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
Comments
that although I become a total formula dweeb  and I've been baking a long time  my sincere wish is that on the first day I started to bake  that someone had taught me baker's math. I spent years and years thinking  "there must be a system to this recipe thing"  and there was  it just wasn't widely available to the home baker.
I know that math can be somewhat intimidating to some folks, but it really cleared up some mysteries for me.
And David,
Have you checked out the BBGA site, yet?? :>)
Pat
Hi David,
I really like what you presented here...I simply panicked when I thought that perhaps I have been doing my calculations wrong...my mistake as I now realize with all of the help I received here...My confusion began with the 'cf' that you presented. Brings up the issue of baking terminology. Not only are there many ways to do things, there are also many words used to label the same thing... There have been many discussions here, as you well know, on what to call a leaven for instance  starter, chief, mother, biga to name but a few...
When I first discovered TFL all of those terms really confused me because I was searching for THE CORRECT TERM.....left over remnant thinking from my school days and final exams....What I have found is that no standardization for baking terms exist that I am aware of and I like that now since I have sorted a lot of it out. Each term tells a story about how it was created in the first place. Like a geography and history lesson all rolled into one.
Your tutorial now gives people who discover this site a solid starting place from which to begin to piece all of this stuff together. Your explanations do describe the principles and, as we have seen above, they have generated a lively discussion out of which someone new can learn a lot  especially that there are indeed many ways to get the same final results. When I first found TFL I had to hunt all over this site for threads containing glimpses and pieces of this information and it generally wasn't the key topic to begin with. I can't even recall in which discussion I got my initial info. about using %'s but I do recall it was contributed here by Andy (Ananda).
One of the primary reasons I joined TFL was for these discussions. Trying to locate info. in a cook book had only left me with more questions than I had to begin with and I had no way to contact authors in order to get those questions answered. This site, and blogs such as yours, has answered most of my questions as well as generating an entire new set of questions. What I have learned here in a relatively short time would have taken me years on my own. To all who contribute here I am infinitely indebted :)
Your other tutorials, with their clarity of words and photos, have helped me out a lot. I can't shape a boule without the image of your toothpicks coming into my mind :)
In closing I would like to add my thanks for all you have presented here. I should have thanked you in the beginning but my panic overcame my manners :/ Now that my panic has subsided I see my grievous mistake in not thanking you in the first place....
I look forward to more of your tutorials whatever they may include as well as the discussions I am sure they will generate :)
Take Care and
THANKS AGAIN :)
Janet
I appreciate your kind words.
Your experience on TFL is such a perfect example of what I was referring to in my comment above regarding TFL's "mission."
David
Coming soon.
There are many ways to skin a cat. But what is a "cat."
Thanks, David. I learned something from this discussion: I understand baker's math enough to use it, but not enough to explain it.
Glenn
It depends on whether you follow Aristotle, Hume or Berkeley. Me? I follow Kipling: "I am the cat, and I walk alone ..."
Eagerly awaiting your tutorial on Baker's Metaphysics, but I'll settle for your pecan rolls.
David
I don't follow Aristotle or Hume. I don't follow Berkeley, though I went to his school for a few years.
If I follow anyone, it'd be Edmund Husserl. A cat can be nothing more or less than one's experience of a cat, more or less.
Pecan rolls are much easier than metaphysics.
Glenn
Schrödinger's Kitty
Just don't open the box and I should be fine.

If not, what about Herr Cheshire Kitty from Alice in Wonderland? (Purple and pink? I'd have to be prepetually intoxicated to pull that off.)
If a ferret were about to dart up your dress, I'd run, too. But first, I'd rescue the ferret. ;)
David
...Simon Cowell voted me off American Idol.
The English and their intolerance for variance must not be tolerated.
Be intolerant of the intolerance!
</1,3,7trimethylxanthine>
If we follow the template from BBGA then the "seed" for building the sourdough starter is included as part of the final formula...here is an example from the BBGA template for a sourdough bread...note that the 0.259 kg of sourdough starter ("seed") is carried over into the final dough formula.In contrast, J. Hamelman in Bread does *not* include the weight of the "seed" in the final dough formula.I prefer Hamelman's approach, as it reminds the baker to *reserve* a portion of the sourdough starter for future breads and does *not* include that reserved portion in the final formula.What's your opinion about this discrepancy between the BBGA standard and Hamelman's standard? Eager to know!
I wrote to the BBGA asking if more had been published on their format:
http://www.thefreshloaf.com/node/28499/bbgaformat2009latestversion
Their response:
I was hoping the answer would be "yes", as there are several questions the BBGA format doesn't answer, like yours.

The reason I like love the BBGA format over other formats is because the math is selfchecking. If total formula = 1000 grams, then preferment(s), soaker(s), final dough, etc. must add up to 1000, not 1100, not 1248. If it doesn't add up, there's a math mistake.
There are drawbacks:
Knowing those drawbacks (and I bet there are plenty more that are not addressed by the BBGA, like "starter composition" (mine is 1:2:4, yours is 1:2:2)), my opinion is still that the formula should be representative in toto, no more or less than the whole of the bread being made, and input(s) should balance output(s).
This doesn't void Jeffery Hamelman's process. (I wouldn't dare!)
They can overlap:
The BBGA formula includes BBGA process, and I think that's where starter perpetuation belongs. That's where you can say "In our bakery, we like to reserve a portion of the final dough to perpetuate the next, but you may have an alternate method. If you choose our method, consider making 11 quantities instead of 10, reserving the 11th for starter perpetuation." This way, the rigidty of the formula is preserved, but you can say something like: "Just make 11 instead of 10 and hold 1 back. You have all the math you need to vary quantity up or down to fit your process."
[And I know what you're thinking: "You can use math for an overage. Just treat it like a deduction and subtract it. There's such a thing as depreciation in accounting! That would preserve the balance and allows you to include it in the formula itself." I have no response to this but Ewwwwwwww!]
All that said, I have less than 9 weeks of baker's math/BBGA format behind me (not including a decade of baking from recipes), so my opinion should carry all the weight of a floppy baguette.

