How To: Calculate Efficiency

If you've read my recent Harvest Pumpkin Ale post, you probably noticed that my OG was lower than that of the original author.

My OG = 1.060
Original Author OG = 1.070

This result was al little puzzling to me since I'm usually within a few points of the OG for the recipe I'm following.  I'm sure that my batch of beer will still be delicious and enjoyable, but this got me thinking about what could have caused the lower OG reading.  I had started with the author's original 10 gallon recipe and scaled it down to 6 gallons.  I later realized the original author had noted an expected efficiency of 85%.  When I planned my batch, the author's efficiency was something I ignored.  I've typically tried to avoid too many calculations in my brewing history, but I know that my efficiency is usually in the 70-80% range (I use a brewing app called iBrewMaster which calculates efficiency on its own).  To this point in my homebrewing career, efficiency has been a fun to follow stat (kind of like on base percentage in baseball), but hasn't really changed my brewing approach.

Here's my hypothesis and what I'm hoping to learn from this post:

The lower OG reading was a result of a lower efficiency than that of the original author and that I should have increased my grain bill to account for this.

Let's begin exploring this possibility.

First, let's learn how to calculate efficiency.  Referencing John Palmer's How To Brew, 2nd Edition, p. 151 (this link is for the 3rd edition):

"In mashing, you are collecting "x" number of gallons of wort that has a gravity of "1.0yy" that was produced from "z" pounds of malt.  To calculate your extraction in terms of PPG (points per pound per gallon), you need to multiply the number of gallons of wort you collected by its gravity and divide that by the amount of malt that was used."

x = gallons of wort

yy = maximum PPG (reference this table, max PPG is the last two digits of the potential SG)

z = pounds of malt

PPG = yy*z/x

I'm going to begin by calculating efficiency for a very simple batch of beer, Be-Otch IPA.  Here is the grain bill with the efficiency calculation (I collected 6 gallons of wort)

14 lbs US 2 row pale malt          (36 x 14) / 6 = 84 max PPG
0.6 lbs Caramel/Crystal 20L      (35 x 0.6) / 6 = 3.5 max PPG

14.6 lbs total                               87.6 max PPG

Max PPG would be the specific gravity (1.087) if you were able to achieve 100% efficiency.  In this case I know that my gravity reading was 1.063

Efficiency = 63/87 = 72%

Now let's try this with my Harvest Pumpkin Ale.  Note, I'm ignoring the rice hulls since they do not contribute any sugars to the mash.

11.4 lbs 6-Row Pale Malt         (35 x 11.4) / 6 = 66.5
0.75 lbs Melanoiden Malt         (37 x 0.75) / 6 = 4.6
0.6 lbs Crystal 60                      (34 x 0.6) / 6 = 3.4
0.6 lbs Victory Malt                  (36 x 0.6) / 6 = 3.6

13.35 lbs total                            78.1 max PPG

OG reading = 1.060

Efficiency = 60/78 = 77%

As expected, my efficiency was lower than the 85% recommended by the original author.  If I was to do this batch again, I would probably assume an efficiency of 75% and increase my grain bill by enough to compensate for my less efficient operation.  To calculate my grain increase I'm going to take the original max PPG (78.1) and multiply that by the recommended 85% efficiency to get my target PPG.

78.1 x 85% = 66.3 target PPG

Next, I'll take the target PPG and divide that by my assumed efficiency of 75% to get my new max PPG.

66.3 / 75% = 88.5 new max PPG

Finally, I'll divide my new max PPG by the original max PPG to determine the percent increase for each of the grains and multiply that increase percentage by each grain in the recipe.

88.5 / 78.1 = 113%

Revised grain bill:

12.9 lbs 6-Row Pale Malt         (35 x 12.9) / 6 = 75.3
0.85 lbs Melanoiden Malt         (37 x 0.85) / 6 = 5.2
0.7 lbs Crystal 60                      (34 x 0.7) / 6 = 4.0
0.7 lbs Victory Malt                  (36 x 0.7) / 6 = 4.2

15.15 lbs total                            88.7 max PPG

After doing this exercise, efficiency is not just another stat to be ignored.  You can see that this makes a significant difference in the grain bill (1.8 lbs!!).  If I were brewing this recipe on a large scale, efficiency would be a huge deal and could cost thousands of dollars.  On the homebrewing scale its only a few extra dollars out of my pocket.  If you're planning recipes in the future, whether its from a magazine or book try to find out what the assumed efficiency is and if it is similar to your system.  The exercise above only take a few minutes and could make a difference in the final product of your batch.

But if you hate math and just enjoy brewing for fun, ignore this post, relax, and have a homebrew!!