Calculating Gravity, Bitterness, and Color
When writing a beer recipe, you start with an idea of the beer you would like to brew. To get from this idea to the finished beer, you can take one of two approaches. You can experiment, perfecting the beer through the trials and errors of several brewing sessions. Or you can carefully crunch some numbers and plan the brew ahead of time.
To plan a brew, you need to know a few details about your ingredients and your brewing process. Armed with this knowledge and a calculator, you can plan the original gravity, bitterness level and color of your beer.
Calculating Specific Gravity
Specific gravity is, essentially, the amount of sugar in your wort. Other compounds in wort affect gravity, but their impact is minor compared to that of sugar. Pure water has a specific gravity of 1.000. Adding sugar to water increases its specific gravity. Most beers have an original gravity between 1.035 and 1.100. (Original gravity is the specific gravity of a beer before the yeast is pitched.) Box 1 (page 50) shows the original gravity of different styles of beer.
Calculating Original Gravity
Original gravity depends on three factors: the amount of grains and extracts used when brewing, how much sugar they contain and how much of that sugar you can extract. To calculate the expected original gravity of a wort, use the following formula:
Equation 1.1:
SGP(GP/gal)=[W(lb.)*EP(GP/lb.)*EE]/V(gallons)
SGP stands for specific gravity points, in gravity points per gallon. Gravity points are the decimal portion of original gravity. A pale ale with an original gravity of 1.048 has 48 gravity points per gallon. A barleywine of gravity 1.105 would have 105 gravity points per gallon.
W is the weight, in pounds, of the grain used. EP is the extract potential of the grain. This is how many gravity points of sugar are contained in a pound of the grain. Weight times extract potential gives you the total amount of sugar in the grains, measured in gravity points. Table 1 (page 51) lists the extract potential of many common grains, malt extracts and adjuncts.
Extraction efficiency (EE) is the measure of how well you extract the sugars from the grain. Values for extraction efficiency range from zero to one. Multiplying total gravity points times extraction efficiency gives you how many gravity points the brewer extracted. This amount is divided by the volume of your beer. This yields specific gravity points, the decimal portion of original gravity.
Calculating Extraction Efficiency from Brewing Data
Extraction efficiency (EE) can be calculated by rearranging equation 1.1 to:
Equation 1.2:
EE=[SGP(GP/gallon) *V(gallons)]/[W(lb.)*EP(GP/lb.)]
Multiplying SGP times V gives you the total gravity points from the batch. W times EP is the maximum amount of gravity points that could have been extracted from the grain. The actual amount of gravity points divided by the maximum amount of gravity points possible is your extract efficiency. If you extracted all of the sugar (100%), your extraction efficiency would be 1.00. If you extracted none of it (0%), your extraction efficiency would 0.00. Homebrewers get efficiency values that range anywhere from 40% to 85% (EE = 0.40 to 0.85).
Example of Extraction Efficiency Calculation
For example, let’s say you brewed a five-gallon batch using 9 lbs. of pale malt and your original gravity turned out be 1.048. From the table, the extract potential for pale malt is 36. So, your extraction efficiency would be:
EE =[48*5]/[8*36]= 0.83
Example of Original Gravity Calculation
Now that we know how to measure or calculate all the terms in the equation, here’s an example of how to calculate original gravity. Let’s say you plan to brew a five-gallon batch of beer again. You plan to use 3.5 lbs. malt extract, plus 4.5 lbs. pale malt and 1/2 lb. crystal malt (40° Lovibond). Your extraction efficiency, from before, was 83%. From Table 1, you can see that dried malt extract yields 45 GP/lb. Extraction efficiency for malt extract is always 100%, so its extraction efficiency is 1.0. The extract potential for pale malt is 36 GU/lb.,while the EP for the crystal is 30. Substituting the numbers for the variables gives you:
SGP = [3.5*45*1.00]/5+ [4.5*36 *0.83] /5 + [0.5*30*0.83]/5=60.9
60.9 specific gravity points is equivalent to an original gravity of almost 1.061.
Calculations from multi-grain grain bills can be extensive. Luckily, there’s a shortcut if you don’t mind sacrificing a little accuracy. You might have noticed that the range in extraction potentials isn’t very large. And the grains with the lowest extract potentials are only used in small amounts. This allows a helpful shortcut.
For pale beers, simply treat all grains as base grains. Add up the total amount of grain that you added and treat it all as pale malt. For dark beers, treat the base grains plus crystal malts as pale malt. Then lump all the specialty grains together. Use the extract potential of the most abundant specialty grain as the value for the lumped grains.
You sacrifice some accuracy by lumping grains of different extract potentials together. But the difference is slight and always goes in one direction — you always overestimate your original gravity. Except for very dark beers, the difference is rarely ever greater than a few
gravity points.
The equations for specific gravity have great practical value for homebrewers. Every variable can be determined to sufficient precision to make the outcome of the calculations worthwhile. Using these calculations, an accomplished brewer can expect to hit target gravities within a point of his calculations.
Calculating Bitterness
In alcoholic beverages, maltiness is usually balanced by another flavor. In wine (and some styles
of beer), maltiness is balanced by acidity. In most styles of beer, maltiness is balanced by the bitterness of the hops. The level of bitterness in beer can be expressed as International Bitterness Units (IBUs). Box 2 (page 52) shows the bitterness levels of various styles of beer. IBUs can be calculated using the following formula:
Equation 2.1:
IBU = [W(oz)*AA%*U*7489]/V(gal)
W is the weight, in ounces, of the hops. AA% is the percentage of alpha acids in the hops, expressed as a number between zero and one. Multiplying weight times alpha acid percent gives you the total amount of alpha acids added to your beer. Often, this number is called AAU.
