BrewingTechniques
Recipe Formulation Calculations for Brewers
by Martin P. Manning

Republished from BrewingTechniques' January/February 1994.

Formulating recipes with ingredients expressed in percentages promotes a better understanding of their influence on the finished product. Key parameters can be adjusted selectively, and variations in raw materials can be easily accounted for while preserving desired characteristics.

When describing a particular example of the brewer's art, the first things that come to mind, except perhaps its status as an ale or a lager, are its color, strength, and bitterness level. Literature on beer styles nearly always includes the ranges of these three parameters that are appropriate for each style. To actually produce an example of a particular style, however, more information is needed. The traditional types and proportions of the malts, adjuncts, and hops and how they present themselves are just as important. If any of these are out of character, the beer may be judged as unrepresentative.

In practice, further considerations beyond those mentioned above arise when seeking a really fine example. Water composition, yeast type and strain, and specific wort production and fermentation techniques all influence the product. These subjects, however, are beyond the scope of this article.

Here I present a systematic approach to recipe formulation that starts with the desired values of original gravity, bitterness, and color, along with the relative proportions of the various malts, adjuncts, and hops to be used, from which the brewer can calculate the specific quantities of the ingredients needed for a given batch size. Using this tool, the brewer is assured of matching the obligatory, objective specifications and is free to focus on the artistic aspects of recipe formulation.

OVERVIEW

All information describing a beer recipe should be related in terms that are independent of the quantity of beer to be made. A commercial brewer who works with 30-bbl batches can converse freely about the effect of a particular malt, adjunct, or hop schedule with an amateur who works with 1/100 of that amount if they both speak in terms of the proportions rather than the actual quantities of the ingredients involved. What I call the general characteristics of strength, bitterness, and color are commonly measured in units that are independent of batch size. In this article, the beer's strength is estimated by the original specific gravity (OG) of the wort, the bitterness of the finished beer is measured in International Bitterness Units (IBUs or mg/L of isomerized a-acids), and its color is measured in degrees Lovibond (°L).

Similarly, the combination of fermentables used can be described by the relative proportion - or percentage of the total - of each type of malt, mash adjunct, and kettle adjunct used. Professionals routinely think in these terms, but most hobbyists still seem to think in terms of absolute quantities, perhaps because they erroneously perceive the calculations involved in working with percentages to be difficult.

Hop rates and schedules are most often described by specifying the estimated IBU contribution of each addition. I prefer to describe the hop varieties and the specifics of their use in relative proportions, each hop addition as a percentage of the total weight of all additions, including those that are added in the secondary fermentor or cask (dry hopping). As described here, the calculations for both the fermentables and hops are executed in an organized and efficient manner and are therefore not difficult even if done using only a simple calculator. Personal computers can be used to speed and enhance calculation ability (see "Computer Shortcuts," page 55).

To describe the specific instructions as succinctly as possible, I first provide a general discussion of the procedure, the rationale for the method, and the system-dependent and controversial aspects. The procedure will work for virtually any batch size because the calculations for extract yield and hop bittering are always the same. A few system-dependent terms, however, exist: extract efficiency, hop utilization, evaporation rate in the kettle, and the loss of runoff in the spent grain, which will need to be adjusted to match the equipment being used.

Determine general characteristics: The first choices to be made are the target values for original gravity, bitterness, and color. These should be selected to fit the style of beer you intend to brew. Consult the literature on beer styles (1-4) for the expected ranges of these parameters.

Determine the specifics for the recipe: This is the creative part of formulating the recipe. The combination of malts, adjuncts, and hops you select, and how you use them in the brewing process, reflects your interpretation of the style of beer you have chosen to brew. Be aware that some styles of beer virtually require certain malts, adjuncts, or hops to be true to that style. Again, consult the literature for guidance on these aspects.

