Wednesday, October 27, 2010

Bread Math: How to Calculate (and understand) Baker's Percentages

The first time I saw baker's percentages in a book, I thought the writer had gone mad. C'mon now, how can anything possibly add up to more than 100 percent? It just doesn't make sense. I thought there must have been some strange mistake in the writing and proofreading, and I moved on, blithely unaware that I had just seen the seekrit spy code for breadmakers.

Okay, maybe it's not that secret, but it's something that tends to boggle the ordinary person who was awake enough in math class to realize that if the pie chart is full, that's 100 percent, and if you've got more, then you need another pie pan.

If you abandon that pie chart and look at it through the bread baker's eyes, it makes a little more sense. Outside the bread-making world, percentages indicate what part of the whole a particular component makes up, while a bakers' percentage is about how various other ingredients relate to the weight of the flour in a recipe.

In baking, as with much of cooking, the actual amounts of an ingredient don't matter much — it's the ratio of ingredients that matters. Think of bakers' percentages this way: the flour is equal to 100 percent. Every other ingredient is then expressed in terms of its ratio to the amount of flour. If, for example, you had a dough with 16 ounces of flour and 8 ounces of water and 0.32 ounces of salt, you'd say that the dough contains 50 percent water because the water weighs 50 percent of what the flour weighs. In baker's talk, that's called 50 percent hydration.

The beauty of expressing recipes in terms of percentages is that the units of measure can be anything: grams, ounces, picograms, whatever. It doesn't matter if you've got 15 ounces of flour or five pounds. And it doesn't matter what kind or how many varieties of flour. Add up the weight of the flour, divide by 100, and that's the unit you use to measure the rest of your ingredients.* It doesn't matter how much a particular ingredient weighs, only how much it weighs in relation to everything else.

If this all sounds confusing, hang on a minute. It gets easier.

Scaling Recipes Using Baker's Percentages

Let's try this with a real recipe.

My standard, everyday white bread recipe breaks down to the following percentages:

Bread flour: 100%
Water: 67%
Sugar: 4%
Yeast: 2%
Salt: 2%
Olive oil: 4%

So let's say I start with 12 ounces of flour on my scale. To calculate the rest of my ingredients, I first divide the amount of flour I have by 100, giving me 0.12 ounces. Now all I have to do to figure out the rest of my ingredients is to multiply them by their various percentages. So, for example, the water recipe is 67% water. Multiply 67 by 0.12, and I get 8 ounces (rounded from 8.04 ounces).

Do the same math across the board (rounding to the nearest 0.05 ounce), and you get the following weights:

Bread flour: 12 ounces
Water: 8 ounces
Sugar: 0.5 ounces
Yeast: 0.25 ounces
Salt: 0.25 ounces
Olive oil: 0.5 ounces

Some more astute readers might note that if you look at the bakers' percentages, it all adds up to 179%. Weird, right? That's just the nature of the beast.

Arriving at a Specific Dough Weight

What if you want to go the other way? Say you know that you want a pound of finished dough. How would bakers' percentages help you figure out how much of each ingredients to use? First, you'd start by adding up all of your percentages. For the white bread, that's 179. Next, divide the weight of the final dough you are trying to achieve by that number to give you the weight of a single unit.

So four a 16-ounce (1 pound) ball of dough, each unit of weight should be equal to 16 ounces/179, or 0.089 ounces.

Now all you have to do is multiply that unit by each of your percentages. So flour, for example, is 100 percent of the recipe. 100 x 0.089 = 8.9 ounces total. Using the same math for every ingredient, you get the following measurements for a one pound ball of dough:

Bread flour: 8.9 ounces
Water: 6 ounces
Sugar: 0.35 ounces
Yeast: 0.175 ounces
Salt: 0.175 ounces
Olive oil: 0.35 ounces

Got it?

Or you can go the other way. You can decide how much dough you want to end up with, and work your math magic from there.

Lacking math skills and a scale, you could follow a baker's percentage recipe with nothing more that a balance scale and some ingenuity. Because it doesn't matter how much a particular ingredient actually weighs, it only matters how much it weighs in relation to everything else.

Using a handy pebble to represent your single unit of measure, or even better, a bunch of those pebbles that each weigh the same amount, you could use that balance scale to weigh 100 units of flour, 67 units of water, 2 units each of salt and yeast, and 4 units of sugar and olive oil.

It wouldn't matter if those pebbles weighed an ounce or a gram or a Sakmar, and it wouldn't matter if you used a coconut instead of a pebble. Well, it would matter in the final volume of dough, but the overall formula would work to make a single loaf or enough to feed the entire village.

Here's a chart showing conversions that would yield 2 pounds of finished dough, to use that 25-pound bag of flour you just bought, or to use metric weights:

Although the initial math is, well...math, once you've got the formula it makes it easier to scale recipes when you need to, as long as you've got a good scale to do the measuring. Or a balance scale and a bucket of coconuts.

This formula is also handy for determining whether a bread recipe makes sense. If you know what the typical amounts of critical ingredients are, you can tell at a glance whether a recipe has the right amount of salt or yeast, even before you even open the container of flour.

You may not ever need to use baker's percentages to make a loaf of bread, but it's good to have that secret decoder ring, just in case.

*There are actually two ways of measuring baker's percentages if you're using a poolish or some other preferment. In some systems, the preferment is considered to be a separate ingredient, and in others the flour weight in the preferment is part of the 100 percent. If you're reading a recipe that uses baker's percentages and a preferment, make sure you know which system is in use. For the sake of this explanation, we're assuming that there is no poolish to worry about.
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