# Appendix B Baker's percentages.

Why are baker's percentages important for the baker?

* Consistency in production

* Ease of calculating the absorption rate of the flour

* Simple increase or decrease in dough size using the same formula

* Ease in comparing formulas

* Ability to check if a formula is well-balanced

* Ability to correct defects in the formula

What are the important characteristics of baker's percentages?

* Baker's percentages are always based on the total weight of the all the flour in the formula.

* Flour is always represented by the value of 100 percent (i.e., all other ingredients are calculated in relationship to the flour). If more than one type of flour is in the formula, the sum of the flour is 100 percent.

* Baker's percentages can only be calculated if the amount of all the ingredients in the formula is expressed in the same unit of measure; for example, you cannot mix grams and ounces, or pounds and kilograms, in the same formula.

* Units of measure must be expressed in terms of weight, not volume (e.g., you cannot mix pounds and quarts in the same formula). Additionally, weights given in pounds and ounces cannot easily be calculated with baker's percents. The easiest system of measurement with baker's percentages is the metric system. The US decimal system may also be used.

* Baker's percentages work best with the metric system because metrics are based on units of 10, as are percentages (e.g., 100 = 10 x 10).

Percentage Basics
```  0.01 = 1%   0.1 = 10%
1/100 = 1%   10/100 = 10%
1/100  = 1%   10/100 = 10%
```

* If the percentage is greater than 100, the number is larger than the number that represents 100 percent.

* If the percentage is less than 100, the number is less than the number that represents 100 percent.

Math Basics

a/b = a/b (23 x a = b) = (a = b / 23) = (a = b/23)

Typical Formula Calculations Using Baker's Percentages

Example 1: From Weight to Baker's Percentages

In this example, we have a formula, and we want to express the amounts of the ingredients in baker's percentages.
```Flour :     50 kg
Water :     30 kg
Salt  :      1 kg
Yeast :   0.75 kg
```

Step 1. Determine the baker's percentage for the flour. We know that flour is always 100%. In this formula, 50 kg = 100%.

Step 2. Determine the baker's percentage for the water. We need to calculate what percentage the weight of the water is in relation to the weight of the flour. Another way to state this calculation is: How many parts of water would be needed to achieve the same hydration ratio if there were 100 parts of flour?

Two calculation methods are possible.

Calculation Method 1: Cross Multiplication

Using this method, crossed lines are drawn.
```Flour : 50 kg x 100%
Water : 30 kg x W
(W = the percentage of water we want to find)
```

The necessary calculation can be expressed as an equation, following the crossed lines, beginning with the flour:

50 x W = 30 x 100

Applying math basics to isolate the unknown variable:

W = (30 x 100) / 50

W = 60

In this formula, the baker's percentage for the water is 60 percent (i.e., the weight of the water represents 60 percent of the weight of the flour).

Calculation Method 2: Fractions

Using this method, the necessary calculation can be expressed as a fraction with the weight of the water on top and the weight of the flour on the bottom:

W = 30/50

Applying math basics, we know that

W = 30/50=30 / 50 = 0.6 = 60%

Step 3. Determine the baker's percenages for the yeast and salt using one of the two calculation methods described in Step 2. Two calculation methods are possible.
```Calculation Method 1: Cross Multiplication

Flour :   50 kg   100%
Water :   30 kg   60%
Salt  :    1 kg   S
Flour :   50 kg   100%
Water :   30 kg   60%
Yeast : 0.75 kg   Y
```

Expressed as equations:
```50 x S = 1 x 100
S = (1 x 100) / 50
S = 2
50 x Y = 0.75 x 100
Y = (0.75 x 100) / 50
Y = 1.5
```

Calculation Method 2: Fractions
```S = 1/50 = 1 / 50 = 0.02 = 2%
Y = 0.75/50 = 0.75 / 50  = 0.015 = 1.5%
```

The complete formula with baker's percentages:
```Flour :     50 kg   100%
Water :     30 kg   60%
Salt  :      1 kg   2%
Yeast :   0.75 kg   1.5%
```