Malts and adjuncts: Using the recipe formulation method presented here, the brewer chooses the percentage of the total weight of all malts and adjuncts for each ingredient used in the mash and kettle. Several sources suggest the approximate composition of the grist, in percentages, for various styles of beer (3,4). As an example, a typical pale ale might be made using 80% pale ale malt and 15% crystal malt in the mash, and 5% of some type of sugar in the kettle (for a total of 100%). Existing recipes that give specific weights for each ingredient are easily converted to this system: the percentage for any mash or kettle ingredient (in decimal form) is found by dividing its weight by the total weight of all the malts and adjuncts, including kettle adjuncts.

For each ingredient, you will need an estimate of the extract yield (in percent by weight) and the estimated color resulting from using a unit weight in a unit volume of beer. Table I, derived largely from reference 5, gives representative values for various sources. If laboratory analyses are available, I use the coarse-grind, as-is (or unadjusted for moisture content) extract figure, because it is closest to the actual situation in the brewhouse.

Hops: As mentioned above, published recipes often describe the hop schedule by specifying the variety, boil time, and expected IBU contribution from each addition. Although the IBUs from each addition must be accounted for if the target level is to be met, the primary purpose of late hop additions is not to add bitterness but to add hop flavor and aroma, which come from the oil content in the hops, and oil content correlates only loosely with bittering power. The typically low a-acid levels of aroma varieties and their variation from year to year mean that huge swings in the weight of hops will be required to yield the specified IBU contribution. The hop flavor and aroma in the finished beer may therefore be much different than expected.

Nineteenth century brewers distributed their hop additions by dividing the total weight of hops into convenient fractions and adding these amounts at intervals from the start of the boil to the end (1). This thinking can be extended to include dry hopping. From this method we can derive a system for varying the amount of hop flavor and aroma that accompanies a specified level of bitterness. If all of the hops are added at the start of the boil, for example, essentially no hop aroma and little hop flavor will remain in the finished beer. As fractions of the total weight of hops are added later in the boil, and even to the secondary fermentor, increasing levels of hop flavor and aroma will result. In the procedure described here, the total weight (of all additions together) will be determined such that the estimated IBUs in the beer will be the same regardless of the schedule. The brewer can therefore select the hop varieties and schedule based on the desired flavor and aroma profile alone and not be concerned about matching the desired bitterness level.

Expressed in these terms, typical hop schedules sound much the same as those of historical practice. To formulate a recipe, the brewer chooses the percentage for each addition, the variety, and the boil time. The hop schedule for a typical English-style pale ale, for example, might specify that 75% of the hops are Fuggles boiled for 60 min, and the remaining 25% are Goldings added at the end of the boil. For increased hop flavor and aroma, as found in American-style pale ales, an increase in the late hops and possibly dry hopping is required. I have had good results from 25% boiled for 60 min, 25% boiled for 15 min, 25% added at the end of the boil, and 25% added to the secondary. Of course, more than one variety can be added at the same time, each with its weight fraction called out separately, as long as all additions together total 100%. This technique also improves the predictability of late hop character when more than one hop variety are being used. Actual weights of the late additions vary with the weighted average of the IBU contribution from all additions and will therefore be less sensitive to year-to-year variations. Another advantage is that dry hop additions are called out in the schedule in the same terms as all other additions (that is, as a percent of the total weight), even though their IBU contribution is essentially zero.

Again, existing recipes that give specific IBUs or weights for each addition are easily converted to this system: the percentage by weight for any hop addition is equal to its weight divided by the total weight of all hop additions. To get from a specified IBU contribution to a weight for a particular addition requires backing through the assumed a-acid content and a utilization factor for the boil time (see box). Published recipes are usually the best source of data from which to construct hop schedules because quantitative, style-specific information is seldom seen in any other form.

For each hop variety used, the brewer needs an estimate of its bittering potential (in percent a-acid). Most hops are now supplied with this information, so it should be unnecessary to resort to published average levels, which are often far from those of the current crop.

