Bread Math

Boules resting

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


(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


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 = 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


(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!


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6 comments on “Bread Math”

  1. Ryan 13 April, 2009 at 9:05 pm

    a. NERD!
    b. Request: Please make some Borscht. Why? Because I said so.

  2. Martha 14 April, 2009 at 9:55 am

    The math must be right because the bread is good.

  3. Amy 14 April, 2009 at 5:45 pm

    I can’t really believe you did this. I hope Uncle Don reads it. I really should take it out to show Dad (Grandpa). It may well contain the formula for deriving all prime numbers…

  4. Uncle Don 20 April, 2009 at 1:14 pm

    Great for bread, but no help to GrandPa.

    Posts linking to this post

  1. MARTHAANDTOM » Bread Calculator 13 April, 2009 at 7:52 pm

    […] 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 […]

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