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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 * SGA simplified version of the equation, rounded to a more reasonable (for homebrewing) number of significant figures, and recast in terms of

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^2This 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

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 = .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.

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 / 7.5Both 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 16.00From:

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 = 148.12calories 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%.

- 6.9 is calories/gram of alcohol (ethanol)
- 4.0 is calories/gram of sugar (I'm not sure about the 0.1, but I suspect it has to do with the non-sugar contribution to specific gravity.)
- 3.55 is the number of deciliters in 12 (US) fluid ounces. Why deciliters? Because there's an implicit multiplication by 100 in using percent alcohol and degrees Plato (% sugar), so we're really getting calories per 100 grams of beer from the parenthesized expression. 100 grams of water is 1 deciliter.
- Finally, the whole thing is multiplied by the FG to convert the volume measure of the bottle to the weight measure of the calorie factors.

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