## Recipe formulation is really quite easy. Compiled in Table 1 is a list of various types of malt along with their respective predicted extracts and colors. Note that the extract values given in this table assume an extraction efficiency of 100%. Of course, your mileage may vary. In fact, your extract efficiency should be considerably less than this ideal case. Such high efficiencies require grinding the grist extremely fine which results in not only the extraction of sugars but also the extraction of tannins and other undesirable substances. Generally speaking, most homebrewers have extraction efficiencies of around 60-80%. Extraction efficiency plays an integral role in recipe formulation; knowledge of this efficiency can allow one to determine the amount of malt required to produce a wort of a given target gravity.

## Once you have brewed with a particular mash/sparge system for awhile you will find that there is a typical extraction efficiency for your system. There will be some variation in efficiency values but in the fullness of time these should eventually average out and a typical efficiency value with come to light. However, if you are new to all grain brewing then you, of course, do not know the typical extraction efficiency of your system. In your case, assuming a value of about 70% is a good starting point. After you have brewed once you can then compute your extraction efficiency and use that value the next time you brew.

## Of course, knowing your extraction efficiency is only part of the equation. The predicted extract of the malt, given in units of gravity per pound per gallon, is also required. The average extract values for various types of malt are given in Table 1. The following equation is employed to estimate a recipe's original gravity:

Equation (1):

## OG

## =

## (M1*X1 + M2*X2 + M3*X3 +...)*E

_____________________________

V## where OG is the estimated original gravity, M1, M2, M3... are the amounts of malts used in pounds, X1, X2, X3... are the corresponding predicted extracts of M1, M2, M3...repectively, E is the estimated extraction efficiency, and V is the final volume of the wort in gallons. Note that for ease of use the values of X1, X2, X3...used in the above equation correspond to the final two digits of the extract values shown in Table 1. For example, for American two-row (1.037) the value used in the equation would be 37.

## The simplest means of showing how one formulates a recipe is through example. There is, of course, software that can be used to formulate recipes. These programs can make life easier for the homebrewer but it is also good to know what the software is doing. Of course, you have heard this sort of thing countless times in high school mathematics classes but this time it happens to be true. In the next section (following Table 1) I will walk you through an example of how to formulate a simple all grain recipe.

TABLE 1*

Malt/Grain

Extract

Color

Pale Malts## American two-row

## 1.037

## 1.8

## American six-row

## 1.035

## 1.8

## Belgian two-row

## 1.037

## 3.0

## British two-row

## 1.038

## 2.5

## Canadian two-row

## 1.036

## 2.1

## British Pilsner

## 1.036

## 1.8

## German Pilsner

## 1.038

## 1.6

## Belgian Pilsner

## 1.037

## 1.8

## British Lager (two-row)

## 1.038

## 1.4

## Lager malt (two-row)

## 1.035

## 1.7

## Lager malt (six-row)

## 1.031

## 1.7

Other Malts## American Wheat

## 1.038

## 2.0

## American soft white Wheat

## 1.040

## 2.8

## Belgian Wheat

## 1.038

## 1.8

## German Wheat

## 1.039

## 1.8

## German Dark Wheat

## 1.039

## 8.0

## American Rye

## 1.030

## 3.5

Specialty Malts - Light## Sauer (acid)

## 1.035

## 1.5

## American Vienna

## 1.035

## 4.0

## German Vienna

## 1.037

## 3.0

## British Mild

## 1.037

## 4.0

## German smoked (Bamberg)

## 1.037

## 9.0

## British Peated

## 1.038

## 5.0

## Scottish Peated

## 1.038

## 5.0

Specialty Malts - Dark## American Victory

## 1.034

## 25.0

## British Brown

## 1.032

## 70.0

## Belgian Biscuit

## 1.035

## 24.0

## Belgian Aromatic

## 1.036

## 25.0

## British Amber

## 1.032

## 35.0

## Canadian Honey

## 1.030

## 18.0

## American two-row (toasted)

## 1.033

## 30.0

## American Special Roast

## 1.033

## 40.0

## Melanoidin

## 1.033

## 35.0

## Belgian Munich

## 1.038

## 7.8

## German Munich

## 1.037

## 8.0

## American Munich (Light)

## 1.033

## 10.0

## American Munich (Dark)

## 1.033

## 20.0

## Canadian Munich (Light)

## 1.034

## 15.0

## Canadian Munich (Dark)

## 1.034

## 30.0

## British Munich

## 1.037

## 6.0

Specialty Malts - Caramelized## Dextrin malt (CaraPils)

