My ideal bread—the bread I want to have for breakfast every morning, around my sandwiches at lunch, and to sop up the remains of whatever sauce adorned my dinner—is a crisp-crusted, chewy, open-crumbed bread, flecked with bran. This is the kind of bread perfect with a slice of cheese, some large-grained cured sausage and a big swig of coarse red wine to wash it all down. Rustic bread.

The concept is one thing, the creation of this imagined bread is another. Recipes from cookbooks have their virtues, but ultimately none has been totally satisfactory. Over the past year, I’ve tried to understand the techniques underlying the recipes, to manipulate the variables and create a bread that lives up to my ideal. I experimented with hydration percentages, finding that a wet — but not too wet — dough helped to create the open structure I was after. Next, I tested delayed fermentation to see what effect it had on my breadmaking. Lately I’ve been thinking about how I was mixing the stuff: kneading.

Never impervious to trends, I went through a no-knead phase. The results of the various no-knead recipes I tried (my favorite was Cook’s Illustrated’s No-Knead Bread 2.0) were always very consistent, and actually pretty close to what I was after: big open crumb, slightly sour flavor, crackly brown crust. That was all well and good, but I couldn’t shake the feeling that I was turning into little more than a bread machine: mix the given amounts of flour, water, salt and yeast, let them rest and bake for the prescribed amount of time, and then poof! bread. It was a good bread but not one over which I felt much ownership of or had any control over. Using the no-knead method, breadmaking felt more magic than craft.

Having rejected not-kneading, I went on a kneading binge. No bread passing through my oven would be kneaded any less than ten minutes, vigorously and by hand. I settled on this method mostly as a sentimental reaction against no-knead — good bread was something you worked for, dammit — but I also had a somewhat technical justification: the repeated working of the dough was helping to create a strong gluten framework that would support the airy internal structure I was after. And sometimes, it did. But I also found that often my kneaded bread would be very fine-textured, lacking the big holes that make me think “good bread.” Rereading Harold McGee’s On Food and Cooking to research delayed fermentation, I came across an explanation for what was happening in my kneaded bread:

Kneading also aerates the dough. As it’s repeatedly folded over and compressed, pockets of air are trapped and squeezed into smaller, more numerous pockets. The more pockets formed during kneading, the finer the texture of the final bread. Most of the air pockets are incorporated as the dough reaches its maximum stiffness. (538)

All my diligent kneading may have been making strong gluten strands, but it was also crushing and dividing the tiny gas pockets that explode in the oven into my sought-after holes.

I needed a third way: a technique by which I could strengthen and bond long gluten chains while seeding the dough with large gas pockets. The answer was stretch & fold, a technique which I had first encountered as a way of dealing with extremely wet doughs, but only began to consider seriously as a general technique after reading and baking Samuel Fromartz’s baguette recipe. In stretch and fold, after dough is initially mixed it is allowed to rest for ten minutes. Then, using a bench scraper, the baker stretches the dough into a long strand in one direction before folding it in half over itself. The stretch and fold is repeated in the other three directions (check out this video!). The dough is then rested half an hour before being stretched again. I suppose this process could be repeated indefinitely, but I usually stretch and fold the dough four times over an hour and a half. After the final fold the dough can rest overnight in the refrigerator (I just can’t give up on delayed fermentation) and it is ready to shape, proof and bake.

Stretch and fold has given me impressive results and I have been tempted to say that it is the technique for achieving the bread I am after. But there had been times when I felt the same way about no-knead, and ten minute kneaded dough — those techniques had just fallen out of favor with me lately. To ensure that stretch and fold really was something different (and better) I conducted a head-to-head-to-head kneading technique breadoff.

I started by preparing a 3# batch of 68% hydration dough using:

• 6 oz wild-yeast starter (100% hydration)
• 16 3/8 oz water
• 23 5/8 oz white all purpose flour
• 2 oz whole rye flour
• 1 T sea salt
• 2 t instant yeast

Immediately after mixing to form a shaggy ball, I divided the dough into three 1# balls. One was placed immediately in a plastic bag and left to rest on the counter: this was the no-knead bread. Another I left in the mixing bowl to rest ten minutes (ample resting seems crucial to the stretch and fold technique). I spent that ten minute resting time kneading the third ball of dough, using no additional flour so as to keep the recipes constant.

