Back when I first started brewing beer, I used to just throw cans of extract together and hoping for the best when I had my Mr. Beer kit.  Although I had some mediocre results for the most part, I did have several beers that were truly superb from that method.  But one thing I did notice from that methodology, I didn’t have consistency.  Even if I tried to make the same recipe over again, there was too many variables to be able to produce the same beer over and over again.  For instance, the Alpha Acid percentage in hops, how viable your yeast is, protein content in the grains, hell..even the extracts can be variable (in regards to the long chain dextrins that yeast can’t metabolize).  With all these variables, I had to do something about it…but what?

As I made the jump from extract (pre-made brewing kits) to all-grain brewing (brewing from scratch), I found two books that made their way in my library as my Beer Bibles.  Gregory Noonan’s New Brewing Lager and John Palmer’s How to Brew really helped me understand the basics of the brewing beer.  Within those books I found that math is my answer to help my consistency problems, ranging from basic geometry formulas, complex logarithmic formulas, and even algebraic equations.  They seemed very intimidating at first, but then I realized that the formulas are merely just plug and chug equations.

Reason why I bring up the topic of Beer Math is because I was busy yesterday doing calculations for the grain bill and other parts of Copperhead Light Ale.  Copperhead Light Ale was originally an accident (just as the original Copperhead Ale), and I decided to give the “accident” a recipe overhaul because of the potential it has of being a great beer in our arsenal of beers we routinely brew.  The accident that created Copperhead Light originally started by forgetting to add a portion of the grain bill before brewing.  I didn’t notice the missing grains until I started sparging (separating the wort from the grains) and I saw that the wort (sugary goodness) was much lighter than it should have been.  From there Copperhead Light Ale was born (or should I say the pilot batch)!

This time around I decided to reduce the overall grain bill from the original Copperhead Ale by 20% (to make up the portion of the grain bill that I missed from the first time Copperhead Light was born from), by doing so that decreased my total weight I would use in grains in the original Copperhead Ale recipe.  Then I removed an additional 30%  from each grain addition to the recipe and replaced that with rice.  To make it more easier to follow here’s an example of the math I conducted:

Copperhead Ale Grain Bill Total 10lb’s; need to reduce grain bill by 20%:

10 × .20 = 2 lb’s

10 − 2 = 8 lb’s new grain bill weight for Copperhead Light

Copperhead Ale Light Grain Bill; reduced for Rice addition by 30%:

Pale Malt – 4 lb  –> 4 × .30 = 1.2 lb reduction

Vienna – 3.5 lb  –> 3.5 × .30 = 1.05 lb reduction

Crystal – .5 lb    –> .5 × .30 = 0.15 lb reduction

Add up your reduced grain bill:

Pale Malt – 2.8 lb

Vienna – 2.45 lb

Crystal – 0.35 lb

Total – 5.6 lb

Then add up your total lb reduction to get your new rice addition:

1.2 + 1.05 + 0.15 = 2.4 lb’s of rice

Check your math by adding your adding your grain bill and rice together to see if you got a total of 8 lbs that was originally desired:

5.6 + 2.4 = 8 lb’s  <– Success!!

Okay, okay, that was really easy but you get the point.  That was the basics of using math to help formulate a new grain bill.  Actually, there’s a lot more to it than that, I already had a pre-determined starting gravity/diastatic power of the grain from the grain bill and also determined how much the rice would offset the maltiness in this brew (please note that this is an example and not the real recipe, I just simplified it for everyone to understand).  Now that I got my grain bill I can now get started on brewing my beer!

Now to determine the strike temperature (initial infusion of hot water mixed with the grains), I need to know my grain bill weight, grain temperature, and volume of water, and desired temperature.  The following equation helps us determine the strike temperature for the mash:

Where:

Ts = strike water temperature in °F

Tt = target mash temperature in °F

Tg = dry grain temperature in °F

R = Water to grain ratio (in quarts to pound / ideally 1.00 – 1.125 qts per 1lb)

Formula: Ts = (0.2/R) ×(Tt – Tg) + Tt

For example: I have 8 lb grain bill and I want to mash in at 148F with only 2.25 gal of Hot Liquor (HL / HL is brewing term for hot water).  Crush your grains and take a temp reading, for example..say its 72F.  Now figure out your Water to Grain ratio by taking your total water volume and multiplying it by 4 (this converts to quarts) then, divide your answer by your grain bill.