Update. Proth (I think it was proth) mentioned the importance of efficiency as it is judged in professional competition. Any amount of waste or overage results in points being deducted. These competitions come down to gram, so your formula had better be in toto, not 10 grams, not +20 grams.
I looked at Hamelman's formula again.
I can see how it would be advantageous in a production environment: measuring the final dough ingredients automatically leaves behind .6 lbs of mature culture, which is then used to perpetuate the process.
I still find it irritating (is that the word?) that the TOTAL FORMULA isn't. It's missing .6 lbs of stuff (mature culture) that's added and then taken away by the method. It's like offbalance sheet accounting. :)
I don't know if the BBGA format would/should accommodate a carryover process like in Hamelman's Vermont Sourdough.
My understanding is the total formula should be in balance. No carryover.
Am I wrong? Anyone? Anyone? Bueller? Bueller?
If it is allowed, this is a guess on how it would/should work:
DIFFERENCE.
HAMELMAN format: The mature culture is not listed as an ingredient of the OVERALL FORMULA. It appears almost like a phantom ingredient in the LIQUID LEVAIN BUILD stage. Also, a portion of the mature culture is not used in the FINAL DOUGH, so there's a .3 kg discrepancy. Where'd it go? Why is it not used? And how does the math magically balance with it missing?
BBGA format: The mature culture is listed as an ingredient of TOTAL FORMULA. You see where it's used in the LIQUID LEVAIN BUILD and you see the residual .3 kg kept as reserve. Whether it belongs in the FINAL DOUGH column, its own column, or at all is up for debate. I suspect the BBGA would say it shouldn't be part of the formula at all.
FILES.
The spreadsheet in Excel 2007 format.
We are in territories here where the words "angels", "dancing", and "head of pin" suggest themselves. :>)
But notice also that the BBGA standard does not concern itself with the hydration of the seed.
This is one of the simplifying assumptions that I mentioned.
So is the inclusion of the seed in the final dough  which frankly many bakers do anyway. I admire the steel nerves of anyone who on a busy (production) baking day will trust that they will remember to remove seed from their pre ferment so as not to bake off their 200 year old sourdough culture. I do not have the stomach for it.
If you put the seed in the final dough  the BBGA standard gives you your exact dough weight  so no troubles there.
In point of fact, these small amounts do not matter  they are not mathematically "perfect" but we are not doing pure math here  we're making product.
The standard is solid as it is  but nothing is perect  it may evolve  but its purpose is for production bakers  not mathematicians.
For those of you who really want to improve the standard, you are going to need to join the BBGA, build up your credentials (by maybe doing some formula checking) and work with the folks who revise the standards. Remember these are mostly people with day jobs and not day jobs in the field of mathematics  in baking.
Hope this helps.
Pat
I was just trying to contrast it with Hamelman's method, which I don't like (for the same reason you mention: I'd forget to remove the seed (ok, I don't like the "off balance sheet" math either! Reminds me of Enron and Jeffrey Skilling's Pancake Recipe.)).
 just sayin' that if you really want to get involved in this  there is a path.
I've tried the whole "accounting for every detail" and while it is interesting to someone who enjoys doing the math  the current standard makes reasonable simplifying assumptions.
Remember that a book is written at a point in time and that time and understanding move on, but the book usually doesn't get changed. It really is no big thing. I've got some recipe cards from the 30's and 40's that were written for professional bakers and the baker's math is just a bubble off from the current methods. Life moves on.
But they can have my Marchant calculator when they pry it from my cold, dead, hand :>)
Pat
So Pat,
Do you have an original Marchant's or one made after Smith Corona took over the company?
In any event, how did your get your live warm hands on one in the first place?
Janet
I left my Marchant in the attic of my first house  so it has passed from my hands, unfortunately. I was less responsible in those days, but dinosaurs were roaming the Earth and sometimes you had to pack light. Left a dress form, too. Wish I had them both.
But I got my hands on my (former) Marchant when I worked at the Youngstown Sheet and Tube Company. I actually used it on the job.
I still have my mechanical stopwatch, though  Old 101  my official job title was "Time Study Man"  yep.
I am that old...
Pat
Pat,
I would be rich if I had kept my hands on just a few of the things I have left behind....
Live and learn. Glad to hear that you were able to recover though :) Gives me hope that I may be able too to someday!
Janet
A Marchant calculator?
You really are Jeanne Louise Calment's sister, aren't you?
Ja, ja, I know. Join the guild. Alas, my anticapitalist sentiments object to being charged for joining any movement. The movement must be of the people! Blood, sweat, tears, and obstinacy (and maybe 100 wpm keystrokes!) alone the cost.
Then again, maybe just a Visa check card.
I've just bought a new set of electronic scales which has a bakers percent button.
Weigh out the flour, say 1,000 gr then hit the percent button. From then on it weighs everything as a percentage of the weight of flour until you reset it. The tare function still works with percentages.
It is a My Weigh KD8000, not cheap, but I hope it will be worth it. It has the usual lb (decimal), lb & oz, oz, gr and kg modes.
An amusing aside  in a recent episode of CSI shown in the UK, the pathologist was weighing a brain and the scales he was using were the KD7000, exactly the same scale without the percent button.
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