Baker percentage

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Baker's percentage is a notation method indicating the proportion of an ingredient relative to the flour used in a recipe when making breads, cakes, muffins, and other baked goods. It is also referred to as baker's math, and may be indicated by a phrase such as based on flour weight. It is sometimes called ''formula percentage'', a phrase that refers to the sum of a set of baker's percentages. Baker's percentage expresses a ratio in percentages of each ingredient's weight to the total flour weight: :$\text_\text = 100\% \times \frac$ For example, in a recipe that calls for 10 pounds of flour and 5 pounds of water, the corresponding baker's percentages are 100% for the flour and 50% for the water. Because these percentages are stated with respect to the weight of flour rather than with respect to the weight of all ingredients, the sum of these percentages always exceeds 100%. Flour-based recipes are more precisely conceived as baker's percentages, and more accurately measured using weight instead of
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...

. The uncertainty in using volume measurements follows from the fact that flour settles in storage and therefore does not have a constant density.

# Baker's percentages

A yeast-dough formula could call for the following list of ingredients, presented as a series of baker's percentages: :

## Conversions

There are several common conversions that are used with baker's percentages. Converting baker's percentages to ingredient weights is one. Converting known ingredient weights to baker percentages is another. Conversion to true percentages, or based on total weight, is helpful to calculate unknown ingredient weights from a desired total or formula weight.

### Using baker's percentages

To derive the ingredient
weight In science and engineering, the weight of an object is the force acting on the object due to gravity. Some standard textbooks define weight as a Euclidean vector, vector quantity, the gravitational force acting on the object. Others define weigh ...

s when any weight of flour ''W''''f'' is chosen:Derived algebraically from Gisslen's formula. :$\begin \text_\text &= \frac \\ &= \text_\text \times \text_\text \end$ : In the example below, 2 lb and 10 kg of flour weights have been calculated. Depending on the desired weight unit, only one of the following four weight columns is used: :

### Creating baker's percentages

The baker has determined how much a recipe's ingredients weigh, and uses uniform
decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...

weight units. All ingredient weights are divided by the flour weight to obtain a ratio, then the ratio is multiplied by 100% to yield the baker's percentage for that ingredient: : Due to the canceling of uniform weight units, the baker may employ any desired system of measurement (
metric Metric or metrical may refer to: * Metric system, an internationally adopted decimal system of measurement * An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement Mathematics In mathema ...

or
avoirdupois The avoirdupois system (; abbreviated avdp.) is a measurement system A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and d ...
, etc.) when using a baker's percentage to determine an ingredient's weight. Generally, the baker finds it easiest to use the system of measurement that is present on the available tools.

### Formula percentage and total mass

: The total or sum of the baker's percentages is called the formula percentage. The sum of the ingredient masses is called the formula mass (or formula "weight"). Here are some interesting calculations: * The flour's mass times the formula percentage equals the formula mass: :$\begin \text &= \text_\text \times \text \\ \frac &= \text_\text \end$ * An ingredient's mass is obtained by multiplying the formula mass by that ingredient's true percentage; because an ingredient's true percentage is that ingredient's baker's percentage divided by the formula percentage expressed as parts per hundred, an ingredient's mass can also be obtained by multiplying the formula mass by the ingredient's baker's percentage and then dividing the result by the formula percentage: ::$\begin \text_\text &= \text \times \text_\text \\ \text_\text &= \frac \times 100\% \\ \text_\text &= \text \times \frac \\ &= \frac \end$ :Thus, it is not necessary to calculate each ingredient's true percentage in order to calculate each ingredient's mass, provided the formula mass and the baker's percentages are known. * Ingredients' masses can also be obtained by first calculating the mass of the flour then using baker's percentages to calculate remaining ingredient masses: ::$\begin \text_\text &= \frac \times \text_\text \\ &= \text_\text \times \text_\text \end$ * The two methods of calculating the mass of an ingredient are equivalent: ::$\text \times \text_\text = \text_\text \times \text_\text$

## Weights and densities

The use of customary U.S. units can sometimes be awkward and the metric system makes these conversions simpler. In the metric system, there are only a small number of basic measures of relevance to cooking: the
gram The gram (originally gramme; SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram. Originally defined as of 1795 as "the absolute weight of a volume Volume is a measure ...
(g) for weight, the
liter The litre (international spelling) or liter (American English spelling) (SI symbols L and l, other symbol used: ℓ) is a metric units, metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubi ...

(L) for volume, the
meter The metre (British English, British spelling) or meter (American English, American spelling; American and British English spelling differences#-re, -er, see spelling differences) (from the French unit , from the Greek language, Greek noun , "m ...
(m) for length, and degrees
Celsius The degree Celsius is the unit of temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated ...