R = 2.25 gal × 4 = 9 qts

R = 9 qts ÷ 8 lbs

R = 1.125

Now that I have my water to grain ratio, I can now continue on with the strike temperature formula!

Ts = (0.2/1.125) × (148 – 72) + 148

Ts = (0.1777) × (76) + 148

Ts = 13.51 + 148

Ts = 161.51ºF

Now I will need to heat my HL to 161.5F to bring my mash to 148F as planned!

Now that we got the strike temperature out of the way, I can start my mash!  After a pre-determined time at that rest temperature, I want to raise my mash to a new rest temperature of 158F.  Since I’m a huge fan of decoction mashing (decoction mashing is where you boil the thick portion of the mash in a separate kettle), I want to decoct my mash to get to the next temperature rest.  A way to do this is by either following the traditional methods of pulling a third of the thickest mash and transferring it into a different pot then boil it as long as needed and then later return the decocted portion until you reach your desired temperature rest and wait to add the remaining decocted mash until it has cooled to the desired temperature.  Or you can use the following equation without having to wait on your remaining grist to cool:

Where:

Dv = volume needed to pull from mash in gal to decoct

Tmt = target temperature of mash

Imt = initial temperature of mash (or current mash temp)

Gw = weight of grain

Wim = volume of water in the mash before infusion (or current water in mash volume)

Iv = volume of water to add to mash to achieve target mash temperature

Iwt = infusion boiling temperature (default 212F/100C) you can modify this to your sea level boiling temps

Formula: Dv = (Tmt – Imt) × (Gw × (0.3125 + (Wim ÷Gw))) ÷ (Iwt – Imt)

This can look very intimidating but be sure to remember your order of operations!  My current mash temperature is 148F, my grain weight is 8 lb’s, my current water volume in the mash is 2.25 gals, and my desired temperature is 158F.  So for example:

Dv = (158 – 148) × (8 ×(0.3125 + (2.25 ÷ 8))) ÷ (212 – 148)

Dv = 10 × (8 ×(0.3125 + 0.28125)) ÷ 64

Dv = 10 × (8 ×0.59375) ÷ 64

Dv = 10 × 4.75 ÷ 64

Dv = 47.5 ÷ 64

Dv = 0.74 gal

To raise my mash temp from 148F to 158F, I will need to pull 0.74 gal of grist to reach my desired temperature.  How long to boil the decoct is up to personal preference or if you’re trying to achieve melanoiden production.  So we then rest our mash at 158F at a pre-determined time and we need to mash out our grains.  How do we do it?  By decoction of course; so we use decoction to mash out our grains.  We then need to figure out how much sparge water we will need to get our pre-boil volume in the kettle.  To do that we use the following formula:

Where:

WGr = water to grain ratio

GAr = 0.13 grain absorption ratio

SWv = WGr × grain weight

GAv = GAr × grain weight

Sv = sparge volume

Bv = boil volume

Formula: Sv = (Bv ÷ 2) – (SWv – GAv)

For example:

Sv = (7 ÷ 2) – ((1.125 ×8) – (0.13 × 8))

Sv = 3.5 – (9 – 1.04)

Sv = 3.5 – 7.96

Sv = 4.46 gals of sparge water

For me to reach my target of pre-boil volume of 7 gallons I will need to prepare 4.46 gallons of HL to sparge my mash with.  So now I can heat my sparge liquor to 170F to sparge my mash!  This is just the tip of the iceburg when it comes to beer math.  I figured I could give everyone Beer Math 101 for the time being before I present a Beer Math 112 course!  At the moment, Copperhead Light Ale is almost finished sparging and it’s time to get a pre-boil starting gravity so I can do my 60 minute hop addition calculations!  😉  Till next time, cheers!

– James (Head Brewmaster)