After kneading I placed the dough in a bag next to the no-knead dough. Because the stretch and fold technique requires the dough sit at room temperature for close to two hours as it rests between stretchings, I left the other two bags on the counter as well so all three dough balls would have the same chance at yeast activity. I followed the procedure as I described above. At the end of the stretching/resting period, all the doughs looked similar, although the kneaded and no-knead doughs appeared more voluminous than the stretch and fold, probably due to their extended rest.

All three bags spent the night in the refrigerator.

Although three 1# dough balls will fit in my oven at the same time, it’s a tight fit and the breads close to the edges of oven tend to burn and grow towards the center. For optimal results, I needed to bake each bread in roughly the same place in my oven: the center of the stone. I couldn’t just pull out every dough ball out of the refrigerator to proof and then bake one at a time. That would give the third-baked far more time to proof than the first. Instead, I staggered the breads, proofing each bread for one hour in a proofing basket then scoring it once down the center and baking for 25 minutes in a 450°F oven with a preheated steam pan bearing 1 cup of room temperature water. True, this meant that the third dough ball would spend more time in the refrigerator than the first and second, but because the cold temperature means nothing happens very quickly, I thought the influence would be negligible. All the breads were baked within two hours.

The first bread I baked was the no-knead, followed by the kneaded bread, ending with the stretch and fold.

As I pulled the breads out of the oven, I was surprised by the extent of the differences. Where the no-knead bread was roughly cracked and browned, giving a very rustic, rough appearance, the outside of the kneaded bread was smooth and uniform.

The stretch and fold bread was similar in appearance to the no-knead but almost a half-inch taller.

The different external appearances were a sign of unique internal structures. The interior of the no-knead bread was familiar: haphazard large holes here and there, largely concentrated on the edges.

The kneaded bread, I was surprised to see, had much larger holes, although it also had large areas of uniform, fine texture. The large air pockets were possibly the result of my technique of forming a loaf; tucking the edges of the dough under it might have trapped large air pockets that were maintained by the strong gluten network.

The stretch and fold bread seemed like a combination of the other two. Although its structure was similar to the no-knead bread, the holes were larger and more evenly distributed. Of the three, here was the closest to the crumb structure I imagined for this style of bread.

But bread was not meant to be looked at; it should be eaten! Would my different techniques result in dramatically different flavors? Although I have been told that mouthfeel (texture) influences perceived flavor, I can say that these differently textured breads tasted essentially the same. All the breads were chewy and substantial, with a deep flavor of grain. I thought that I noticed the crust of the kneaded bread was slightly more chewy and less crispy than that of the other two, but after a few more bites I couldn’t be sure. The stretched and folded bread had slightly more fermented flavors than the other two. Overall, though, once the bread was in my mouth I couldn’t notice a major difference. A blind tasting panel, a more sophisticated palate, or a battery of chemical and mechanical tests would all have helped to better discern the differences. As far as I’m concerned, it was all pretty good.

Looking over the three slices, stretch and fold is the best technique for making rustic bread. Both other techniques yielded good enough breads, but neither could compete with the open crumb and lofty structure of the stretched and folded dough. In some ways, this is also the most involved technique: no-knead bread is over almost before it starts, and kneaded bread takes just ten minutes of intense activity. The act of stretching and folding is not particularly time consuming, but the dough does require attention every half hour for a couple of hours. You can’t just walk away from it. Maybe the technique’s appeal comes back to the sentimental: after working with stretched and folded bread over the course of an afternoon, it feels like I actually did something.

Do It Green! Annual Green Gifts Fair

• Saturday, November 21st, 2009
• 10am to 5pm
• Midtown Global Market in Minneapolis on Lake St. & Chicago. Ave.
• FREE entrance (vendors accepting cash or check only, though, so come prepared!)