## 1.033

## 1.8

## Belgian Caramel Pils

## 1.034

## 7.9

## British CaraMalt

## 1.035

## 12.0

## American Crystal 10 °L

## 1.035

## 10.0

## American Crystal 20 °L

## 1.035

## 20.0

## American Crystal 30 °L

## 1.035

## 30.0

## American Crystal 40 °L

## 1.034

## 40.0

## American Crystal 60 °L

## 1.034

## 60.0

## American Crystal 80 °L

## 1.034

## 80.0

## American Crystal 90 °L

## 1.033

## 90.0

## American Crystal 120 °L

## 1.033

## 120.0

## British Light Carastan

## 1.035

## 15.0

## British Carastan

## 1.035

## 34.0

## British Crystal 50-60 °L

## 1.034

## 55.0

## British Crystal 70-80 °L

## 1.034

## 75.0

## British Crystal 95-115°L

## 1.033

## 105.0

## British Crystal 135-165°L

## 1.033

## 150.0

## German Carahell

## 1.034

## 12.0

## German Light Caramel

## 1.037

## 2.5

## German Dark Caramel

## 1.037

## 65.0

## German Wheat Caramel

## 1.038

## 55.0

## Belgian CaraVienne

## 1.034

## 22.0

## Belgian CaraMunich

## 1.033

## 75.0

## Belgian Special "B"

## 1.030

## 220.0

Specialty Malts - Roasted## American Chocolate

## 1.029

## 350.0

## Belgian Chocolate

## 1.030

## 500.0

## British Chocolate

## 1.034

## 475.0

## German Carafa

## 1.030

## 400.0

## German Carafa Special

## 1.030

## 600.0

## American Black Patent

## 1.028

## 500.0

## British Black Patent

## 1.027

## 525.0

## Belgian Black

## 1.030

## 600.0

Unmalted Grains## Flaked Barley

## 1.032

## 2.2

## Flaked Corn

## 1.040

## 0.5

## Flaked Oats

## 1.033

## 2.2

## Flaked Rice

## 1.040

## 0.5

## Flaked Rye

## 1.036

## 2.8

## Flaked Wheat

## 1.032

## 2.0

Unmalted Grains - Roasted## American Roasted Barley

## 1.028

## 450.0

## American Black Barley

## 1.027

## 530.0

## Belgian Roasted Barley

## 1.030

## 575.0

## British Roasted Barley

## 1.029

## 575.0

## German Roasted Wheat

## 1.030

## 650.0

## Roasted Rye

## 1.029

## 500.0

## German Carafa Chocolate

## 1.030

## 525.0

*The values appearing in Table 1 were taken from Gudmestad and Taylor (1995). Extract and Color are in units of specific gravity per pound of malt per gallon of wort and °Lovibond per pound of malt per gallon of wort respectively. Note that, as with most things, there is a range of possible values for both extract and color. The values given above are mean values.

Formulating an Example Recipe:## In this example, we are brewing 5-gallons of an American Pale Ale. The original gravity of this style should be 1.045-1.060. Assuming we are a novice all grain brewers we will use an extraction efficiency of 70% and we will shoot for a target gravity in the middle of the accepted range (i.e. O.G. = 1.053). Targeting the midpoint in the accepted gravity range is good practice when just starting out so as to allow for relatively large deviations from the assumed efficiency. American Pale Ales are generally not particularly diverse in terms of the malt bill. For our example we will use only American two-row malt (Extract = 1.037) and 60 °L American crystal malt (Extract = 1.034). Equation (1) is shown again below:

## OG

## =

## (M1*X1 + M2*X2 + M3*X3 +...)*E

_____________________________

V## Generally speaking, when one formulates a recipe the amount of the specialty grains (e.g. crystal malt, chocolate malt, etc.) and the target gravity are decided upon prior to doing a single calculation. These values can, therefore, be treated as constants. One can then algebraically solve for the amount of base malt (e.g. two-row, six-row, etc.) required to produce the desired gravity with an assumed extraction efficiency. The equation for this is as follows:

Equation (2):

## M1

## =

## OG*V

____

X1*E## -

## (M2*X2 + M3*X3 +...)

________________

X1## Since most recipes tend to use less than a pound of crystal malt, I decided to use 0.5 pounds of crystal malt in our example recipe. Only M1, the amount of two-row malt required to bring the gravity up to 1.053, is not known. All of the other values are now known. OG is 53.0, V is 5.0 gallons, E is 70%, M2 is 0.5 lbs of crystal malt, and X2 is 34. Substituting these values into the equation above:

## M1

## =

## 53.00*5.00

__________

37.00*0.70## -

## 0.50*34.00

__________

37.00## =

## 9.77

## Therefore, a recipe for 5-gallons of wort which includes 0.5 lbs of 60 °L American crystal malt and 9.77 lbs of two-row malted barley with a 70% extract efficiency will produce a wort with an original gravity of 1.053.

