# Top-down Brew: Recipe Calculator Technical Information

An old legal saying is that the devil is in the details. If details are important to you, the following technical information explains some of the inner workings and assumptions that the recipe calculators are based upon.

For the mash, the calculator begins by determining the total number of gravity points that are needed for a particular batch. (If gravity points are unfamiliar to you please check out this explanation from Brad Smith, the creator of BeerSmith software.) The next step is to use the percentage of each malt type from the user input to determine the gravity points that are needed for each grain type. The final step for each grain is to determine the weight that will be needed to achieve the desired gravity points.

Here is an example to illustrate how it works. Let's say that we want to produce 5 gallons of wort at a specific gravity of 1.050. The total gravity points for this beer will be 5 (gallons) * 50 (gravity points; from 1.050) for 250 total gravity points.

The next step is to determine the percentages that compose the wort. The simple recipe for this example will be for a wort that is 5% medium crystal malt and the rest (95%) will be two-row base malt. For 5% of the wort, we will need to get 12.5 gravity points of crystal malt (250 gravity points * .05 percent as a decimal = 12.5 gravity points of crystal malt). These gravity points are the first part of the weight formula that will go in the numerator.

To determine the corresponding crystal malt weight it will be necessary to know our mash efficiency and the theoretical gravity points from our grains. This will be the denominator of the weight formula. For this example we will use a mash efficiency of 75%, which is a good estimate for mashes that use batch sparging, and a value of 1.034 for the specific gravity of crystal malt. Multiplying the possible gravity points (34) by efficiency (.75) gives us 25.5. In other words, we can get 25.5 gravity points from each pound of crystal malt in our system. This part forms the denominator of our overall formula.

To complete the calculation, we need to divide the crystal malt gravity points that we need (12.5) by the amount that we can get from a pound of malt (25.5). Doing this step yields 12.5/25.5 = .490 lbs. Rounded off, we will need 1/2 lb of crystal malt for our recipe.

In summary:

[5 (gallons) * 50 (gravity points) * .05 (crystal malt percentage)] / [ 34 (crystal malt gravity points) * .75 (mash efficiency)] = approximately .5 lb crystal malt

Let's do the base malt now using the same kind of math:

[5 (gallons) * 50 (gravity points) * .95 (base malt percentage)] / [ 37 (base malt gravity points) * .75 (mash efficiency)] = approximately 8.5 lbs of two-row malt

The calculator is careful to distinguish between the differences in efficiency for malts vs. sugars or malt extracts. The calculator adjusts the theoretical gravity points for each grain by the mash efficiency, as shown in the above example. For sugars and malt extracts, the efficiency is calculated at 100%.

An important part of the mash assumptions is that the percentages that the user enters are the percentages of the gravity points in the final wort composition. This is reasonable because from a top-down viewpoint what we really care about the most is the percentages in the final wort, not the weights of the ingredients going into the wort. The weights are simply a means to obtaining the percentages that we want in the overall wort.

The use of percent by gravity point raises a minor but important cautionary note. Calculating the percentages for the wort may not be the same as calculating malt percentages by weight. The reason for this is that some malts vary significantly in regard to their extract potential. For example, the potential yield from two-row malt is 1.037 but the yield from roasted barley is only about 1.025. Some stout recipes call for 10% roasted barley by weight. If we factor in the lower yield of roasted barley, a 10% by weight corresponds to about 6% of the gravity points in the final wort. The practical implication is that entering 10% (percent by weight) into the present calculator (which uses percent by gravity points) might result in excessive amounts of roasted barley. The user needs to be aware that percent by weight and percent of gravity points are similar but are not exactly equal in some circumstances due to the gravity differences between malts. This difference is usually not a huge concern because the differences are typically small at the homebrew level. The differences between percent by weight and percent by wort composition are most likely to occur for roasted malts (low extract potential - 1.025 for roasted barley is much lower than 1.037 for base malts) and various sugars (high extract - sucrose is 1.046, much higher than base malt).

A similar approach is used to determine the hop weights that are needed for the late hop additions. The calculations begin with the user entering the overall target of IBUs for the recipe. If desired, the later aroma or flavor hop additions can be declared as a percentage of total IBUs. The percentage of IBUs needed for each of the multiple hop additions is then calculated to determine the necessary weights. The weights needed for the late hop additions are determined first, then the remaining IBUs are used to determine the weights needed for the bittering hop additions. This approach of calculating the late IBUs first and the bittering IBUs last is recommended by Ray Daniels in Designing Great Beers.