Do It Green! Minnesota’s Green Gifts Fair takes place this Saturday, conveniently before the crazed post-Thanksgiving shopping. Organizers envision the event as an introduction to green giving and low impact ideas to celebrate the holidays with over 70 vendors to explore. Shoppers are encouraged to bring their own bags and coffee mugs. If you plan to eat at Midtown while you shop, consider bringing silverware and a reusable napkin as well. Those who bike, bus, or carpool will receive a free gift at the event. More information doitgreen.org.

Gastro Non Grata: A Salute to Comfort Food and Cans

• Sunday, November 22, 2009
• Doors at 6pm
• 21+
• At the TRIPLE ROCK, 629 Cedar Avenue in Minneapolis
• $5 at the door, additional donations help Craig & Jeff break even.

Beer, food, and music! What more could you want? Northern Brewer will start the night with a Lambic tasting and chef Landon Schoenfeld will present three sample courses as the night goes on. The beer guest for the night is 21st Amendment Brewery. Music by Falcon Crest, Arctic Universe, School of Rock, Cadillac Kolstad, Cornbread Harris, and The Annandale Cardinals. As before, Clancey’s Meat and Fish will provide meat door prizes as only they can. More info at Gastro Non Grata’s blog.

Midtown Farmers’ Market‘s Thanksgiving Market

• Wednesday, November 25, 2009
• 1pm to 4pm
• Lake Street and 22nd Ave S near the Light Rail in Minneapolis

Meat, vegetables, apples, bread, chocolates, and canned goods will all be available. Weather permitting there may be crafts as well. Real Bread bread will be available by advanced order: contact Brett at brettlaidlaw (at) eckmeier (dot) com for options. Hilltop Pastures will be at the market as well. According to the market website, they have a waiting list for turkeys, but they’ll be dropping off orders and selling other products on Wednesday. Thanks to midtownfarmersmarket.org for the details!

No exclamation points were harmed in the writing of this post!

When someone I respect as much as Peter Reinhart claims to have discovered a technique that “has the potential to change the… bread landscape in America,” it’s worth taking notice. In The Bread Baker’s Apprentice Reinhart writes:

[Delayed fermentation] has the potential to change the entire bread landscape in America. I’ve begun teaching it to my students…. Within the next few years I fully expect to see variations of this method appearing in both artisan bakeshops and at the industry level. It is the next frontier in breads. When we deconstruct the process, it takes us beyond fermentation, actually beneath fermentation, down to the level of enzymes. It is the enzyme that serves as the catalytic converter, freeing up the sugars that are bound up in the complex starches of flour. The delayed-fermentation technique, revealed to me by Gosselin, and intuited by many others without knowing why, is all about how enzymes affect fermentation and release flavor. (24)

Delayed fermentation, also called retarding, is the method of making bread by mixing the dough and refrigerating it overnight or longer. The dough is then baked following the usual method, as if it had been  made fresh. Most of the recipes in The Bread Baker’s Apprentice take advantage of this technique in some form. By the time he published Whole Grain Breads: New Techniques, Extraordinary Flavor, he was even more convinced of the virtues of delayed fermentation, particularly for fussy whole-grain breads:

The delayed fermentation method used in this book capitalizes on enzyme activity while also incorporating the parallel drama of the living microorganisms: yeast and bacteria. It uses a new approach to draw out the full flavor potential of the grain, delaying much of the fermentation until after the enzymes have done their work. (Conventionally, fermentation begins right away, so enzyme activity happens concurrently with fermentation.) This new approach addresses the whole grain baking puzzle by combining several distinct entities to create a dough that performs well and yields a loaf of bread with wonderful flavor. (46)

I have learned more about bread from Peter Reinhart than any other author in print; the methods he presents in these two books are the basis for the way I make bread. Many times have I made bread over two or three days, following his delayed fermentation method. I’ve never had cause to complain about the resulting bread.