## Of course, there is more to recipe formulation than merely using these equations. There is also researching the style one is brewing. In the examples given here I selected straight forward styles. Whenever brewing a style new to you it is essential to do some research to determine what malts, hops and perhaps other ingredients are appropriate.

Extraction Efficiency Computation:## Once you have brewed an all grain batch you can compute a value for your extraction efficiency. For a given recip, the ratio of the predicted original gravities to the corresponding extraction efficiencies is equal which can be shown as:

## OG1

___

E1

## OG2

___

E2

## OG3...

______

E3...

## =

## =

## where OG1 is the original gravity resulting from extraction efficiency E1, OG2 is the original gravity resulting from extraction efficiency E2 etc. Note that carrying out this division yields the original gravity of the ideal case in which there is a 100% efficiency.

## The inverse of the above ratios are also equal and this fact can be used to determine the extraction efficiency. This equation is shown below:

## E1

___

OG1

## E

(obs)

_______

OG(obs)

## =

## where are OG1 is the original gravity computed with an assumed efficiency of E1, and OG

(obs)is the original gravity measured following a brewing session. E(obs)is the corresponding extraction efficiency which is not known. Solving the above equation for E(obs) one arrives at the following expression:

Equation (3):

## E

(obs)

## E1

*OG(obs)

__________

OG1

## =

## Let us say that in the above example we produced an American Pale Ale with an original gravity of 1.050 instead of the predicted value of 1.053 assuming a 70% efficiency. Plugging plugging these values into Equation (3):

## E

(obs)

## 0.70

*50

_______

53

## 0.66

## =

## =

## we find that in our example an original gravity of 1.050 is the result of an extraction efficiency of 66%.

Using Non-mashed Fermentables:## Recipes often do not call for just the use of malted barley and the other ingredients appearing in Table 1, but rather also employ malt extracts, corn sugar, honey and other fermentables. Extract values for some of these additional fermentables are given in Table 2. Note that 100% of the extract of these fermentables goes into the wort. Therefore, when formulating a recipe an extraction efficiency need not be applied to the fermentables listing in Table 2. For recipes using both malted barley plus non-mashed fermentables the equation to estimate the original gravity becomes:

Equation (4A):

## OG

## =

## (M1*X1 + M2*X2 + M3*X3 +...)*E + (F1*

X1+ F2*X2+ F3*X3 +...)

___________________________________________________________

V## where M1, M2, M3..., X1, X2, X3..., E and V are as before and F1, F2, F3... are the amounts of the non-mashed fermentables and

X1,X2,X3... are the corresponding extract values for F1, F2, F3....In the following section an example of such a recipe calculation will be given.

TABLE 2**

Non-mashed Fermentables

Extract## Belgian Candy Sugar

## 1.036

## Cane Sugar

## 1.046

## Corn Sugar

## 1.037

## Honey

## 1.030-1.035

## Malt Extract (Dry)

## 1.045

## Malt Extract (Liquid)

## 1.037-1.039

## Maple Sap

## 1.009

## Maple Syrup

## 1.030

## Molasses

## 1.036

## Rice Extract

## 1.034

**The values appearing in Table 2 were taken from Papazian (1994) and Daniels (1996). The Extract is in units of specific gravity per pound of fermentable per gallon of wort. Note that "non-mashed fermentables" refers to the fact that the brewers need not mash these ingredients when using them. The malt extracts, are, of course, the products of mashing.

Recipe Formulation Using Malt and Non-mashed Fermentables:## Equation (4A) can be rewritten in a more that is more useful for our purposes which is shown below:

Equation (4B):

## OG

## =

## (M1*X1 + M2*X2 + M3*X3...)*E

_____________________________

V## +

## (F1*

X1+ F2*X2+ F3*X3 +...)