Calculating actual quantities: Once you have determined the general characteristics and the specifics of the recipe and noted the specific data for the required raw material (extract and color for grains and a-acid levels for hops), you can find the actual weight of each ingredient for any desired batch size.

Malts, adjuncts, and hops: For malts and adjuncts, first find the extract yield for a unit weight of the mixture of malts and adjuncts, taking into account an assumed mash extract efficiency (see below). Once this figure is known, a simple equation is used to find the total weight of the mixture required to achieve the desired gravity. The individual weights are then found by multiplying the percentage of each by the total weight.

The procedure is exactly the same for hops. First find the expected IBU yield for a unit measure of the specified mixture of hops, when used according to the schedule. Then find the total weight of all hops required for the planned batch size and finally the weights of the individual additions. The hop utilization factor is analogous to the extract efficiency above; it will vary with boil time, but the equations involved are of the same form, differing only in their units and the associated use of a constant.

Hop utilization factors are the subject of much debate, but I have used the data given in reference 6, recast in the graphical form shown in Figure 1, with reasonable results. The calculation procedure described here will be unaffected if better or more accurate information becomes available at some later date.

Color: The color calculation may not be completed until the total weight of malts and adjuncts is known, but it is otherwise similar. First find the color resulting from a unit weight of the mixture of malts and adjuncts used in a unit volume of beer, then adjust this value to the actual weight of the ingredients and the actual volume of beer to be made. The beer color is therefore already determined when the percentages of the various malts and adjuncts and the target original gravity are fixed. If the predicted color is outside of the desired range, it can be adjusted only by trial and error, changing the percentages of the colored malts and/or adjuncts until an acceptable color is indicated.

Prediction of beer color is complicated by two factors. The first is that the wort may darken 2-3 °L because of oxidation and caramelization. This color change is not accounted for in the color prediction calculation. The color increase due to these mechanisms is system- and process-dependent and can be adjusted for only empirically. The second factor is that the measured color does not develop linearly with increases in the concentration of the coloring agents present. The calculation most often used to predict beer color - and the method used to assign color values to malt and adjunct grains - assumes that it does. Fortunately, there is a way to correct for this effect, which can be significant in the amber to very dark amber color range.

Reference 7 describes a method of visually assessing the color of a sample of beer by comparing it to a reference beer of known color, which is diluted until it matches the test sample. A curve showing the color of the reference beer (in °Lovibond) as a function of the dilution water added is used to determine the color of the test sample. Data from this curve are recast here as Figure 2, showing °Lovibond versus the concentration rather than the dilution of the reference beer. I have extrapolated the curve from 17 °L (the color of the reference beer) to 20 °L, to fully cover the meaningful range of the Lovibond scale (in practice, anything over 20 °L is generally considered black).

From Figure 2 it is evident that up to about 10 °L, color increases with concentration in a nearly linear fashion. A straight line is drawn from the origin (0 concentration and therefore 0 °L) through the 10 °L data point. This line represents the simple model in which color is proportional to concentration. Extending this line out to higher concentrations shows how the error increases dramatically beyond 10 °L. If the shape of the curve drawn through the measured data is generally representative of color development, a simple correction to the linear model is suggested. If, for example, a color of 17 °L is desired, the recipe must be formulated such that the linear model estimate is 30 °L (reading the value of the straight line at the same concentration as 17 °L on the curve). Using values from Figure 2, I constructed Figure 3 to provide a direct conversion from the linear model to the measured data.

Volumes and boil time: The method includes a simple calculation to determine the volumes of water required for mashing and sparging and the volumes that will be lost in the spent grain and to evaporation. It is necessary to work through this process if you expect to end up with the planned volume of bitter wort. Even if you follow a published recipe, differences in equipment and technique will likely be present. If you perform the calculations for your system, you will be able to come closer to the target gravity and bitterness levels with a minimum of adjustments along the way. It also allows you to predetermine process variables such as mash thickness, sparge-to-mash water ratio, and boil time, all of which may need adjustment depending on the batch size, the capacity of your system, and the original gravity of the beer being brewed.