But as I have learned to rely less directly on recipes in my bread baking and start to improvise and develop my own techniques, I have begun to wonder if delayed fermentation is worth the trouble: it means you have to plan to make bread over a day in advance and that you have to somehow clear enough space in the refrigerator to accommodate a covered mixing bowl of dough (or, even worse, a half sheet). Was the payoff—a supposed marked improvement in flavor—worth this effort?

I decided to do a test. I made a basic bread dough (4 oz starter, 2 tsp sea salt, 1 tsp yeast, 7 3/4 oz water, 10 1/8 oz AP Flour, 2 1/8 oz WW flour) using my handy-dandy bread calculator at 68% hydration; my standard level of wetness: not overly dry but manageable. I kneaded the dough for ten minutes. I made my first batch of the dough at 5 PM on Saturday. I started an identical batch around noon on Sunday: at 12:15, the second batch was ready to go through its first rise and I took the refrigerated batch from the night before out of the refrigerator so it could begin its first rise. At this point, the doughs looked almost identical, although up-close the delayed-fermentation dough had a smoother surface, possibly from its night of rest.

After three hours of rising time, neither dough had quite doubled but there were signs of yeast activity. The air pockets visible through the bottom of my glass bowls were more evenly-distributed than in the delayed fermentation dough, which had several large air pockets. By this time the doughs’ temperatures had more or less evened out; the non-delayed dough was a few degrees warmer. Shaping the doughs into boules and transferring them to proofing baskets I could feel no significant difference.

After 90 minutes of proofing in which both doughs seemed to grow evenly in their respective baskets, I was ready to bake. I had my oven set to 475°F and baking stone in place, with a sheet pan ready to serve as a steam distributor. As I turned the doughs out onto my peel, I noticed that the delayed-fermentation dough held more tightly to the shape of the proofing basket; the fresh dough was more apt to spread out. In order to tell the breads apart after baking, I labeled them with an F (for fermented — both doughs are actually fermented and very little extra fermentation happens in the refrigerator since yeast are nearly dormant at this temperature; as of baking time, I did not realize all this) and a U (for unfermented).

Into the oven for 30 minutes, they emerged nicely brown and crusty.

In the baked breads the differences between the two doughs are more apparent: the delayed fermentation bread was slightly taller and less spread out – it very nicely matched the oval shape of the basket. The fresh dough had spread out a lot more and was consequently a bit squatter. Cutting the loaves open revealed starker contrasts: while the delayed-fermentation dough had small holes from trapped gases, the fresh dough bread had a more even texture.

Cosmetic differences aside, what about the taste? Expecting great things, Martha and I eagerly sat down with our two slices of bread. I took a bite from the delayed fermentation dough first. It was good! Next, I tried the fresh loaf. It was also good! The flavor differences, if they existed, must have been subtle, because to my coarse palate these breads tasted the same. Martha, who is much more taste-sensitive than I, agreed. There was also very little textural difference: I thought I could detect more crunchiness in the fresh crust and more chewiness in the delayed fermentation crust. The delayed-fermentation bread also felt slightly denser.

Consulting additional references after baking, I saw that the differences I did detect — the tighter rise and larger gas pockets of the delayed-fermentation dough — were scientifically predictable results. As Shirly O’Corriher writes in Cookwise:

Reduces ovenspring and loaf volume Chilling for a period as long as overnight reduces ovenspring (oven rise) and reduces loaf volume. Alcohol that was made by the yeast from the beginning changes to a gas in the hot oven and is a contributor to ovenspring. During a lengthy cold period, alcohol simply evaporates from the surface of the dough and some goes to vinegar. So, there is a reduced amount of alcohol to contribute to ovenspring…

Opens texture slightly Chilling dough retards the action of yeast and influences texture, though much more subtly than breadmaking method. The air-bubble nuclei worked into the dough during mixing and kneading are enlarged by gases from the yeast. Initially these tiny bubbles contain air, which is mostly nitrogen (78 percent) and oxygen (21 percent). Immediately the yeast uses up the oxygen so you have mostly nitrogen in these tiny bubbles. The gases from yeast are essentially carbon dioxide, and they enlarge the same bubbles. The longer the dough rises, the more carbon dioxide there is in the enlarged bubbles.