(°C) for temperature; multiples and sub-multiples are indicated by prefixes, two commonly used metric cooking prefixes are
milli- ''Milli'' (symbol m) is a metric prefix, unit prefix in the metric system denoting a factor of one thousandth (10−3). Proposed in 1793, and adopted in 1795, the prefix comes from the Latin , meaning ''one thousand'' (the Latin plural is ). Sinc ...
(m-) and
kilo- Kilo is a decimal prefix, decimal metric prefix, unit prefix in the metric system denoting multiplication by one thousand (103). It is used in the International System of Units, where it has the symbol k, in Letter case, lowercase. The prefix ' ...
(k-). Intra-metric conversions involve moving the decimal point. Common avoirdupois and metric weight equivalences: :1 pound (lb) = 16
ounce The ounce () is any of several different units of mass, weight or volume and is derived almost unchanged from the , an Ancient Roman units of measurement, Ancient Roman unit of measurement. The #International avoirdupois ounce, avoirdupois ounce ...
s (oz) :1
kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. ...
(kg) = 1,000 grams (g) = 2.20462262 lb :1 lb = 453.59237 g = 0.45359237 kg :1 oz = 28.3495231 g. In four different English-language countries of recipe and measuring-utensil markets, approximate cup volumes range from 236.59 to 284.1 milliliters (mL). Adaptation of volumetric recipes can be made with
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek language, Greek letter Rho (letter), rho), although the Latin letter ''D'' ca ...

approximations: : Due to volume and density ambiguities, a different approach involves volumetrically measuring the ingredients, then using ''scales'' or ''balances'' of appropriate accuracy and error ranges to weigh them, and recording the results. With this method, occasionally an error or
outlier In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are ...

of some kind occurs.

# Drawbacks

Baker's percentages do not accurately reflect the impact of the amount of gluten-forming proteins in the flour on the final product and therefore may need to be adjusted from country to country, or even miller to miller, depending on definitions of terms like "bread flour" and actual protein content. Manipulation of known flour-protein levels can be calculated with a Pearson square. In home baking, the amounts of ingredients such as salt or yeast expressed by mass may be too small to measure accurately on the scales used by most home cooks. For these ingredients, it may be easier to express quantities by volume, based on standard densities. For this reason, many breadmaking books that are targeted to home bakers provide both percentages and volumes for common batch sizes. Besides the need for appropriate readability scales, a kitchen calculator is helpful when working directly from baker's percentages.

Baker's percentages enable the user to: * compare
recipe A recipe is a set of instructions that describes how to prepare or make something, especially a dish of prepared food. A sub-recipe or subrecipe is a recipe for an ingredient that will be called for in the instructions for the main recipe. His ...

s more easily (i.e., which are drier, saltier, sweeter, etc.). * spot a bad recipe, or predict its baked characteristics. * alter or add a single-ingredient percentage without changing the other ingredients' percentages. * measure uniformly an ingredient where the quantity per unit may vary (as with eggs). * scale accurately and easily for different batch sizes.

# Common Formulations

Common formulations for bread include 100% flour, 60% water/liquid, 1% yeast, 2% salt and 1% oil, lard or butter.

# Dough hydration

In a recipe, the baker's percentage for water is referred to as the "hydration"; it is indicative of the stickiness of the dough and the "crumb" of the bread. Lower hydration rates (e.g., 50–57%) are typical for
bagel A bagel ( yi, בײגל, translit=beygl; pl, bajgiel; also spelled beigel) is a bread roll originating in the History of Jews in Poland, Jewish communities of Poland. It is traditionally shaped by hand into a roughly hand-sized ring from yeaste ...

s and
pretzel A pretzel (), from German pronunciation, standard german: Breze(l) ( and French language, French / Alsatian dialect, Alsatian: ''Bretzel'') is a type of baking, baked bread made from dough that is commonly shaped into a knot. The traditional pr ...

s, and medium hydration levels (58–65%) are typical for
bread Bread is a staple food prepared from a dough of flour (usually wheat) and water, usually by baking. Throughout recorded history and around the world, it has been an important part of many cultures' diet. It is one of the oldest human-made food ...

s and rolls. Higher hydration levels are used to produce more and larger holes, as is common in artisan breads such as
baguette A baguette (; ) is a long, thin type of bread of French origin that is commonly made from basic lean dough (the dough, though not the shape, is defined by French law). It is distinguishable by its length and crisp Bread#Crust, crust. A baguet ...

s or
ciabatta Ciabatta (, ; literally "slipper") is an Italian cuisine, Italian white bread made from wheat flour, water, salt, yeast and olive oil, created in 1982 by a baker in Adria, province of Rovigo, Veneto, Italy, in response to the popularity of French ...

. Doughs are also often classified by the terms stiff, firm, soft, and slack. Batters are more liquid doughs. Muffins are a type of drop batter while pancakes are a type of pour batter. :