Example 2: From Baker's Percentages to Weight

In this example, we have the baker's percentages, we want to make a dough using 40 kg of flour, and we want to express the formula in quantities for each of the ingredients.
```Flour :   100%
Water :   65%
Salt  :   2%
Yeast :   1%
```

Remember that flour is always 100 percent and that other amounts are calculated in relationship to flour.
```Flour = 100% = 40 kg
Water = 65%  = 40 x 0.65 = 26 kg
Salt  = 2%   = 40 x 0.02 = 0.8 kg = 800 g
Yeast = 1%   = 40 x 0.01 = 0.4 kg = 400 g
```

The complete formula with baker's percentages:
```Flour :   40 kg 100%
Water :   26 kg 65%
Salt  :   800 g 2%
Yeast :   400 g 1%
```

Example 3: From Baker's Percentages to Weights Using Desired Production Quantity

In this example, we have a production order to fill:
```50 baguettes @ 350 g of dough
40 balls @ 400 g of dough
300 rolls @  80 g of dough
```

All these breads will be made from the same dough. The baker's percentages for the formula are
```Flour : 100%
Water : 67%
Salt  : 2%
Yeast : 1%
```

We want to express the formula in quantities for each of the ingredients.

Step 1. Determine the total amount of dough needed:
```50 x 350 g  = 17,500 g = 17.5 kg
40 x 400 g  = 16,000 g = 16 kg
300 x 80 g  = 24,000 g = 24 kg
```

Total Dough = 57,500 g = 57.5 kg

Step 2. Determine the amount of flour needed. The baker's percentages for all the ingredients in this formula total 170 percent. Here is another way to state this is: We know that with 100 parts of flour, we can produce 170 parts of dough. We need to calculate the amount of flour needed to make 57.5 kg of dough.

Two calculation methods are possible.

Calculation Method 1: Cross Multiplication
```Flour : 100% F
Water : 67%
Salt  : 2%
Yeast : 1%
Total : 170% 57.5 kg
```

Expressed as an equation:
```100 x 57.5 = 170 x F

F = (100 x 57.5) / 170

F = 33.82
```

Calculation Method 2: Fractions

First, we need to calculate what proportion of the total dough in the formula is represented by the flour. The necessary calculation can be expressed as a fraction with the baker's percentage of the flour on top and the total of baker's percentages on the bottom:

F% = 100/170 = 100 / 170 = 0.5882 = 58.82%

We now know that 58.82 percent of the total dough in the formula is flour. Now we need to calculate the weight of the flour for the quantity of total dough we need to make.

F = 57.5 kg x 58.82% = 57.5 kg x 0.5882 = 33.82 kg

Now we know that 33.82 kg of flour will be necessary to obtain 57.5 kg of dough.

To simplify the rest of the calculations and to make sure we will produce enough dough, we will round up the amount of flour to the next whole number: 33.82 kg will become 34 kg. However, we only round up the weight of the flour; we do not round up the weights of the other ingredients.

Step 3. We must apply the baker's percentages of the formula to the weight of the flour to determine the desired weights of the remaining ingredients:
```Flour = 100% = 34 kg
Water = 67%  = 34 X 0.67 = 22.78 kg
Salt  = 2%   = 34 X 0.02 =  0.68 kg = 680 g
Yeast = 1%   = 34 X 0.01 =  0.34 kg = 340 g
```

To verify our calculations, if we total the weights of all the ingredients, we should find the amount of dough needed to accommodate this order:
```Flour :  34 kg      100%
Water :  22.78 kg    67%
Salt  :  680 g        2%
Yeast :  340 g        1%
Total :   57.8 kg
```

With 57.5 kg of dough needed, this formula will produce 57.8 kg of dough. We have a small amount of extra dough because we rounded up the amount of flour.

Using Baker's Percentages with Preferments

When using preferments, the principles of baker's percentage stay the same. However, because a preferment is a preparation made from a portion of a formula's total flour, water, yeast, and sometimes salt, and because the proportion of those ingredients in the preferment may differ from the proportion in the total formula, additional calculations are often necessary.

