# Class Time: Baker's Math 101

### (Sorry, it had to happen at some point)

[*Photo credit: Lewis Hine, 1916*]

There are a handful of bread-baking topics that I’ve put off writing about here because they aren’t terribly sexy. But they are *important*, especially when you want to step beyond “breadbaking beginner” stage and create your own recipes, or at least understand other people’s recipes in a more fundamental way. I want you to be able to make that step if you do, but if you don’t—or don’t *yet*—feel free to skip this post for the time being and file it away for later. I will strive to keep my recipes here beginner-friendly so that understanding all that I’m about to explain isn’t absolutely necessary for success.

One such topic is **baker’s math. **It sounds dry (it is, a little) and complicated (it isn’t, really). Compared to the math that you likely studied in high school, it’s pretty basic, and not really all that difficult to comprehend once you wrap your mind around it and work with it awhile.

Baker’s math—also known as **baker’s percentages—**is simply the **representation of a bread recipe in terms of a ratio**, specifically **a ratio by weight**, **relative to the total amount of flour. **

The reason for the latter choice is that a) every bread recipe contains flour, and b) it is nearly always the ingredient present in the greatest quantity. Which means that every other ingredient can be represented by a number smaller than 1—in other words, as a fraction or a percentage.

And the reason the ratio is determined by *weight* and not volume is because **ingredients vary in density**, so volumes cannot be compared usefully to one another (i.e., 1 cup of water and 1 cup of flour do not weigh the same amount, while 100g of water and 100g of flour do, no matter their volumes).

### Lesson 1: Converting to Baker’s Percentages

It’s easier to grasp baker’s math by example than description, particularly when you start from a specific recipe. Take this hypothetical, perfectly reasonable ball of dough, containing:

*500g all-purpose flour*

*375g water*

*75g honey*

*10g salt*

*2g instant yeast*

To convert this recipe into baker’s percentages is simple: **Take each individual ingredient, divide it by the amount of flour, then convert the result into a percentage by moving the decimal two places to the right.** Thus:

*500/500 = 1 = 100% flour*

*375/500 = 0.75 = 75% water*

*75/500 = 0.15 = 15% honey*

*10/500 = 0.02 = 2% salt*

*2/500 = 0.004 = 0.4% instant yeast*

Removing all the math leaves us with:

*100% flour*

*75% water*

*15% honey*

*2% salt*

*0.4% instant yeast*

The above is the recipe expressed in baker’s percentages, a universal formula for that hypothetical loaf that can be scaled to any size, large or small (more on how below).

A few refinements:

One:** The total amount of flour always equals 100%, no matter how many different flours the dough contains. **Meaning that if a recipe contains two different flours, you first combine them to determine their total weight before calculating the baker’s percentages. And you then treat each of them separately to determine their individual percentages. In other words, a recipe containing:

*400g all-purpose flour*

*100g whole-wheat flour*

Contains 500g flour, total, and converts to:

*400/500 = 0.8 = 80% all-purpose flour *

*100/500 = 0.2 = 20% whole-wheat flour*

Two:** In recipes that contain preferments—like a levain or a biga—you need to break out the flour and water they contain to get the correct calculations**. (The same goes for any other component that is two or more ingredients already combined together in an earlier step, like a porridge.) Take this formula:

*475g all-purpose flour*

*350g water*

*75g honey*

*50g 100% hydration levain*

*10g salt*

It contains a levain made from 25g flour and 25g water. When you add these amounts into their respective rows and calculate the overall percentage of each, you get:

*500g all-purpose flour (100%)*

*375g water (75%)*

*75g honey (15%)*

*10g salt (2%)*

The above list is commonly referred to as an **overall formula** because it gives you the total amount of each of the individual ingredients present, but says nothing about how they are actually used in the recipe itself.

When recipes give both amounts and percentages in overall formulas (as in the example above), it can sometimes be confusing to sort out how much to weigh at any one step. For this reason, I find it clearer to write my overall formulas *only* as percentages, and leave the amounts to the individual steps, without percentages.

Three: **When bakers refer to **“**hydration”, they are talking specifically about the ratio of water to flour.** This is useful for getting a sense of how wet a dough or how moist the resulting loaf might be. The recipe above is 75% percent water to flour, or *75% hydration*.

What that number *means* is of course determined by what kind(s) of flour the recipe contains, since different flours absorb water at different rates. In other words, a dough made entirely with all-purpose flour at 75% hydration will be very different in texture compared to one made entirely with whole-wheat flour (specifically, the whole-wheat one will be much drier). Nonetheless, hydration is a useful shorthand for getting a sense of how the water-flour ratio in a dough will affect the result.

### Lesson 2: Converting from Baker’s Percentages

Converting a ratio into a specific recipe is where baker’s math can get a little more complicated. This is also known as **resizing**, because—after first converting a recipe into percentages as described above—you can then create a recipe with the identical ratio as the original, but of another dough weight.

The way you do this is to first calculate the **formula conversion factor**, which is the **desired dough weight divided by the combined** **total of all of the individual percentages in the ratio**. Again, it’s easier to understand by example. Here’s our original formula:

*100% flour*

*75% water*

*15% honey*

*2% salt*

*0.4% instant yeast*

Adding these percentages together (100 + 75 + 15 + 2 + 0.4) we get **192.4***

Now say we want to make 2500 grams of dough using this same formula, so we divide 2500 by 192.4:

formula conversion factor = 2500 / 192.4 = 12.993… = **13 **

**(**I rounded *up* in this case from 12.993…, since that way we’ll end up with a little *extra* dough rather than too little.)

Finally, to sort out the specific amounts of ingredients you need to make 2500 grams of dough, you simply **multiply the individual percentages of each ingredient by the formula conversion factor**, like this:

100% x 13 = *1300g flour*

75% x 13 = *975g water*

15% x 13 = *195g honey*

2% x 13 = *26g salt*

0.4% x 13 = *5.2g instant yeast*

To double check that our calculations are correct, we simply add all these amounts back together. The total should equal the desired total amount of dough, or 2500g, plus whatever extra rounding up leaves:

1300 + 975 + 195 + 26 + 52 = 2501.2

*One way to understand this seemingly weird number is it represents the total number of “units” in the recipe. If our original hypothetical dough just happened to weigh 192.4 grams, each unit would then weigh 1 gram (100g flour, 75g water, 15g honey, etc.). The formula conversion factor is then what each unit weighs when the dough is of *another* scale.

That—in a giant nutshell—is baker’s math. If you are new to it and totally confused right now, not to worry. As I said, you don’t *need *to understand it to use my recipes. And if you want to practice *using* baker’s math, just look for bread recipes in cookbooks or online—preferably ones already in gram amounts, for obvious reasons—and apply the above formulas to them. Over time the process will become second nature, I promise.

—Andrew

Chiming in long after the fact with a question: I'm confused about how the water and flour comprising the levain are factored into the total. If I'm using a levain of, say, 50g flour and 50g water, do I reduce the amounts of flour and water in my formula by 50g each to account for those ingredients in the levain?

Thanks for such a clear and concise explanation!