_______________________

V## which can be thought of basically as:

## OG

## =

## M

## +

## F

## where M is the expression in Equation (4B) to the left of the plus sign and F is to the right of it. Generally speaking, when formulating recipes in which malt plus the non-mashed fermentables are used, the amount of either M or F in the above equation is decided upon before hand and one must compute the amount of the remaining variable required to produce the desired original gravity.

## In our first example, let use assume we are once again brewing 5-gallons of an American Pale Ale with an original gravity of 1.053 and a 70% extraction efficiency. Let us also assume we are using 0.5 lbs of 60 °L American crystal malt (Extract = 1.034). The difference this time is that we are using 3lbs of honey as well. The extract for honey will be assumed to be the midpoint of the range or 1.033 per pound per gallon.

## The first step would be to compute the contribution of the honey (F) in the above equation:

## F

## =

## (3 lbs of honey)*33

__________________

5-gallons## =

## 19.8

## M, therefore, must produce a gravity of 53.0-19.8 or 33.2. Equation (2) can then be used with this value to determine the required amount of two-row.

Equation (2):

## M1

## =

## OG

(new)*V

_________

X1*E## -

## (M2*X2 + M3*X3...)

________________

X1## where OG

(new)is the required gravity contribution of just the malted barley. Substitute values in Equation (2):

## M1

## =

## 33.2*5.0

_______

37.0*0.70## -

## (0.5*34.0)

________

37## =

## 5.95

## Therefore, using 5.95 lbs of two-row malted barley, 0.5 lbs of 60 °L American crystal malt and 3 lbs of honey in a 5-gallon batch will yield an original gravity of 1.053. Assuming a 70% extraction efficiency, of course.

## In our next example, we will start with the our original American Pale Ale recipe for 5-gallons (i.e. 9.77 lbs of two-row and 0.5 lbs of 60 °L American crystal malt with an original gravity of 1.053 and assuming an efficiency of 70%) and add sufficient dry malt extract to brew an Imperial IPA which has a gravity range of 1.075-1.090. Our target gravity in this case will be 1.083.

## In this example, the value of M in the simplified version of Equation (4B) would be 53. The dry malt extract will, thus need to produce a gravity of 83-53 or 30.

## After the contribution of the malted barley is removed the new equation for the required amount of non-mashed fermentables is given by the equation:

## OG

(new)## =

## (F1*

X1+ F2*X2+ F3*X3 +...)

_________________________

V## Solving for F1 the equation becomes:

Equation (5):

## F1

## =

## OG

(new)*V - (F2*X2 + F3*X3 +...)

_________________________

X1## where OG

(new)is the required gravity contribution from just the non-mashed fermentables. The other parameters are as before. Substituting our values (there are no values in this example for F2, F3...) and solving for F1 were get:

## F1

## =

## 30.0*5.0

_______

45.0## =

## 3.3

## Therefore, using 3.3 lbs of dry malt extract along with 9.77 lbs of two-row and 0.5 lbs of 60 °L American crystal malt will produce an original gravity of 1.083.

Extraction Efficiency Computation - Using Malt and Other Fermentables:## Determing the extraction efficiency in this case is carried out much the same way as before. However, one must first remove the contribution of the non-mashed fermentables from the resultant gravity. For example, if our Imperial IPA had a gravity of 1.087 then we would first remove the contribution of the dry malt extract from this value. In this example, the contribution was 30.0. Therefore, the gravity value that would be used in the efficiency calculation would be 87-30 or 57.0. After this then it is a simple matter of using Equation (3) to determine the observed extraction efficiency.

Equation (3):

## E

(obs)

## E1

*OG(obs)

__________

OG1

## =

## Substituting in our values and solving for E

(obs):

## E

(obs)

## 0.70

*57.0

__________

53.0

## 0.75

## =

## =

## Therefore, in this example we had a 75% extraction efficiency.

_{ }

_{ }References:

Daniels R, (1996), Designing Great Beers: Brewers Publications, Boulder, CO. 390 pp._{}

_{ }Gudmestad, N. C. and R. J. Taylor (1995), Malt: A Spectrum of Colors and Flavors,Zymurgy, Vol. 18, No. 4, p. 8-14._{}

_{ }Papazian, C.N. (1994), The Home Brewer's Companion: Avon Books, New York, NY, 446 pp.

## Should you have any questions or comment please e-mail Scott Stihler at stihlerunits@mosquitobytes.com.