Baker's Math: A tutorial
In October, 2008 I posted a formula for Greenstein's Jewish Sour Rye which converted his recipe, which was written in volume measurements, to ingredient weights. I have made this bread many times since, but I've never bothered to calculate the baker's percentages for the formula. I decided to do so today and thought I would post the procedures as a tutorial on “baker's math” for new baker's and others who have just never gotten comfortable with this very valuable tool.
Here is the formula I wrote in 2008.
Ingredients  Wt (g) 
First Clear flour  500 
Water (80199ºF)  240 
Sea salt  12 
Ripe rye sour (100% hydration)  750 
Instant yeast  7 
Altus (optional)  1/2 cup 
Caraway seeds  1 T 
Cornmeal for dusting parchment 

Cornstarch glaze 

Converting the formula to baker's math
Baker's math is a method of expressing the quantity of all ingredients, always expressed as weights, as a proportion of the total flour in the formula. This provides a way of comparing formulas and of easily converting them to make a larger or smaller batch of dough. By convention, the total flour is always 100%. If your formula uses more than one type of flour, their total is 100%. So, to use a simple baguettetype dough as an example, the formula might be:
Ingredients  Baker's % 
AP flour  100 
Water  65 
Salt  2 
Instant yeast  1 
Total  168 
Note that the total is over 100%. This is confusing to many initially. Get used to it. This total baker's percentage is an important number, as you will soon see. Again, this formula does not tell you how much of any ingredient to use, so far, only their proportionate amounts. In fact, knowing these proportions gives you all the information you need to make any amount of dough you need for a bake, whether its 500 g or 100 kg.
We have the ingredient amounts for a “batch” of Greenstein's rye bread, and we want to calculate the baker's percentages, so we can make a bigger (or smaller) batch of dough than the original recipe produces.
This bread uses a rye sour – a rye sourdough starter. When working with a preferment like a poolish or a rye sour, there are two ways of representing it in baker's math. One is to treat it a distinct ingredient, like water or salt. The other is to break the preferment down into its flour and water content and add the flour to the total flour and the water to the total water in the formula. These two approaches are equally accurate, but the second approach provides the more accurate representation of the dough characteristics, especially in regard to hydration. In the following table, I have used the second approach.
The rye sour is 100% hydration. That means that the amount of water in it is exactly equal to the amount of water (water = 100% of total flour.) So, 750 g of rye sour consists of 375 g of rye flour and 375 g of water. Therefore, for example, the total water in the dough consists of the 375 g from the rye sour plus the 240 g added to the final dough.
Total Ingredients  Wt (g)  Calculations  Baker's % 
First Clear flour  500  Total flour =500+375=875. 500/875=57.  57 
Rye flour  375  Total flour =500+375=875. 375/875=43.  43 
Water (80100ºF)  615  Water/Total flour=615/875=70  70 
Sea salt  12  Salt/Total flour=12/875=1.4  1.4 
Instant yeast  7  Yeast/Total flour=7/875=0.8  0.8 
Total  1509 
 172.2 
Now we can see that the original recipe makes 1509 g of dough. (Well, it is actually more because the weight of the caraway seeds and altus, if used, is not included in these calculations.) Adding up the Baker's percentages, you have 172.2. Think of this as meaning that the dough consists of 172.2 “parts,” 100 of which is flour, 70 of which is water, etc. Recall that these numbers represent the relative amounts of each ingredient.
Scaling the recipe
Now, let us assume you want to make Greenstein's Jewish Sour Rye, but you want to make 600 g loaves, and you want to make two of them. So you will need 1200 g of dough.
Since you know your formula consists of 172.2 parts, to determine the weight of each ingredient needed to make 1200 g of dough, what you need for your calculations is the weight of each part. If the total is 1200 g, you get this by dividing 1200 g by 172.2 parts. This equals 6.97, rounded off. This number is called “the conversion factor.” Now we can calculate the amounts of each ingredient in 1200 g of dough. Weights are rounded to the nearest gram.
Total Ingredients  Baker's %  Calculations  Wt (g) 
First Clear flour  57  57x6.97=397  397 
Rye flour  43  43x6.97=300  300 
Water (80100ºF)  70  70.6.97=488  488 
Sea salt  1.4  1.4x6.97=10  10 
Instant yeast  0.8  0.8x6.97=6  6 
Total  172.2 
 1201 
What this way of representing the formula does not show is how much rye sour you have to build. However, we know from the original recipe that the weight of the rye sour is 1.5 times the weight of the First Clear flour (See the first table, above.) So, for the 1200 g of dough, we will need 1.5x397=595 g of Rye Sour. In the bread books written for professionals, for example, Hamelman's Bread and Suas' Advanced Bread and Pastry, the formulas have separate tables for “Total Dough” which takes the second approach described above and another for “Final Dough” which takes the first approach. You get the best of both worlds. The “Final Dough” would be as follows:
Final dough ingredients  Wt (g)  Baker's % 
First Clear flour  397  100 
Water (80199ºF)  191  48 
Sea salt  10  2.4 
Ripe rye sour (100% hydration)  596  150 
Instant yeast  6  1.4 
Total  1200 

Altus (optional)  1/2 cup 

Caraway seeds  1 T 

Cornmeal for dusting parchment 


Cornstarch glaze 


You can see that, while this representation of the formula is more helpful for making the final dough, the Baker's Percentages distort the ingredient proportions. They make the dough look like it has a lower hydration than it really does, and it makes the amounts of salt and yeast seem very high.
Baker's math is an invaluable tool. Once you understand the basic approach and scale a few of your favorite recipes, it becomes easy to use. After a while, if you use it regularly, it becomes intuitive. You will find yourself doing it in your head as you look at new recipes. You can use it for modifying recipes you want to tweak. It will make you a better baker. It is not yet known if it prevents senile dementia, but I bet it helps. I'll let you know, if I remember to.
Enjoy!
David