Math for Bakers

What are Baker's Percentages?

Baker’s percentages, also known as baker’s math, is a method of writing baking formulas where each ingredient is listed as a percentage of the total flour weight.

Why use Baker's Percentages?

Baker’s percentages make it easy and intuitive to get precise measurements for ingredients, to scale a recipe up and down, and quickly assess the difficulty of a recipe.

While mostly commonly used in a professional settings, baker’s percentages can still prove extremely useful for the home baker.

Baker’s percentages rely on weighted measurements and will not work using volume. Metric is recommended even if you are American because the math will be much easier.

Most baked goods inherently rely on a specific ratio of ingredients to come out as expected, and the recipes require more accuracy when compared to regular cooking. While volumetric measurements may be enough for the average home baker to get by, if you are looking for consistency and to take records so you can tweak future bakes, weight measurements and baker’s percentages are the way to go.

Using baker percentages and weights also makes it super easy to scale recipes up and down. Whether you are using a formula from a professional bakery which yields 100 loaves and need to scale it down to one loaf, or you need to scale up your usually recipe that makes one loaf to five loaves for a crowd, baker's percentages will help you do all of this with ease.

Baker’s percentages give the baker a quick way to assess a recipe’s difficulty and expected dough consistency. For example, for a baker living in a humid environment seeing a bread formula that calls for 78% water instantly lets them know this will be a slack dough that will ferment faster, potentially making it more difficult to mix and shape.

Reading a Baker’s Percentage Formula

When using baker’s percentage, each ingredient is described as a ratio of the total flour in the recipe. The total flour in a recipe should always add up to 100%. Let’s take a look at this simple formula:

As expected our formula starts with flour at 100%. Next is water at 65%. This means the water in the recipe should weigh 65% of our total flour weight. In this case we have 1000g of flour, so we should have 650g of water. Same logic applies for salt and yeast.

The formula is as follows: $${\mathrm{Weight}}_{\mathrm{Ingredient}}={\mathrm{Ratio}}_{\mathrm{Ingredient}}*{\mathrm{Weight}}_{\mathrm{Flour}}$$

Which can be rearranged as: $${\mathrm{Ratio}}_{\mathrm{Ingredient}}=\frac{{\mathrm{Weight}}_{\mathrm{Ingredient}}}{{\mathrm{Weight}}_{\mathrm{Flour}}}$$ To get the ratio again.

At the bottom of the table we have our total yield, which has the totals for our ingredient percentages and weights . The sum of ratios is known as the total percentage, while of the sum weights if the total dough weight

What if we're using multiple types of flour? Have a look at the following:

Like other ingredients, weight is calculated as ratio * total flour weight for different types of flours, but sum of all the flours in a recipe should always add up to 100%

Modifying a Formula

After subbing out half of the white flour in the original recipe for thirsty whole wheat flour, the dough is much stiffer and too dry to work with, so we need to increase the hydration. How could you go about modifying the formula and adding more water?

Easy, lets say you want to increase the hydration from 65% to 75%, change your percentage and then recalculate the totals and ingredient weight for water:

But you may have noticed one problem. Doing this increases our total dough weight.

For the home baker making a small batch, this might not matter. But if you are making a larger batch or just want to keep a consistent dough weight, then you will need to do a little more math. This is where the total percentage factor comes into play.

First, increase the percentage as desired, so in this case 65% -> 75% for water. Then, get the sum of the ratios, but only the ratios. Do not calculate the weights just yet. This gets us 178%.

Since we want to keep our total dough weight constant, we must recalculate the total flour weight. The math formula looks like this: $${\mathrm{Weight}}_{\mathrm{Flour}}=\frac{{\mathrm{Total\; Dough\; Weight}}_{}}{{\mathrm{Formula\; Percentage\; /\; 100}}_{}}$$

To find our new flour weight, first convert the percentage to a ratio by dividing by 100 to get 1.78. Then divide the total dough weight by the total ratio (1680 / 1.78) to get 944. This is our new total flour weight.

You can than calculate the new weights of each ingredient as before. The table now looks like this:

Whether you want to keep dough weight constant when adjusting your ratios is up to you. When I bake I like to target a specific dough weight so I will keep it constant and recalculate the weights for all ingredients.

Adding an ingredient is also easy. If we wanted to add 5% honey for example, just add the ingredient and ratio to the table then calculate the new weights.

Constant dough weight:

Variable dough weight:

Scaling a Formula

The one of the greatest advantages of using baker’s percentages is how easy it makes scaling a formula up and down. Working with the same recipe, let’s say we want to bake bread for your entire extended family, and need to scale up to 10 x 1.5 lb loaves. 1.5 lb is 681 grams, times 10 that would be 6810 grams or 6.81 kilograms. Our table so far:

In order to get our new weights, like before we need to calculate our new total flour weight using our total percentage factor, so 6.81 / 1.78 = 3.826 kg flour.

Scaling down works the exact same way. If we wanted to scale down the formula to one loaf, it would look like this.

Formulas with Preferements

What if we want to add a preferment to our formula? Mabye now we want to incoporate a poolish into our recipe using about 20% of the total flour weight. Our formula will now include two more tables, one for the poolish and one for the final dough formula (including the poolish as an ingredient)

To construct the poolish table, first take the percentage of prefermented flour and multiple that by total flour in the recipe. In this case, that would be .2 * 383, giving us 77 for our total flour in the poolish. Then calculate the ingredient weights for the poolish.

The final dough formula represents the final weights of all the ingredients, including the weights of any preferments. To get the weight of a given ingredient in the final dough formula, you must subtract the weight of that ingredient in all preferments from weight of that ingredient in the overall formula. For example, to calculate the weight of water in the final dough formula of our recipe, take the weight of overall weight of the water (287g) and subtract by the amount we put in the poolish (77g) to get 210g. When measuring out all our ingredients to begin mixing the dough, we should use 210g of water because 77g is already in the poolish.

Here is an example with two preferments, poolish and levain.

Here is an example with a soaker:

When using a soaker, the majority grain or seed is used as the “flour” for the calculation.

Convert a Recipe To Baker’s Percentages

Converting a recipe to baker’s percentage is straight forward if the original recipe was measured in weight. Say we are given the following recipe:

To get the ratios, divide each ingredient by total weight of the flour.

Tips

• Using a formula does not mean you should be a slave to the numbers. If you are afraid a recipe is going to be overly hydrated, you can with hold ~5% of the water, and add it slowly during mixing until the dough is the right consistency. Then you can adjust the formula for future bakes.
• Using a spreadsheet application is a good way to save formulas and automatically calculate weights.
• Even though all the formulas shown were bread, this doesn't mean you can use baker's percentages in non-bread recipes! You can apply it in any baking recipe that is majority flour.