PROCEDURE

Even though I mechanized the procedure using a spreadsheet program, I describe the calculations as if they are to be done by hand, and I provide an example recipe (Figure 4). I chose this Belgian abbey ale recipe, adapted from reference 8, to illustrate the use of both a kettle adjunct and a dry hop addition. Also, its relatively high original gravity (1.077) shows the problems that such beers present regarding the sparge-to-mash water ratio and required boil time. In this case, I made a somewhat thicker than normal mash (~10% less water per pound of grist) and used a 2-h boil time to get the sparge-to-mash water ratio above 1.0 (see below).

It is probably wise to work through the example, checking that you can get the same calculated values before trying your own recipes. A blank worksheet is included for use in formulating a new recipe (Figure 5).

The worksheet: On the worksheet, the areas that are not shaded are either recipe design choices (for example, original gravity and bitterness units), process assumptions (such as extract efficiency), or ingredient data (such as extract potential for various malts and adjuncts). To fill in these areas, you must rely on your judgment, past experience, or published sources. The shaded areas are the calculated values. They will be filled in as described in the steps below. Note that all percentages are entered in decimal form (5% = 0.05).

General characteristics: Enter the desired values for the following at the top right corner of the worksheet:

  • original gravity in points (for example, OG 1.050 = 50 points)
  • IBUs (mg/L)
  • Color (°L)
  • Batch size (gal or L)
    Note that batch size is net volume at the end of the boil, including trub losses, at 60 °F (15.5 °C). I usually make ~5% more wort than I need, which covers the amount left in the spent hops and the hot break as well as the losses in racking from the primary to the secondary fermentor.

    Malts and adjuncts: First, estimate the mash extract efficiency and enter it on the worksheet. Use past experience, or assume something around 80-85% for the typical amateur brewery.

    Next, for each ingredient in the mash and kettle, fill in the values for the percent total weight and look up and enter the extract potential (%), and color potential (°L/lb/gal or °L/kg/L), using the extract and color data from Table I. Be sure that the sum of all entries under "% Total Wt.," including both the mash and kettle adjuncts, is 100% (1.00).

    For each ingredient in the mash and kettle, calculate the values in the extract column using the following equation:

    extract = % total weight
             X extract potential
             X extract efficiency

    and calculate the values in the color column using the following equation:

    color = % total weight
             X color potential

    Extract efficiency in the kettle is always 100%.

    Next, total the values in the "Extract" column, first for the mash alone (mash extract), and then for the mash and kettle together (total extract). The total extract is the expected yield, in percent by weight, from the mixture of malts and adjuncts used.

    Next, calculate the total weight of all ingredients for the mash and kettle using the following equation:


    total weight=OGpoints x batch size/
    total extract x 46.31

    where units are in pounds. If using metric units, use 386.5 instead of 46.31 (units are then in kilograms and batch size is in liters).

    The weight for each ingredient can then be calculated:

    weight = % total weight
              X total weight

    Next, calculate the mash weight by totaling the weights of the mash ingredients.

    Total the "Color" column, including both the mash and kettle values to get the total color per unit weight and volume.

    Last, calculate the predicted color using the following equation:

    predicted color= total color x total weight/batch size

    Using the predicted color, determine the corrected color by reading Figure 3. Check this value against the target color, and adjust the proportions of the ingredients as necessary. Usually only small adjustments to the percentages of the highly colored materials will be required. Remember to keep the sum of the percent total weight column at 1.00.

    Hops: For each hop addition, fill in the percent total weight, percent a-acid, and boil time for the hops you will be using. Again, be sure that the sum of the percent total weight entries is 1.00.

    For each addition, determine the utilization factor from the boil time and wort gravity using the hop utilization chart (Figure 1).