Example 1: From Formula for Total Dough to Formulas for Preferment and Final Dough

In this example, we have a formula, with baker's percentages. We want to make the dough using 20 percent of the flour in a preferment (sponge).
```Flour :    10 kg  100%
Water :   6.7 kg  67%
Salt  :    200 g  2%
Yeast :    150 g  1.5%
```

For this example, the baker's percentage for the water in the sponge will be 64 percent, and the baker's percentage for the yeast will be 0.1%. The sponge will contain no salt.

Step 1. Determine the weight of the flour to use in the preferment.

10 kg x 20% = 10 kg x 0.2 = 2 kg

Step 2. Determine the weight of the water and the yeast to use in the preferment.
```Water = 64%  = 2 kg x 0.64  = 1.28 kg
Yeast = 0.1% = 2 kg x 0.001 = 0.002 kg = 2 g
```

If the preferment contained salt, the weight of the salt would be determined in the same way.

The complete formula for the preferment, with baker's percents, is
```Flour :    2 kg   100%
Water : 1.28 kg   64%
Yeast :    2 g    0.1%
```

Step 3. Determine the weight of the ingredients in the final dough. We need to subtract the quantity of each ingredient used in the preferment from the quantity in the total formula.
```Flour =  10 kg - 2kg     =    8 kg
Water = 6.7 kg - 1.28 kg = 5.42 kg
Salt  =   200g - 0       =   200 g
Yeast =   150g - 2g      =   148 g
```

The formula for the final dough is
```Flour :    8 kg
Water : 5.42 kg
Salt  :   200 g
Yeast :   148 g
```

Step 4. Determine the baker's percentages for all the ingredients in the final dough. We know that flour is always 100 percent. Baker's percentages for all the other ingredients are calculated using the cross multiplication or fractions method.

Two calculation methods are possible.

Calculation Method 1: Cross Multiplication
```Water

8 x W = 5.42 x 100
W = (5.42 X 100) / 8
W = 67.75

Salt

8 x S = 0.2 x 100
S = (0.2 X 100) / 8
S = 2.5

Yeast

8 x Y = 0.148 x 100
Y = (0.148 X 100) / 8
Y = 1.85

Sponge

8 x P = 3.282 x 100
P = (3.282 x 100) / 8
P = 41.02
```

Calculation Method 2: Fractions
```W = 5.42/8  = 5.42 / 8  = 0.6775 = 67.75%
S = 0.2/8   = 0.2 / 8   = 0.025  = 2.5%
Y = 0.148/8 = 0.148 / 8 = 0.0185 = 1.85%
P = 3.282/8 = 3.282 / 8 = 4102   = 41.02%
```

The complete formula with baker's percents:
```Flour     :     8 kg   100%
Water     :  5.42 kg   67.75%
Salt      :    200 g   2.5%
Yeast     :    148 g   1.85%
Preferment: 3.282 kg  41.02%
```

Note: For a poolish preferment, the weight of the water is determined in Step 1 (usually 1/3 or 1/2). The weight of the flour in the poolish is always equal to weight of the water. Therefore, the baker's percentage for the water in the preferment is 100 percent.

Example 2: From Baker's Percentages forTotal Dough and Preferment to Formula for Final Dough Using Desired Production Quantity

In this example, we have a production order to fill for which we need 40 kg of sourdough dough. This method is important for scheduling production using sourdough so enough can be on hand for all production needs.

We know the baker's percentages for the total dough. We already have a sufficient quantity of the levain that was prepared according to a formula with known baker's percentages, and we want to incorporate this levain into the final dough in the ratio of 50 percent in relation to the weight of the flour in the final dough.

The formula for the total dough is
```Flour : 100%
Water : 67%
Salt  : 2%
```

The formula for the preparation of the levain is
```Flour   : 100%
Water   : 50%
Culture : 150%
```

Note: In this example, the number of feedings of the culture is not important, but we will assume that the same formula has been used for all the feedings.

