These days, most homebrewers use recipe formulation software to calculate their original gravity(OG), bitterness (in IBUs), and beer color (in SRM) from their list of ingredients. Likewise, the final gravity (FG) and alcohol content (usually ABV) is also calculated, based on the apparent attenuation of the yeast. In addition, extract efficiency is either calculated or can be identified by trial and error (changing the extract efficiency in the program until it predicts your actual OG). However, there are some additional equations that may help out the average homebrewer. Some of these appear in some software packages. If your brewing software doesn’t do these calculations for you, the easiest way to use them is to make a spreadsheet of the equations you use most often.
You can calculate how much strike water you need given the weight of your grains (in either pounds or kilograms) and your intended mash thickness (in qts./lb. or L/kg). A common mash thickness for single infusion mashes is 1.25 qts./lb. (2.6 L/kg). For any mash that you need to stir, such as step infusion mashes done via applying direct heat, a slightly thinner mash thickness of 1.5 qts./lb/ (3.1 L/kg) would be better. The equation is:
where V(strike) is the volume of strike water in either quarts or liters, W(grain) is the weight of the grain in pounds of kilograms and MT is the mash thickness in either quarts per pound or L per kilogram.
If you have a false bottom (or any other space that fills with liquid) in your mash tun, you’ll need to add the volume underneath it to your calculation. For example, if you had a 1-gallon space under your false bottom and you calculated that you needed 3.2 gallons of strike water using the equation above, you’d actually need 4.2 gallons of strike water.
Knowing your heating rate will help you plan future brew days. For a given volume of water and heat output from your burner, the equation is:
where HR is the heat rate in either degrees Fahrenheit per minute or degrees Celsius per minute. Capital “T”s are the start and stop temperatures (in °F or °C) and lowercase “t”s are the start and stop times. Once you have this figure, you can multiply it times your desired increase in temperature to calculate the time it will take to heat that volume. For example, let’s say you had 10 gallons of water. You started heating at 12:00 (noon), when the water was at 60 °F. At 12:34, the water was at 163 °F, your desired strike water temperature. This gives a heat rate of 103 °F over 34 minutes, or 3.0 degrees per minute. If on a subsequent brewday, you had the same volume of water (10 gallons) and needed to heat it 120 °F, you would take 120 °F and dived it by 3 °F/minute to get 40 minutes. To compensate for different volumes of water, multiply your expected time to heat the volume at your known volume (in our case 40 minutes to heat 10 gallons by 120 °F) by a fraction consisting of the new volume divided by the old volume. For example, if we wanted to heat 12 gallons of water by 120 °F. We’d take our result based on heating 10 gallons (40 minutes), and multiply it by 12/10, yielding 48 minutes. Note that, for a couple reasons, this estimation gets progressively worse the larger the difference in volumes.
You can also use this equation to calculate your wort chilling rate. This will be a negative number (as the temperature is decreasing).
Water Absorption and First Wort Volume
If you measure the amount of water that your grains absorb, you can use that to calculate your estimated volume of first wort. This is important for batch spargers and also comes in handy when brewing very big beers. To calculate your absorption rate, use this formula:
where AR is the volume of water absorbed per weight of grain, in either gallons per pound or L per kg. V(absorbed) is the volume of water absorbed by the grain and W is the weight of the grain. V(absorbed) is calculated from the following equation:
where the volume of strike water is subtracted from the sum of the first wort (which you need to measure) and the volume of any water that ends up anywhere other than absorbed into the grain (which you need to measure).
You can also measure your absorption rate by weighing your (drained) grain bed after mashing. Subtracting the initial (dry) weight from the final (wet) weight will give you the weight of the water absorbed. If you’re using English units, you can convert this to volume (in gallons) by dividing the weight (in pounds) by 8.34 pounds/gallon. In metric, a liter of water weighs a kilogram. Divide the volume of water absorbed by the weight of the grains and you’ll have your absorption rate.
Once you know your absorption rate, you’ll know how much first wort you’ll yield for any weight of grain in future brews. The equation for that is:
Amount of Wort to Collect
If you fully sparge your grain bed each time you brew, the volume of wort you collect will depend on the weight of your grains. (Note that many, if not most, homebrewers collect a fixed volume of wort no matter what their grain bill. Thus, their extract efficiency gets progressively worse at higher original gravities.) If you measure how much wort you collect once (or better yet, a few times), you can estimate how much wort you can collect from any grain bill weight. The equation for that is:
where V is the volume of wort to collect (or equivalently, your pre-boil wort volume), W is the weight of your grain and FS (fully sparged) is the ratio of wort volume to grain weight that you must measure. To calculate this, just note the volume of wort you collect from one grain bed (when the pH of the final runnings rises above 5.8 or the specific gravity dips below SG = 1.010) and divide by the weight of your grain.
Volume of Sparge Water Required
If you know how much wort you plan to collect, and the volume of your first wort, you can estimate how much sparge water you’ll need with this equation:
V(other) is the amount of water you plan to leave behind in the grain bed (anywhere other than in your kettle). If this is zero, you’ll run your grain bed dry, empty the space below your false bottom (if any) and not leave any wort behind in tubing or sight glasses or anywhere else. From a practical standpoint, it always pays to heat a little extra sparge water than you think you’ll need.
Estimating OG from Pre-Boil Wort Concentration and Volume
Once your wort is collected, you may wonder if you are on track to hit your target OG. To figure this out, you can use CV=CV equation from chemistry. Put in a form useful to brewers, this is:
Stovetop extract brewers who dilute their wort in the fermenter need to use this equation “in reverse.” For example, let’s say you’re brewing 5 gallons of pale ale at a target OG of 12 °Plato (OG 1.048). You start boiling 3 gallons of wort and it’s at 18 °Plato, so you’ll solve for C(diluted). This equals 16*3)/5 or 10.8 — in other words roughly ~11 °Plato.
Early in the boil, soluble proteins contribute slightly to the density of the wort. These coagulate and sediment out (as the hot break and cold break) so this equation tends to overestimate your OG very slightly (by a “gravity point” or two, at most).
So there are a few equations that may help make your brewday run more smoothly.