 - (6.21 °P / 17.06 °P) = 0.636
4. Alcohol Level
Given the OG and FG, several empirically derived formulas estimate the alcohol content (alcohol-by-volume, ABV in (ml alcohol)/(ml beer)) of beer. Dave Miller (The Complete Handbook of Homebrewing, 1988, Storey Communications) gives a simple formula, where the easy-to-remember constant (0.75) has dimension of (g beer)/(ml ethanol):
(4a) ABV = (OG - FG) / 0.75
A convenient number (to be used in eq. 5 below) is the percent alcohol by weight (ABW) of beer, which has dimension of (g ethanol)/(100 g beer). This is easily calculated from the ABV, the density of ethanol (0.79 g/ml), and the FG:
(4b) ABW = (0.79 × ABV) / FG
If the FG of the beer is unknown, but it has "normal" levels of alcohol and attenuation, then the ABW may be estimated as:
(4c) ABW = (0.78 × ABV)
George Fix [see Homebrew Digest 880-9] gives another formula, proposed by Karl Balling many years ago:
(4d) ABW = [°Pi - RE] / [2.0665 - (0.010665 × °Pi)]
Jan DeClerk [A Textbook of Brewing, 1957, reprinted by the Siebel Institute External in 1994] also gives a method for estimating the percent alcohol by weight (ABW) of beer based on measurements of the specific gravity (FG) and refractive index (RI) of beer. Unfortunately, DeClerk expresses refractive index in "Zeiss Units", an out-dated metric. Louis Bonham [see Homebrew Digest 2923-13 & Homebrew Digest 2925-3] converted DeClerk's Zeiss Units to the more commonly used Refractive Index (RI):
(4e) ABW = 1018. - (277.4 × FG) + RI × [(937.8 × RI) - 1805.]
Example: The original gravity of a wort is 1.070 and the final gravity of the resulting beer is 1.015. The beer has a refractive index of 1.3466. What is the alcohol level?
According to eq. 4a
ABV = (1.070 - 1.015) / 0.75 = 0.0733 = 7.33% v/v
According to eq. 4b
ABW = (0.79 × 0.0733) / 1.015 = 0.0571 = 5.71% w/w
According to eq. 4c
ABW = (0.78 × 0.0733) = 0.0572 = 5.72% w/w
According to eq. 4d
ABW = [17.06 - 6.21] / [2.0665 - (0.010665 × 17.06)] = 5.76% w/w
According to eq. 4e
ABW = 1018. - (277.4 × 1.015) + 1.3466 × [(937.8 × 1.3466) - 1805.] = 5.79% w/w
The number of calories in beer, all of which come from alcohol and carbohydrates, can also be estimated from measurements of specific gravity before and after fermentation. The ASBC ["Caloric Content, Beer-33" in: American Society of Brewing Chemists, 1992, Methods of Analysis of the ASBC. American Society of Brewing Chemists; Homebrew Digest 800-9] gives a formula for calculating calories in beer:
(5) cal per 12 oz beer = [(6.9 × ABW) + 4.0 × (RE - 0.1)] × FG × 3.55
The first item in brackets gives the caloric contribution of ethanol, which is determined from the ABW and the known value of 6.9 cal/g of ethanol. The second item in brackets gives the caloric contribution of carbohydrates, which is determined from the RE (see eq. 2) and the known value of 4.0 cal/g for carbohydrates. An empirically-derived constant (0.1) accounts for the ash portion of the extract. Together, these terms give the calories per 100 g beer. This is easily converted to calories per 100 ml beer by accounting for the final gravity (FG, in (g beer)/(ml beer)). In turn, 100 ml is converted to 12 oz by a scalar (3.55, in (100ml/12 oz)).
Example: The original gravity of a wort is 1.070 and the final gravity of the resulting beer is 1.015. How many calories in a 12 oz bottle?
According to eq. 5
cal per 12 oz beer = [(6.9 × 5.72) + 4.0 × (6.21 - 0.1)] × 1.015 × 3.55 = 230