Step 1. Determine the baker's percentages for the final dough. Starting with the flour, we know that flour is always 100 percent.

To calculate the correct amount of water and salt in the final dough, we must consider that the flour in the levain will be added to the final dough. For 100 parts of flour in the final dough, there are 50 parts of levain. We must calculate how much of those 50 parts is flour.

Two calculation methods are possible.

Calculation Method 1: Cross Multiplication
```Flour : 100% F
Water : 50%  W
Total : 150% 50 parts
```

Expressed as an equation:
```F x 150 = 50 x 100
F = (50 x 100) / 150
F = 33.33
```

Calculation Method 2: Fractions

First, we need to calculate what proportion of the 150 parts is represented by the flour:

F = 100/150 = 100 / 150 = 0.6667 = 66.67%

We now know that 66.67 percent of the 50 parts is flour. Now we need to calculate the number of parts.

F = 50 parts x 66.67% = 50 parts x 0.6667 = 33.33 parts

Now we know that we must take into consideration 133.33 parts of flour when we calculate the amount of water and salt in the final dough.

The total amount of water in the final dough will be

133.33 parts x 67% = 89.33 parts

We must consider that the water in the levain will be added to the final dough. Because we know that 33.33 parts of the 50 parts of levain are flour, the number of parts that are water is

50 parts - 33.33 parts = 16.67 parts

The number of parts of water in the final dough is

89.33 parts - 16.67 parts = 72.66 parts

The baker's percentage for the water in the final dough is 72.66 percent.

The total amount of salt in the final dough will be

133.33 parts x 2% = 2.67 parts

There is no salt in the levain, so the baker's percentage for the salt in the final dough is 2.67 percent.

The baker's percentages for the final dough are
```Flour  : 100%
Water  : 72.66%
Salt   : 2.67%
Levain : 50%
```

Step 2. Determine the weight of the flour in the final mix to make 40 kg of total dough.

Two calculation methods are possible.

Calculation Method 1: Cross Multiplication
```Flour  : F       100%
Water  : W       72.66%
Salt   : S       2.67%
Levain : L       50%
Total  : 40 kg   225.33%
```

Expressed as an equation:
```F x 225.33 = 400 x 100
F = (40 x 100) / 225.33
F = 17.75
```

Calculation Method 2: Fractions

First, we need to calculate what proportion of the total dough is represented by the flour. The necessary calculation can be expressed as a fraction with the baker's percentage of the flour on top and the total of baker's percentages on the bottom:

F% = 100/225.33 = 100 / 225.33 = 4438 = 44.38%

We now know that 44.38 percent of the total dough is flour. Now we need to calculate the weight of the flour.

F = 40 kg x 44.38% = 40 kg x 0.4438 = 17.75

Now we know that 17.75 kg of flour will be necessary to obtain 40 kg of dough.

To simplify the rest of the calculations and to make sure we will produce enough dough, we will round up the amount of flour to the next whole number: 17.75 kg will become 18 kg. However, we only round up the weight of the flour; we do not round up the weights of the other ingredients.

Step 3. We must apply the baker's percentages of the formula to the weight of the flour to determine the desired weights of the remaining ingredients:
```Flour  = 100%     =    18 kg
Water  = 72.66%   =    18 x 0.7266   =     13 kg
Salt   = 2.67%    =    18 x 0.0267   =   0.48 kg
Levain = 50%      =    18 x 0.5      =      9 kg
```

To verify our calculations, if we total the weights of all the ingredients, we should find the amount of dough needed to accommodate this order:
```Flour  :    18 kg   100%
Water  :    13 kg   72.66%
Salt   :    480 g   2.67%
Levain :     9 kg   50%
Total  : 40.48 kg   225.33%
```

With 40 kg of dough needed, this formula will produce 40.48 kg of dough. We have a small amount of extra dough because we rounded up the amount of flour.
Author: Printer friendly Cite/link Email Feedback Suas, Michel Advanced Bread and Pastry Appendix Jan 1, 2009 2886 Appendix A Conversions. Appendix C Temperature conversions. Bakery additives Measurement conversion