Just how do You Calculate the Number of Calories in your Homebrew

As many of you know I have a handy chart that shows how many calories are in your beer.  Today I got a question about how exactly did I get the numbers, well here is the nitty gritty of how to do it using good old math!

(Formulas were obtained from Realbeer.com)

so if take the formula:

cal per 12 oz beer = [(6.9 × ABW) + 4.0 × (RE – 0.1)] × FG × 3.55

OG = Original Gravity (1.048 in the example)
FG = Final Gravity (1.010 in this example)
ABW = Alcohol By Weight
RE = “Real Extract” (RE, in °P) is a measure of the sugars which are fermented
OE = Original Extract (The sugar content of a wort/beer is typically expressed as extract in degrees Plato)
FE = Final Extract (or apparent extract)

To calculate the calories first you need alcohol by weight:

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

However before we can do this we need the Original Extract (OE) by using the OG in points (basically the 3 numbers after the decimal place)
points = 1000 * (SG – 1)

OE = 0.258*(1-0.0008*Pts)*Pts + 0.003
OE = 0.258*(1-0.0008*48)*48 + 0.003 = 11.9114544

FE = 0.258*(1-0.0008*Pts)*Pts + 0.003
FE = 0.258*(1-0.0008*10)*10 + 0.003 = 2.56236

With the OE and FE we can now calculate the RE (Real Extract) for the A (Alcohol) part of the equation.

RE = .1808*OE + .8192*FE
RE = .1808*11.9114544 + .8192*2.56236
RE = 2.15359095552 + 2.099085312 = 4.25267626752

Now the OE and RE have been calculated we can figure the Alcohol by Weight.

A = (OE-RE)/(2.0665-.010665*OE)
A = (11.9114544-4.25267626752)/(2.0665-.010665*11.9114544)
A = 7.65877813248/1.939464338824 = 3.948914130137563 (% by weight)

The Alcohol by Weight (NOT ABV, Alcohol by Volume) is about 4% and the Real Extract (RA) is 4.3 we can calculate the calories in the beer

cal per 12 oz beer = [(6.9 × ABW) + 4.0 × (RE - 0.1)] × FG × 3.55
cal = [(6.9 × 3.948914130137563 ) + 4.0 × (4.25267626752 - 0.1)] × 1.010 × 3.55
cal = [27.247507497949185 + 4.0 x 4.15267626752] × 1.010 × 3.55
cal = [27.247507497949185 + 16.61070507008] × 1.010 × 3.55
cal = [43.858212568029185] × 1.010 × 3.55
Cal = 157.253621162668643