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baker's math

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dmsnyder's picture
dmsnyder

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 (80-199ºF)

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 baguette-type 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 pre-ferment 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 pre-ferment 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 (80-100ºF)

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 (80-100ºF)

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 (80-199ºF)

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

MIchael_O's picture

Recipes Understood, Converted, and Screened

August 17, 2010 - 11:23pm -- MIchael_O

In response to hearing people ask recipe-related questions I have created a


chart that graphs all baked goods (cookies, cakes, muffins, etc) using three numbers. The chart is easy to understand There is some math behind it so I automated everything with a web application called Caked-Face Menace.

mlucas's picture

Calculating Final Dough Hydration from Baker's Percentages

April 27, 2010 - 6:55am -- mlucas

When baking with any type of starter/levain/biga, it seems pretty important to know the final dough hydration of a recipe, as that is a much better way to gauge the feel of the dough than just the base hydration. (especially when a large amount of starter is used)


Of course, if the hydration of the starter matches the hydration of the dough recipe, there's no need to calculate. But usually this is not the case...

dmsnyder's picture

Need help with baker's math in spreadsheet!

February 4, 2010 - 11:16pm -- dmsnyder

I am building a spreadsheet to help me develop formulas for breads. I'm gaining a much better understanding of baker's math in this process. However, I am getting some discrepancies in my calculations that I just can't seem to understand. I'm looking for help.


As an exercise, I'm working with a dough with the following parameters:



 

flournwater's picture

Bread Dough Formula Math Dilemma (Some Help, I Hope)

December 29, 2009 - 12:57pm -- flournwater
Forums: 

From time to time I read posts with questions like this:


"I want to use 435 grams of starter at 70% hydration in a bread dough formula that calls for 500 grams of flour at 60% hydration.  How do I figure out how much flour and water I need to add in order to meet that requirement?"


Here's a primer that should alleviate the headache you might normally experience trying to figure it out.

Doc Tracy's picture

Confused about the math-

December 19, 2009 - 12:52am -- Doc Tracy
Forums: 

Ok, so I'm pretty good at math. I had to get by to get through graduate and medical school. But, I'm seeing recipes with 448.5% of total ingredients? How does that work? Also, how do you figure out the hydration of your starter? What is the difference between a levain and starter as far as the percentage in hydration? Can I convert a starter to a levain? How do I figure the amount of water/ flour used by my starter or levain when making a recipe if the recipe is not properly done with percentages?

cafe-moi's picture

Question on relationship of bulk ferment and final proof times especially in slow breads

April 12, 2009 - 8:24pm -- cafe-moi
Forums: 

Are there any "rules of thumb" for the ratio/relationship of bulk fermentation time to final proofing times? 


For fast, straight doughs, I've generally found that the amount of time needed for the final proof is about half as long as for the initial bulk fermentation.  Now that I'm experimenting with the "yeast and time equation" to convert recipes to slow ripened ones, I'm beginning to wonder about this relationship.  If I convert a recipe to a 12 hour bulk fermentation, does that mean that I should plan on a 6 hour final proof? 

Uberkermit's picture

Bread formula utility for Excel

June 27, 2007 - 7:34am -- Uberkermit
Forums: 

I put together an Excel workbook for working with bread formulas. Although there are other similar tools on this site, this one has some nice additional features. Let's say you have a formula for a sourdough bread, but you want to make a couple changes. First, you want to add 10% spelt flour, you want to up the hydration from 65% to 68%, change the salt form 1.8 to 2%, reduce the dough yield from 3.5 pounds to 3.0 pounds, and increase the percent of pre-fermented flour from 15-20%.

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