Attenuation and related formulae

Most of these formulae were brought to our attention by George Fix in various HBD postings.

Embedded in this page are JavaScript calculators that let you plug your own values into the formulae. If your browser doesn't support JavaScript, or if you have it turned off, you won't see the calculators.

  • Extract: Convert between Degrees Plato and Specific Gravity Points.
  • Attenuation: Compute the real attenuation of your beer.
  • Alcohol content computation.
  • Calorie content of beer.
  • Extract

    In technical beer literature, the sugar content of a wort/beer is typically expressed as extract in degrees Plato. One degree Plato corresponds to a 1% by weight sugar solution of sucrose. For other sugars, the actual percent weight will be slightly higher. Sucrose produces the heaviest solution from a given mass of sugar.

    The Plato tables express conversion from specific gravity to degrees Plato. The following equation is a quadratic curve fit to the table, from deClerck:

    	E = 668.72*SG - 463.37 - 205.347 * SG * SG
    
    A simplified version of the equation, rounded to a more reasonable (for homebrewing) number of significant figures, and recast in terms of points = 1000 * (SG - 1), is
    	E = 0.258*(1-0.0008*Pts)*Pts + 0.003
    

    To go the other way, use

    	Pts = 0.082636 + 3.8480*E + 0.014563*E^2
    
    This differs from the "true equation" by less than 0.1 in the range E=0..19, and by about -1.0 at E=30.

    Here's a quick conversion table

    Plato	Points		Plato	Points		Plato	Points	
     0	 0		10	40		20       83
     1	 4		11      44		21       87
     2	 8		12      48		22       92
     3	12		13      53		23       96
     4	16		14      57		24      101
     5	20		15      61		25      105
     6	24		16      65		26      110
     7	28		17      70		27      115
     8	32		18      74		28      119
     9	36		19      78		29      124
    10	40		20      83		30      129
    

    Attenuation

    Attenuation is defined as the %sugar converted to alcohol and CO2 by the yeast. Apparent attenuation is computed from the measured specific gravity (converted to extract) of the beer, as follows:
    	AA = 1 - AE / OE,
    	AE = Apparent Extract of beer, as measured by a hydrometer
    	OE = Original Extract of the wort.
    
    However, the specific gravity of the beer is depressed by the lower specific gravity of alcohol (0.8, approximately), so the measured apparent extract is smaller than the real extract (sugars remaining in the finished beer). Real extract, RE, can be measured by dealcoholizing the beer (typically by boiling gently), adding distilled water back to the original volume, and then taking the specific gravity. Or, we can use an approximation (due to Balling):
    	RE = .1808*OE + .8192*AE,
    

    With this approximation, we can compute an approximation to the real attenuation as

    	RA = 1 - RE / OE,
    	RA = 1 - (.1808*OE + .8192*AE) / OE.
    

    Alcohol content

    Everybody seems to be interested in the alcohol content of their brews. There are many formulae floating around to approximate alcohol content. My favorite "quickie" is this: With typical attenuation, the alcohol content in finished beer will be approximately 100*(OG-1) %volume.

    Balling gives the following, more accurate formula:

    	A = (OE-RE)/(2.0665-.010665*OE) (% weight)
    

    Then, there are the old favorites for % alcohol by volume.

    	A = (OG - FG) * 125 * 1.05, or
    	A = (OG - FG) * 1000 / 7.5
    
    Both of these estimate a little bit high for most worts, but only by 0.1 to 0.2 percent.

    Ralph Snel (ralph@astro.lu.se) wrote: A quite simple way that will give accuracy up to 0.1% is to boil off all the alcohol and substitute by water. This means boiling down to less than a third of the original volume in most cases, it's not that hard to smell if there are alcohols in the vapour. Fill with water so you have your original volume and take the difference in gravity, then look up alcohol content in the table:

    SG      Alcohol         SG      Alcohol         SG      Alcohol
    diff.   vol %           diff.   vol %           diff.   vol %
    0	0.00		10      7.18 		20      16.00
    1	0.64		11      7.98 		21      17.00
    2	1.30		12      8.80 		22      18.00
    3	1.98		13      9.65 		23      19.00
    4	2.68		14      10.51		24      20.00
    5	3.39		15      11.40		25      21.00
    6	4.11		16      12.30		26      22.00
    7	4.85		17      13.20
    8	5.61		18      14.10
    9	6.39		19      15.10
    10	7.18		20      16.00
    
    From: Technisch handboek voor de amateur wijn- en biermaker by Leo van der Straten ISBN 90-245-0969-6

    Caloric content of beer

    Fix writes: Walter Gude asked in HBD#878 about the determination of calories in beer. The following empirical formula is remarkably accurate, and widely used to check direct measurements. Let A, FG, and RE be defined as follows:
    	A = alcohol content of finished beer in % by wt.
    	RE = real extract of finished beer in deg. Plato
    	FG = final gravity of finished beer.
    
    Then the number of calories per 12 oz. bottle is the following:
    	(6.9*A + 4.0*(RE - .1))*3.55*FG .
    

    To take Walter's specific case, first note that from Plato tables an OG of 1.045 is equivalent to

        OE = 11.25 deg. Plato,
    
    while a FG of 1.010 is equivalent to
        AE = 2.5 deg. Plato.
    
    Therefore,
          RE = .1808*11.25 + .8192*2.5 = 4.08 deg. Plato,
    
    and
           A = (11.25 - 4.08)/(2.0665 - .010665*11.25) = 3.68 % wt.
    
    We conclude that there are
         ( 6.9*3.68 + 4.*3.98)*3.55*1.010 = 148.12
    
    calories in Walter's beer. Note that 61.5% come from alcohol, and 38.5% come from the residual extract.

    Errors in the formula for calories using A and RE will be under 1%. Errors in Balling's approximations can be as large as 3-5%.

    Notes on calorie formula

    Where do the numbers in the calorie formula come from?
    Back to Spencer's beer page.