After a long rise, the bubbles contain a very high percentage of carbon dioxide and a very low percentage of nitrogen. The longer the rise, or after multiple punch-downs, the higher the percentage of carbon dioxide. After a very long rise or two or three shorter rises, the bubbles contain essentially 100 percent carbon dioxide.

Carbon dioxide dissolves very well in cold water. So, if the dough is chilled, the carbon dioxide in a great number of bubbles will completely dissolve. The dough now has fewer bubbles for the gases from the yeast to enlarge. When the dough is warm again, the yeast puts much more gas into these fewer bubbles, creating bigger bubbles and a coarser bread. (29)

Neither of my breads had the open texture that I prefer, but of the two the delayed fermentation bread had larger air bubbles, giving it a slightly more rustic appearance.

Harold McGee in On Food and Cooking concurs about the effects of delayed fermentation, with a little less detail on the process:

In addition to giving the baker greater flexibility, retarding has useful effects on the dough. Long, slow fermentation allows both yeasts and bacteria more time to generate flavor compounds. Cold dough is stiffer than warm dough, so it’s easier to handle without causing a loss of leavening gas. And the cycle of cooling and rewarming redistributes the dough gases (from small bubbles into the water phase, then back out into larger bubbles), and encourages the development of a more open, irregular crumb structure. (539)

Both McGee and O’Corriher (just before the quoted section) agree with Reinhart that the enzyme activity engendered by delayed fermentation improve the flavor of bread. In this one test, I didn’t find that to be the case; at least not noticeably so. If I haven’t planned ahead, I know I can still making pretty flavorful bread without relying on a rest in the fridge. But that doesn’t mean I’m ready to give up on delayed fermentation. The benefits I did observe — the open texture (which can be further improved by alterations to my kneading technique) and the firmer, easier to manipulate dough — are a big step in the direction of my search for ideal loaves of bread. And as long as you’re capable of a little advanced planning, delayed fermentation can actually help with time management, since it allows you to mix the dough on one day and complete the baking on another. As long as there’s room in the fridge.

Eighty degree weather notwithstanding, I can’t shake the feeling that summer is soon to end and that a short fall will in no time at all be heralding in dark, cold winter. But as far as the farmers’ market is concerned, these fears are unfounded: fall might be around the corner, but there is still an abundance of ripe summer produce. In fact, with eggplants and summer squash, tomatoes, onions, red peppers and herbs all in season now is the time for ratatouille, the Provençal vegetable stew.

When I am looking to make French food, I always turn first to Elizabeth David’s French Provincial Cooking (I am inordinately proud of my first American edition—thanks Mom and Dad), a shining example among the many books that treat the subject of French cooking. On ratatouille, David says:

There are any amounts of versions of this dish, the variations being mainly in the proportions of each vegetable employed, the vegetables themselves being nearly always the same ones: aubergines, sweet peppers, onions, tomatoes, with courgettes sometimes being added and occasionally potatoes as well. Some people add mushrooms, but this is a rather pointless addition because they get completely lost in the mass of other vegetables. Garlic is optional, but the cooking medium must be olive oil.

To make a dish of ratatouille sufficient for about eight people, the ingredients are 3 medium-sized onions, 3 large aubergines, 3 large sweet red peppers, 3 courgettes [zucchini], 4 large tomatoes, 2 cloves of garlic, a few coriander seeds, fresh or dried basil if available, or parsley, 2 coffee-cups (after-dinner size) of olive oil. (242)

The first thing was to deal with the eggplant (ahem, aubergine) and summer squash, specifically with their overabundance of moisture. To get rid of some of their extra liquid, I sliced 3 long, spindly japanese eggplant and 4 thin, bright-yellow summer squashes into 1/4″ rounds on the mandoline (easily my favorite new kitchen tool this year). I then tossed them with a teaspoon of salt and spread everything out on a cooling rack set over a sheet pan to drain (you can also use a colander, but I feel spreading the vegetables out over a cooling rack helps them to drain more effectively). After an hour, I pressed the vegetable slices firmly with an absorbent towel to push out as much moisture as possible. A soggy ratatouille won’t do!

