# A Practial Method for Grist Formulation and Scaling

Posted Jan 20th 2014 | By:

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**Introduction **

The hobby has come a long way since the I started brewing all-grain beer in the early nineties. While not unheard of, it was very rare for an amateur brewer to jump straight into all-grain brewing at that point in time. Almost every new amateur brewer started out as a can-based kit brewer. From there, he/she usually transitioned to extract plus steeped specialty grain brewing using recipes out of books. Many amateur brewers never transitioned beyond this point before abandoning the hobby.

At some point after brewing his/her kit beer, an adventurous brewer attempted partial-mash brewing, usually using standard kitchenware and a Zapap lauter tun. This approach to brewing was driven primarily by the layout of what was considered to be the amateur brewer's bible; namely *The Complete Joy of Homebrewing*. However, the fact that amateur-scale all-grain brewing equipment had to be fabricated played a large roll in the step-wise progression from kit to all-grain brewing. The Internet had not yet been commercialized, which meant that a brewer had to source stainless steel fittings and commercial-grade stockpots through trade-oriented supply channels that often did not sell to retail customers.

With that said, brewers who took the "old school" route to all-grain brewing often built up a sizable portfolio of extract and/or partial-mash recipes that needed to be converted to all-grain recipes. A fundamental concept that is learned while formulating recipes that include dry or liquid malt extract is points per pound per gallon; therefore, it was natural for brewers who took this path to continue to use points per pound per gallon after making the transition to all-grain. Those who jump into all-grain recipe formulation with the aid of brewing software often do not learn this concept or only see it as intermediate unit of measure that is used while calculating table-based extraction efficiencies. However, points per pound per gallon is powerful concept that can simplify the formulation and scaling of all-grain recipes. This article focuses on a practical application of points per pound per gallon in an all-grain brew house. The method that is outlined in this article will completely eliminate the need to use brewing software to calculate and/or scale recipe grists.

**Incorporating Points Per Pound Per Gallon**

In order to use points per pound per gallon effectively, a brewer needs to establish the average extraction rate for his/her brew house. This process starts by calculating the points per pound per gallon values for batches of wort that one has made in the past using the following equation.

points_per_pound_per_gallon = (batch_original_gravity - 1.0) x 1,000 x batch_volume_in_gallons / batch_grist_mass_in_pounds

In practice, the (batch_original_gravity - 1.0) x 1,000 subexpression can be simplified by taking the original gravity reading, lopping off the "1," and converting the number to the right of the decimal point to a whole number (e.g., 1.056 becomes 56).

Using a 5.5-gallon batch of 1.056 wort that was made with 11 pounds of grist to put the equation into practice yields:

batch_original_gravity = 1.056

batch_volume_in_gallons = 5.5

batch_grist_mass_in_pounds = 11

points_per_pound_per_gallon = (1.056 - 1.0) x 1,000 x 5.5 / 11 = 28

Now, if we perform this calculation for several batches, sum the points per pound per gallon values, and divide by the number of batches that were summed, we will arrive at our average brew house extraction rate in points per pound per gallon.

Batch #1 = 26.5 points per pound per gallon

Batch #2 = 27 points per pound per gallon

Batch #3 = 30.5 points per pound per gallon

Batch #4 = 28 points per pound per gallon

Batch #5 = 29 points per pound per gallon

average_points_per_pound_per_gallon = (26.5 + 27 + 30.5 + 28 + 29) / 5 = 28.2

In practice, the only time that a brewer should experience the large variance in values shown above is when he/she is working with a new brew house or purchasing grain one batch at a time. A brewer who is looking for predictable batch-to-batch results should purchase his/her base malt in bulk.

With that said, it is important to use a sliding sample point window that is weighted towards the most recent batches, so that variations in extract potential are tracked accurately. The maximum extract that can be obtained from any given malted grain can change from season to season, malting to malting, and even bag to bag.

**Putting Points Per Gallon Gallon Into Practice**

Let's put the average brew house extraction rate calculated above into practice using a hypothetical 11-gallon recipe that we would like to adjust for our 5.5-gallon primary volume brew house.

A Simple Pale Ale

batch_original_gravity = 1.064

batch_volume_in_gallons = 11

batch_grist_mass_in_pounds = 23

Grist Composition

British Pale Malt: 20.75 pounds

60L Crystal Malt: 2.25 pounds

Calculating the recipe points per pound per gallon extraction rate yields :

recipe_points_per_pound_per_gallon = (1.064 - 1.0) x 1,000 x 11 / 23 = 30.6

If we compare the recipe's extraction rate to ours, we will clearly see that we cannot just cut the recipe in half; therefore, we need to scale the grist to fit our brew house extraction rate. We can handle scaling two different ways. The easiest and most logical way is to calculate the amount of grist that we will need to hit the recipe's original gravity (O.G.) in our brew house, and then divide this mass into grist percentages that are proportional to those found in the original recipe.

