How to calculate the alcohol in your beer, wine, or mead
Homebrewing — By DJ Spiess on March 5, 2009 at 6:39 pmI’ve been working the last few days on a new web project for homebrewers and one task is calculating alcohol content. You’d be surprised how many different ways there are to estimate the same value.
How much sugar, sugar (ahh honey, honey)
Before you can make any calculations, you need to know how much sugar you have in your beer, wine, or mead. Plato (also called Brix or Balling) and specific gravity are two common measurements to determine sugar in a solution.
Brix, Plato, and Balling all determine the weight perentage of sucrose dissolved in water. So a solution which is 25 Plato is a solution which has 25% sucrose and 75% water. The differences between Brix, Plato, and Balling is refinements and the baseline temperature. The original Balling scale (named after Karl Balling) was determined at 17.5 C. Adolph Ferdinand Wenzeslaus Brix recalculated the scale at 15.5 C.
Specific gravity measures how much heavier the solution is than water. For example, a solution which has a specific gravity of 1.040 is 4% heavier than water.
These mesurements are accomplished using either a hydrometer or refractometer. The hydrometers usually measure specific gravity and Plato, while refractometers usually measure in just Plato.
Since Brix, Plato, and Balling are all slightly different, the conversion to specific gravity for each is slightly different. The brix scale can be approximated using the specific gravity and the following formula:
Brix = 261.3 * (1  1 / Specific Gravity)
Specific Gravity = 261.3 / (Brix / 261.3)
Plato uses the following formulas to calculate back and forth:
Degrees Plato = 259  (259 / Specific Gravity)
Specific Gravity = 259 / (Degrees Plato / 259)
Sometimes you will see Plato use 260 instead of 259. Since both are approximations, feel free to use either value. The reason both use similar functions, but not the same value (259 vs 261.3) is the difference in temperature.
If you are looking for a much more accurate calcuation of degrees Plato, you can use a third degree polynomial curve fit for a table of values which gives the following equation:
Degrees Plato = 1286.4 * SG  800.47 * SG2 + 190.74 * SG3
Using these measurements of sugar content, you can estimate the alcohol content in a variety of methods. The alcohol content calculated will be either alcohol by weight (ABW) or alcohol by volume (ABV). ABV is commonly used in the United States, but in the past ABW was used. ABW will yield smaller numbers (thus the Canadian beer vs American beer myth), but both numbers are valid measurements.
Calculating Alcohol Content Using Miller[88]
Dave Miller estimates the alcohol by volume using a very simple formula in his book “The Complete Handbook of Brewing (1988)”. Simply subtract the final gravity reading from the initial gravity reading, and then divide by 0.75.
Alcohol by Volume = (Initial Gravity  Final Gravity) / 0.75
Since we know the density of alcohol (0.789), you can easily convert ABV to ABW. Weight density is weight over volume. Simple algebra gives the following equation:
Alcohol by Weight = ABV / 0.789
Calculating Alcohol Content Using Fix[92]
George Fix suggested another formula on the homebrew digest back in 1992. His formula was based on work done by Karl Balling. This formula relies on Plato values and the “real extract”.
Alcohol by Weight = [Initial °P  Real Extract] / [2.0665  (0.010665 × Initial °P)]
The real extract is a measure of the sugars which are fermented in the solution, but it also takes into account the density of alcohol. The real extract is calculated using this formula:
Real Extract = (0.1808 × Initial °P) + (0.8192 × Final °P)
Calculating Alcohol Content Using DeClerck[57]
The formula from “A Textbook of Brewing Vol2″ by Jean De Clerck uses the final gravity and the refractive index to determine alcohol content. The refractive index determines the speed at which light moves through a solution at 20°C. This varies with the compostion of liquid and the amount of dry matter in solution. Since the refractive index for water is constant for a given temperature, any variation is used to determine the amount of solids in solution.
When you start, your solution should be all water and sugar (and adjuncts). At the end of fermentation there is alcohol in solution, so your values are skewed. The reason is alcohol has a different refractive index than water, causing many to believe the refractometer is useless once fermentation starts. The truth is you can use the refractive index with the final gravity to determine the alcohol content (and even the starting gravity). According to DeClerck, this was the method “adopted in 1939 as the official method in Germany, with the proviso that in any cases of dispute, the determination must be carried out by distillation”.
The formula is very accurate for calculating ABW, but it uses an outdated “zeiss unit” for the refractive index. Most refractors use brix or refractive index readings, so Louis Bonham on the Homebrew digest converted the formula to use refractive index readings (brix can be used in other formulas).
ABW = 1017.5596  (277.4 * finalGravity) + (refractiveIndex * ((937.8135 * refractiveIndex)  1805.1228))
Take your pick
Each method has it’s tradeoffs and does compute slightly different values. For example if you had a starting gravity of 1.050 and a final gravity of 1.010 you get the following results:
Miller ABV = 4.1663% Fix ABV = 4.1621% DeClerck = 7.1741% (assuming refractive index of 1.3466)
Miller and Fix are close to each other, but since DeClerck requires a refractive index it’s value can vary quite a bit.
Other Reading
 Beer Data: Alcohol, Calorie, and Attenuation Levels of beer
 Understanding Specific Gravity and Extract
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