With the eggplant and squash prepped, I was ready to start cooking. I first sautéed three sliced onions in a generous amount of olive oil (not quite as generous as two teacupfuls, after-dinner or otherwise) until the onions were soft but not browned. To this I added the eggplant, squash and 3 finely chopped bell peppers. I cooked this mixture covered over medium-low heat for 40 minutes.

While the eggplant, squash, peppers and onions were stewing away I peeled and seeded 10 roma tomatoes (I had heirlooms from the market but it seemed a shame to cook them) and chopped them fine. Per Elizabeth David’s suggestion I also ground up a few coriander seeds and added them to the tomatoes. After the prescribed 40 minutes of cooking, I added the tomatoes and coriander to the pot with the eggplant, squash, onions and peppers and let it cook, mostly covered, for another 20 minutes while the tomatoes softened.

After the hour of cooking, I used a spoon to try the broth that had developed. What an amazing taste of late summer! The broth was rich, earthy and even very sweet. The vegetables really required no additional seasoning, but I added a little salt to brighten the flavor even more.

Just before serving, I mixed in 1/3 cup of basil chiffonade and 1/4 c of minced parsley. I only just realized that David suggests using one or the other, but really, who could choose?

One essential accompaniment for eating ratatouille is plenty of crusty bread to use to mop up all the juices. Given the farmers’ market theme of this lunch my dining companions and I were happy to indulge in a delicious and culturally appropriate pain de campagne from Brett of Real Bread.

And while I couldn’t bear to cook my heirloom tomatoes, neither could I resist eating them immediately. They were typically sweet, acidic and tomato-ey in a salad with cucumber and goat cheese. I added a little olive oil and vinegar, but the tomato juice itself is dressing enough.

Ratatouille is such an ideal dish for this time of year. For one thing, it is a good way to use all that zucchini/summer squash and eggplant that you are feeling so guilty about not eating yet. More importantly, it is a dish of great simplicity that depends entirely on the quality of its ingredients. For some people French cooking has the reputation of being highly technical and focused on transforming raw ingredients into something entirely new—the English used to accuse the French of inventing sauces as a way of disguising bad ingredients buried underneath. But French cooking understands—along with many other culinary traditions— that dishes will only be as good as the ingredients they started with. For something as straightforward as ratatouille, the phrase “garbage in, garbage out” very much applies. Luckily, the produce available in farmers’ markets right now is about as far from garbage as you can get.

There’s really a lot in ratatouille’s favor: it’s simple, it’s hearty, it’s full of flavor, it’s even vegan! About the only downside I can think of is that it can only be made at this time of year, when the peak seasons of its various parts coincide. All the more reason to enjoy it while you can.

Many factors affect the way bread turns out: what kind of flour is used, if and how long the bread gets kneaded, the amount of salt, natural yeast versus canned yeast, the ambient conditions, etc.  Of these, none is more influential than the ratio of water to flour. Bakers express this ratio as a baker’s percentage, which compares the mass of water in a dough to the mass of flour. For example, a dough consisting of 500 grams of flour and 300 grams of water has a baker’s percentage of 60%. The level of hydration of flour makes a big difference in terms of texture: dense bagels might be as low as 57% while chewy ciabatta with an open, airy crumb comes to 80% or more. A French-style baguette is around 65%. Although there are technical differences in how each of these breads are made, their varying water contents explain most of the difference in their texture.

Since water content has such a fundamental influence on bread, one of the most important ways to master bread making is to understand and manipulate the amount of water in your dough. With this in mind, I created a bread calculator as a tool for adjusting water content. One need only decide how much bread to make (the mass of the dough) and what percentage of water to use, which is where the fun experimentation comes in. Generally, the higher the percentage of water the bigger the crumb and the chewier the bread, but the dough will also be more difficult to work with and less shapeable. Going in the opposite direction makes denser breads that more easily hold their shape. I am always amazed at how varying the water even a little bit can make a dramatic difference.