For example, a pale ale recipe might call for 40 IBUs total with 30% of the IBUs to come from a single late hop addition to the boil at zero minutes. This means that 40 * .3 = 12 IBUs must come from the late hop addition. These 12 IBUs are used to determine the amount of hops needed at zero minutes to achieve 12 IBUs. The remaining 28 IBUs for the bittering hop additions are then calculated to determine the weight needed for the bittering hop addition.

There are a number of assumptions that influence the calculation of IBU utilization. The boiling gravity change during the time course of the boil is somewhat crudely estimated by subtracting 1.001 from the target specific gravity for each 10 minutes of the boil. The IBU calculations for the bittering and flavor hop additions are based upon the Tinseth formula for hop utilization. The Tinseth formula is somewhat conservative given that it was developed for whole hops. This formula will work well for most situations but when brewing with fresh, pelletized hops it might be necessary to decrease the weights by about 10%.

A significant limitation of the Tinseth formula is that it does not calculate hop utilization for aroma hop additions added at zero minutes. This is problematic for hop stands and other approaches to obtaining hop flavor from hops added at the end of the boil. New evidence shows that hop bitterness is extracted as long as the wort temperature stays above 170F. The Tinseth limitation is addressed by estimating the hop utilization of aroma hops (defined as less than 5 minutes of boil time) to be 5%. This 5% value for late hop utilization is based upon a recent study of bitterness from aroma and steeped hops, which found that the utilization of steeped hops was consistently about 4% to 5% under a variety of post-boil time and temperature conditions.

The yeast pitching rates are based upon recommendations made by the largest yeast producing companies. The dry pitching rate is based upon Lallemand/Danstar's recommendation of .5 to 1.0 g/L, with 1.0 g/L being recommended for beers over 16 degrees Plato (about 1.066 SG; Lallemand catalog, 2017, p. 18; personal communication). The liquid yeast pitching rate is based on Wyeast's recommendations: 6 million cells/mL for less than 15 plato (approximately 1.060 SG), 12 million / ml for 15 to 19 plato (approximately 1.060 to 1.076 SG), and 18 million/ml for 19 to 25 plato (approximately 1.076 to 1.100 SG). Lager yeast are pitched at approximately double the ale rates. Lager pitching rates are also based on the recommendations made by the yeast manufacturing companies.

The recommendations made by Lallemand/Danstar and Wyeast are similar to the recommendations made by other manufacturers but there are some slight differences. If you're interested, you can explore the pitching rate from other yeast products with the yeast pitch rate calculator.

Some readers might be asking why a common standard of .75 or 1 million cells * milliliters of wort * degrees plato isn't being used to determine the pitching rate. This commonly cited standard in homebrewing literature is meant for repitching yeast that is harvested from commercial fermenters (White and Zainasheff, 2010, p. 122). My direct correspondence with Lallemand/Danstar has informed me that the repitching standards used by commercial brewers are not appropriate for their products. A fresh, vital yeast culture simply needs a lower pitching rate than the commercial repitching formula suggests. Please see the yeast pitch rate calculator for additional information and calculations for other yeast producers.

The default values for the malt specific gravities and the hop alpha acids are mostly from the BYO.com resources pages, such as the grains and adjuncts chart page and the hops chart page. If the resource guide gives a range of values, such as 5 to 6% alpha acids, the default value is an average of the high and low values (5.5%). In a few cases, values have been obtained from homebrewing books, like Beer Captured, or from other web sites.

Some checks have been built into the software. For example, if the specialty grain percentages are over 100% it will produce an error message. Although a few checks are present, the software relies to a large degree on your own expertise and good judgment. Putting extreme values into the calculations might yield some odd recipes. There is no software solution for inputs that are unusual or misguided. It is important to use good brewing judgment. The style recommendations resource is provided to give some guidance for several beer styles. Start with these recommendations if you are a new brewer that needs help with deciding on appropriate values.

It is important to acknowledge the limitations of the present calculator. The program has been deliberately kept simple to make it easy to use. Some of the simplicity is also due to the limitations of a web-based computation. An infinite number of choices for grains and hops is simply not feasible. Likewise, complex late hopping schedules may be beyond the capability of this software. There will be no cloud storage options or other fancy features due to my limited budget, lack of free time, and amateur-level programming expertise.

If you have remaining questions, please feel free to contact the author of this web site.

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