    For each addition, calculate the iso-a-acid using the following equation:

    iso-a-acid = % total weight
            X percent a-acid
            X utilization factor
            X 7490

    For metric units, use 1000 instead of 7490.

    Next, total the iso-a-acid column. The result is the combined IBU/oz/gal (or IBU/g/L) for all hop additions.

    Next, calculate the total weight of hops:

    total weight=IBU's x batch size/total iso-a-acid

    Units are in ounces (or grams, for metric units).

    Calculate the weight for each addition using the following equation:

    weight = % total weight
             X total weight

    Volumes and boil time: First, estimate the evaporation rate during the boil based on past experience. A typical evaporation rate is 1.15 gal/h (4.4 L/h) for 6.6-gal (25-L) batches in my converted half-barrel kettle. Evaporation rates of 10%/h are typical in commercial systems but may be larger (>15%/h) on amateur equipment. The evaporation rate may also vary with the batch size on a particular system.

    Next, enter the desired boil time, which should be at least 1 h to promote a good hot break and to get full hop utilization. If you are making a high-gravity beer, you may have to boil much longer to concentrate the wort.

    Calculate the volume of water evaporated using the following equation:

    water evaporated =
         evaporation rate X boil time

    Add to this value the batch size to arrive at the net volume to the kettle:

    net volume to kettle =
         batch size + water evaporated

    Determine and enter on the worksheet the amount of water to be used per unit weight of grist in the mash (in gal/lb or L/kg) for each of the following:

    • Mashing: Mash water usually totals about 0.33 gal/lb (2.75 L/kg) for direct-heat-step, single-infusion, and decoction methods. Add up all planned infusions to arrive at a figure for your particular method.

    • Water absorbed in the spent grain: Grain usually absorbs 0.1 gal/lb (0.84 L/kg) of water, regardless of method, assuming all of the liquid is run out of the lautering vessel.

      Next, using the above and the mash weight, calculate the volumes for mash water and water remaining in the spent grain.

      Determine the sparge water volume using the following formula:

      sparge water volume =
           net volume to kettle
           - mash water volume
           + water absorbed

      Last, calculate the sparge-to-mash water ratio:

      Vs/m=sparge water volume/mash water volume

      The sparge-to-mash water ratio should be between 1.0 and 2.0, assuming an average mash thickness. Low sparging rates (VS/M < 1) will result in reduced extract efficiency, and oversparging (VS/M > 2) will increase extraction of grainy-tasting tannins from the husk material. For high extract efficiency, adjust the mash thickness and/or desired boil time to get the VS/M ratio into the middle of the 1.0-2.0 range. High-gravity beers are a problem in this regard and require a very long boil time if such a sparging rate is used. The boil time can be reduced if the sparge water is limited, though some extract efficiency is lost because the wort remaining in the spent grain will be of a higher gravity.

      Calculation of actual extract efficiency: Extract efficiency is the actual yield of extract from a mash ingredient (lb or kg [w/w]) divided by the potential yield, as shown on the extract data sheet. Typical mashes are made up of a mixture of grains with differing potential yields, and this fact has been properly accounted for in the calculation of the mash extract and the total weight of grains and adjuncts needed to achieve the desired original gravity. The extract figures already calculated on the worksheet, plus two additional measurements, are all that is needed to determine the actual extract efficiency of your mashing and lautering process.

      When all of the runoff has been collected from the lauter tun (and before any kettle adjuncts are added), determine the net volume of wort and its specific gravity, both corrected to 60 °F (15.5 °C). Be sure that the runoff has been well mixed before taking a sample.

      The actual extract efficiency of the mash and lautering process is given by

      extract efficiency= wort SG x vol. x assumed extr. eff./mash extract x 46.31 x total weight

      where 46.31 is a constant. For metric units, use 386.5 instead of 46.31 (with volume in liters and weight in kg).

