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!

This form allows you to calculate the amount of flour and water needed to make bread doughs at various percentages you choose. Please refer to the bread math post for a detailed discussion of why and how I got here.

If you are planning to use a starter, for Starter Mass enter the amount of starter you want to use and for Starter % the percentage of water (refer to Bread Math for explanation of baker’s percentage). If you aren’t planning to use starter, leave Starter Mass blank or enter 0. The final dough mass is the amount of bread you want to have; most loaves of bread I have seen seem to fall between 1 and 2 pounds. Dough % is the percentage of hydration of the final dough. This is where the fun comes in!  Try playing with various amounts and see what a huge difference it makes on the crumb of your bread. Remember, there is  no magic bread ratio but rather the ratio is the key to determining the kind of bread.

Example: Here’s my standard loaf of bread, and how I used these calculations to arrive at it. Because of the size of my oven and my household’s bread needs, I know I want to bake three 1.5# loaves of bread. This means I will need 4.5# of Final Dough Mass, which is 72 oz (16oz/lb * 4.5lb = 72 oz). I also make bread with a natural yeast starter. Whenever I refresh my starter, I add equal masses of water and flour, so I know my starter’s percentage is 100%. The Starter Mass I use varies depending on how much starter I have around, but I usually pick 8 oz. I have yet to determine the effects of drastic variations in starter use. With my Starter Mass, Starter % and Final Dough Mass decided, it’s just a matter of deciding on the Dough %. Although I continue to tweak this, I have had a lot of success with dough at 68% hydration, so I’ll enter that and hit calculate. The calculator tells me that my final dough will require 38.86 oz of flour and 25.14 oz of water. My scale’s smallest unit is 1/8 oz so we’ll call that 38 7/8 oz and 25 1/8 oz. So, in the kitchen, I measure my starter into the bowl, then cover it with 39 oz of flour and 25 oz of water. I also add salt. Salt can be factored into this calculation as a percentage of flour (bakers do this) but my scale is not accurate enough to measure this little salt so I always just wing it. I usually add about a Tablespoon to 4.5# of dough. With the salt added, you’re ready to mix, knead and otherwise proceed as normal.

Note that this form is unit agnostic, you can use grams or ounces or metric tons. Percentages should be in the 0-100 format, although you can go above 100%. Don’t type in any units or symbols, it will confuse the calculator!

Have fun! Bake bread!

Since I don’t have to work on the weekend I avoid that nagging pressure to interact with the other humans by baking bread. The rhythm of bread baking is such that it is both leisurely and consuming.

The first thing I did in the morning was cover 10 grain hot cereal mix with boiling water as the starter for the multigrain bread that was featured in Cook’s Illustrated a year or two ago. This is my go-to basic bread to have around the house, great for toast and sandwiches. The crumb is not so dense as a lot of multigrain breads thanks to copious amounts of white flour and instant yeast makes for a predictable rising schedule. The flavor is earthy, as multigrained breads should be, and tinged with honey. This recipe is simple, not very time consuming and reliably produces a pretty pair of loaves.

With that out of the way, I went to the store to get more flour (3 lbs was not going to cut it). I had refreshed my sourdough starter the day before and left it out all morning to bubble and grow. I needed to make pitas for dinner and I also wanted to make a couple of european-style breads. I like a loose crumb so I was aiming for about 66% hydration, and I wanted to use a pound of my starter, mostly to facilitate storing the rest of it in the fridge. I was figuring I wanted about 3# of final dough for my european breads and at least 2# to be able to make 8 four ounce pitas. Math time!

A pound of starter was 8oz water and 8oz flour. I wanted to end up with about 80 oz of dough and I was going to have 2/3 as much water as flour (and I like round numbers that my scale can handle) so I planned to add 40 oz of flour. That gave me 48 oz of flour total, 66% of which is 31.68, which I rounded to a nice even 32 (which meant I would add 24 additional ounces).

With my formula figured out, I proceeded to mix and knead the dough, adding a good amount of salt. With wild yeast rising times are pretty unpredictable, and salt inhibits rising, so I had no idea when the dough was going to double in size. I set out to work on some other things.

Around 5 p.m. I got tired of waiting and decided to weigh and shape my dough. I recently discovered that weighing individual dough pieces so they are the same really helps with the uniformity of the final product (durh) so I got out my scale. 1.5# of dough went to a boule which I left to proof in a heavily oiled and floured glass bowl. Three .5# pieces got rolled into baguettes and placed on my couche to grow. The remaining 8 4 oz pieces (plus a small leftover piece) I shaped into small boules to rest for pitas.

Mostly because we were hungry I rolled out the pitas within an hour of shaping the dough even though they had not grown much at all. Apparently, that is not very important with pitas. Here they are in the oven:

That is what we like to call pocket-city. Below you’ll see them in a nice little stack (wrapped in a towel to keep them warm and chewy):

After dinner I decided it did not make much sense to wait up till all hours for the rest of my breads to proof in the meantime wasting all that heat in the stone in my oven, so the baguettes were transferred to a floured peel, scored and baked. For the record, they were underproofed, but I think they turned out fine.

Lastly, the boule. I apparently did not flour my bowl enough because this bread stuck to the sides and did not want to land on the peel. When it finally did, it was horribly deformed. It is pretty annoying to spend this much time on a piece of bread only to have some stupid mistake destroy everything you worked and fought for; much can be learned about life from bread baking, evidently. I made a feeble attempt at scoring this bread artfully to make the mistakes look intentional and then slid it onto the stone. I was surprised by a good amount of oven spring, but upon eating the bread the next day found dense areas that suggested underproofing. Great crumb for the most part though thanks to the relatively high hydration!

And so passed another Saturday.