U is the utilization factor, the percent of the alpha acids that end up contributing towards the bitterness of the beer. U is also expressed as a number between zero and one.
The value for U is affected by many things, including wort gravity and the form of hops used (pellet, plug or whole). But the primary variable is boil time.
Table 2 (page 51) gives ranges of values of U for various boil times. When wort is boiled, alpha acids are converted to isomerized alpha acids, the substances that contribute to bitterness. Multiplying the utilization factor times AAU (total alpha acid units added) yields the amount of isomerized alpha acids in the beer. The number 7489 is a conversion factor; if you enter the weight of the hops in grams and the volume of the beer in liters, this term drops out of the equation. Dividing by volume gives you bitterness in IBUs.
Example of Calculating IBUs
Let’s say you brew your pale ale again. You add 2.0 ounces of Northern Brewer hops with 8.5% alpha acid and boil them for 1 hour. With 15 minutes to go in the boil, you add 1.5 oz. of Fuggles hops with 4.0% alpha acid. After choosing values of U from Table 2, we get:
IBU = [2*0.085*0.25*7489]/5+ [1.5*0.04*0.075*7489]/5 = 70.4
Another factor that influences the equation is the aging of the hops. The alpha-acid percentage of the hops may have decreased since the measurement was made. The amount of decrease would depend on how the hops were stored after the initial alpha-acid measurement.
Unfortunately, the homebrewer usually has no way of determining the storage history of his hops. Even if the homebrew shop has stored the hops properly you don’t know how they were treated by the wholesaler or the conditions of transport. To take aging into account, you need to multiply alpha-acid percent by a factor that measured what percentage of the alpha-acids were lost.
The IBU calculation is not as valuable to homebrewers as the calculation of gravity. There is no simple way to measure IBU for homebrewers. Since IBUs can’t be directly measured, the utilization factor can’t be accurately estimated for a brewer’s own equipment. As a consequence, most homebrewers use a value of U from a table or graph. The value chosen may not match their brewing practices. In addition, the electronic scales most homebrewers use only measure to the nearest 0.25 oz. so the homebrewer can’t add precise amounts of hops for small-scale variations in IBU.
Despite all this, using the IBU calculation can get the brewer to the right ballpark. Fine-tuning the bitterness calculation further can be done by trial and error.
Calculating Color
From straw-colored pilsners to jet-black stouts, beers vary greatly in color. Box 3 (page 53) shows the color ratings of various styles of beer in Standard Reference Method (SRM). SRM is a common color scale that is similar to degrees Lovibond. Lovibond tends to be used to describe malt color while SRM describes the finished beer. A beer with a low SRM is pale (Budweiser is 2) and a high SRM number indicates a dark beer (stouts are over 50 SRM). The SRM scale uses the following comparisons: water at 0.0, straw at 1 to 5.5, amber at 5.5 to 40 and black at 40+.
You want your brew to have a color that properly represents the style you’re brewing. Unfortunately, the tools available to the homebrewer aren’t really up to the task.
Another measure of beer color is HCU, homebrew color units. It is calculated as:
Equation 3.1:
HCU = [W(lbs) * CR(° L)]/V(gallon)
W(lb.) is the weight of a grain. CR(°L) is the color rating in degrees Lovibond. Multiplying the two yields total color added by the grains. The number for total color is then divided by volume.
The HCU equation is similar to the SGP and IBU calculations, except it is missing a utilization or efficiency term. Essentially, it is only a measure of how much color is put into the beer from the grains. How that color is changed by the brewing process is ignored.
Ignoring the effect of the brewing process on beer color is unfortunate, since many brewing processes affect wort and beer color. Some factors increase color. These include: high hop rates, longer boil times, finer grain crushes and oxidation from wort abuse or aging. Fermentation, in contrast, reduces the color of the wort.
The equation could be improved if a factor was added to account for changes in color due to the brewing process. In fact, two factors would be needed. Some color changes are modifications of the grain color added to the beer. Loss of color during fermentation, for example, depends on the amount of color initially in the wort.
Other color changes do not depend on the initial beer color. Some of the wort darkening during the boil is due to the sugars caramelizing. In solution, the sugars are colorless. The color that sugar caramelization contributes does not come from the roasting of the grain.
So, an equation that took both of these factors into consideration would need two new variables. The resulting equation would be:
Equation 3.2
NHCU=[W(lbs) * CR(degrees L)*TF + AF]/V(gallon)
NHBU is New Homebrew Color Units. The two new factors are TF and AF. TF is the transforming factor, the extent that the grain color is modified. AF is the additive factor, the amount of color that appears during the brewing process or aging that is not dependent on roasted grain-derived color.
There are other problems with homebrew color units (old or new). HCU does not correspond to any of the common measures for beer color. For example, HCU cannot be directly compared to SRM values such as those given in Box 3. Additionally, there is no common method of measuring HCU available to homebrewers.
If methods are developed to measure HCU, the TF and AF factors could be estimated by solving the equation for these factors. The values could then be determined by substituting the other variables with data from brewing sessions.
Are you confused yet? If you work with these equations often enough, they will become familiar to you. Many brewers set up spreadsheets in Excel or other programs to aid them in doing these calculations. If you try brewing new styles of beer often, you may soon become convinced that your calculator is as valuable a brewing tool as your hydrometer or pH meter.