Why a bread calculator, instead of say, a recipe? For most of my life, I have been told that while in cooking one can be fast and loose with measurements and improvisations, baking requires precision; slight variations in any ingredient amount could spell disaster. Taking this for truth, I dutifully made bread according to recipes in a few very good bread cookbooks. Sure, I noticed that most recipes were remarkably similar, but I assumed that there was some kind of alchemy at work and I should just follow the directions.

After working for three months in a professional kitchen and gaining a lot of confidence, I have come to rely on recipes less and less. This applied immediately to my cooking, where I had always assumed that improvisational ability would come with experience, but eventually spilled over into my bread baking. When I ran out of yeast and had to substitute some sourdough starter in a recipe, it began to dawn on me that there was also a lot of leeway in bread, if not quite as much as in a stir-fry. As long as I had water, flour, salt and some kind of leavener, bread would inevitably result. With this discovery came a new-found freedom: I knew what kind of bread I wanted to make, how its dough would feel when it was ready; I just needed to understand the influence of water content and experiment with it until I got what I was looking for. So I put the cookbooks away (I do not disparage cookbooks: they are what got me to this point) and got out a spreadsheet. After making many batches of bread based on ad-hoc calculations, I created this calculator to avoid having to remember the formulas I was using. And thus, bread math and the bread calculator were born. 

To be honest, I created the calculator mainly for my own use and understanding (there are others online). But if it is useful to you, feel free to use it as well. You can always make bread by feel, but working out the numbers gives a greater feeling of control, not to mention better consistency.

For those of you interested in what’s going on inside the calculator, here’s the math behind bread (please keep in mind that I was a liberal arts major and this is the best I could do):

In a bread using a starter, there are four known quantities we can input: the amount (mass) of the starter to be used, the percentage of hydration of that starter, the amount (mass) of dough we want to end up with and the percentage of hydration for that dough. We want to find out the amount of flour and the amount of water we need to add.

All this information about the bread is contained in these two equations:

Mass of Flour in Starter + Mass of Flour Added + Mass of Water in Starter + Mass of Water Added = Mass of Final Dough

and

(Mass of Water in Starter + Mass of Water Added)/(Mass of Flour in Starter + Mass of Flour Added) = Percentage Hydr. of Dough

The first thing is to deal with the starter, so we know how much flour and how much water the starter is contributing. The starter is represented in the following equations:

Mass of Flour in Starter + Mass of Water in Starter = Mass of Starter  or F + W = MS

and

Mass of Water in Starter/Mass of Flour in Starter = Pct Hydration of Starter or W/F = PS

We’re interested in solving for the two variables F and W, and since there are two equations it’s very simple to substitute one in for the other. 

Solving the first for W gives us W = MS – F, which plugs into the second as (MS-F)/F = PS. 

Solving for F:

MS-F = FPS

MS = FPS + F

MS = F(PS+1)

MS/(PS+1) = F

So using the given values for MS and PS we can calculate the amount of flour in the starter, F. With F known it’s easy enough to return to the first equation and calculate W. That takes care of the starter.

Back to the final bread: we know the mass of bread we’d like to end up with (M), the hydration percentage of that dough (P), the amount of flour in the starter (F) and the amount of water in the starter (W). We’re interested in the amount of flour to add (f) and the amount of water to add (w). Returning to the first two equations with these symbols we have:

W + w + F + f = M

and

(W + w) / (F + f) = P

Two equations and two variables! Solving for f:

w = M – f – F – W

(W + M – f – F – W)/(F+f) = P

M – f – F  = PF + Pf

M – F – PF = Pf+f

M – F – PF = f(P+1)

(M-F-PF)/(P+1) = f

Since we already know M, F and P it is easy enough to calculate f. And w is just M-MS-f! And there you have it!