Calculating how many pounds of grist that we need to hit 1.064 yields:

batch_grist_mass_in_pounds = (batch_original_gravity - 1.0) x 1,000 x batch_volume_in_gallons / average_points_per_pound_per_gallon

batch_grist_mass_in_pounds = (1.064 - 1.0) x 1,000 x 5.5 / 28.2 ~= 12.5lbs

With that calculation complete, we need to calculate grist percentages from the original recipe.

recipe_total_grist_mass = 23lbs

recipe_british_pale_ale_percentage = 20.75 / 23 x 100 ~= 90%

recipe_60L_crystal_percentage = 2.25 / 23 x 100 ~= 10%

With these numbers, we can now formulate our grist.

Our Simple Pale Ale

batch_original_gravity = 1.064

batch_volume_in_gallons = 5.5

batch_grist_mass_in_pounds = 12.5

British Pale Malt: 12.5 x 0.9 = 11.25lbs (11.25 is 90% of 12.5)

60L Crystal Malt: 12.5 x 0.1 = 1.25lbs (1.25 is 10% of 12.5)

The second way to adjust a recipe based on one's brew house extraction rate is to calculate a grist scaling factor that takes into account the differences in brew house extraction rates and a batch volume divisor that takes into account the differences in batch volumes.

grist_scaling_factor = recipe_extraction_rate / our_average_extraction_rate

grist_scaling_factor = 30.6 / 28.2 ~= 1.085

batch_volume_divisor = recipe_batch_volume / our_batch_volume

batch_volume_divisor = 11 / 5.5 = 2

brew_house_extraction_rate_adjusted_malt_mass = malt_mass x grist_scaling_factor / batch_volume_divisor

Our Simple Pale Ale

batch_original_gravity = 1.064

batch_volume_in_gallons = 5.5

batch_grist_mass_in_pounds = 23 x 1.085 / 2 ~= 12.5

British Pale Malt: 20.75 x 1.085 / 2 ~= 11.25

60L Crystal Malt: 2.25 x 1.085 / 2 ~= 1.25

(note: the symbol "~=" denotes approximately equal to)

Over a period of time, a brewer will more than likely begin to cluster brew house extraction rates into groups based on the percentage of base malt used in the grist, which will lead to even more accurate average points per pound per gallon extraction rates. For example, I have a cluster known as the 90/10 group. This group contains recipes in which 90% of the extract is derived from base malt with the remaining 10% of the extract being derived from specialty malts and/or adjuncts. If one examines the grain ratios found in the most common pale ale recipes, one will discover that most fall into the 90/10 group +/- a few percentage points. Another popular cluster is the 80/20 group. While there are outliers such as wheat beer recipes, these two groups encompass a large percentage of recipes in use today.

**The Metric System**

The system that I outlined above works with the metric system. When using the metric system, a brewer works in points per kilogram per liter using the equations shown below.

points_per_kilogram_per_liter = (batch_original_gravity - 1.0) x 1,000 x batch_volume_in_liters / batch_grist_mass_in_kilograms

batch_grist_mass_in_kilograms = (batch_original_gravity - 1.0) x 1,000 x batch_volume_in_liters / average_points_per_kilogram_per_liter

points_per_pound_per_gallon_to_points_per_kilogram_per_liter = points_per_point_per_gallons x 8.35

points_per_kilogram_per_liter_to_points_per_pound_per_gallon_ = points_per_kilogram_per_liter / 8.35

While I am comfortable working with English and metric units of measure, I prefer to formulate recipes using English units of measure. In my humble opinion, points per pound per gallon is more intuitive because it is a non-concentrated unit of measure. If I want to formulate a beer with an original gravity of 1.056, and my brew house extraction rate is 28 points per pound, then I know that I need to use two pounds of grain for every gallon of wort that I want to produce. Points per kilogram per liter is not nearly as tidy.

**Concluding Remarks **

Points per pound per gallon is a powerful unit of measure that is rarely used directly by modern all-grain amateur brewers. Modern amateur brewers tend to prefer to use software for grist formulation and scaling. However, I guarantee that brewers who put the method outlined in this article into practice will find that they rely on software far less than they did before adopting it.

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