      To illustrate the use of this equation, suppose we brew the Belgian abbey ale shown on the example worksheet (Figure 4). When all of the runoff is collected, we find that we have 12.9 gal of wort with a specific gravity of 1.055 (at 60 °F). Referring to the worksheet, the assumed extract efficiency was 84%, and the calculated mash extract and total weight were 0.566 and 27.12 lb, respectively. The actual extract efficiency is

      extract efficiency= 55 x 12.9 x 0.84/
      0.566 x 46.31 x 27.12 = 0.838

      This is very close to the assumed value, and therefore everything seems to be going as planned. Careful measurements are required here. A 1% error in measured volume (only ~1 cup for a 5-gal batch) or a ~1/2-point error in gravity will change the calculated effect by 1%. If your calculated extract efficiency and that which you assumed on the worksheet disagree, you will likely miss your target gravity. For the current batch, increasing the boil time (if you overestimated) or adding water to the kettle (if you underestimated) can correct the gravity of the finished wort (9). In either case, you may also have to adjust the quantities and timing of the hop additions to maintain the desired IBU level in the finished beer. Extract efficiency is determined mainly by the quality of the milling of mash constituents, the mash temperature schedule, the sparge-to-mash water ratio, and the equipment and technique used in the lautering process. Next time, assuming the process of wort production is similar, use the efficiency you calculated to improve the accuracy of your prediction.

      COMPUTER SHORTCUTS

      Given the example worksheet and the detailed description of the calculations, it should be little trouble to build a spreadsheet model like the one I use on whatever software you have available. Additional enhancements can also be made.

      First, it is useful to reserve the first row in the mash and hop tables for a base malt and a long-boil bittering hop addition. In the first cell ("% Total Wt.") of the mash and hop portion of the worksheet, you can insert a calculation that adjusts the values for the base malt and the long-boil bittering hops to make up the difference between any other entries and 100%. The other entries can then be manipulated at will, and the sum of the percent total weights will always be 100%. This refinement also enables you to use the iteration capabilities in most spreadsheets to vary one or more of the percentages of the colored grains until the desired color is indicated.

      My spreadsheet has a few additional calculations that estimate the hot volume of the lauter mash, the depth of the grain bed, and the hot volume of the mash water, sparge water, and mash runoff. These are useful if you are pushing the limits of your system's capacity. If you are really ambitious, you can build macros that automatically determine things like estimated hop utilization, the color correction, and even malt and adjunct extract and color data inputs.
      Return to Overview

      REFERENCES

      (1) F. Eckhardt, The Essentials of Beer Style (Fred Eckhardt Associates/All Brewers Information Service, Portland, Oregon, 1989).

      (2) M. Jackson, The New World Guide to Beer (Running Press, Philadelphia, Pennsylvania, 1987).

      (3) Zymurgy 14 (4), Traditional Beer Styles Special Issue (1991).

      (4) G. Bauer, "The Influences of Raw Materials on the Production of All Grain Beers," Zymurgy 8 (4), 9-13 (1985).

      (5) G. Noonan, Brewing Lager Beer (Brewers Publications, Boulder, Colorado, 1986), p. 179.

      (6) J. Rager, "Calculating Hop Bitterness in Beer," Zymurgy 13 (4), 53-54 (1990).

      (7) G. Fix and L. Fix, Vienna, Marzen, Oktoberfest, Classic Beer Style Series (Brewers Publications, Boulder, Colorado, 1991), pp. 87-92.

      (8) P. Rajotte, Belgian Ale, Classic Beer Styles Series (Brewers Publications, Boulder, Colorado, 1992), p. 121.

      (9) M. Manning, "Understanding Specific Gravity and Extract," BrewingTechniques 1 (3), 30-35 (1993).

  • Issue 2.1 Table Of Contents
    [Home]  [BrewingTechniques Library]  [Contact Us]  [Order]