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Baker percentage
Baker's percentage is a baker's notation method indicating the flourrelative proportion of an ingredient used when making breads, cakes, muffins, and other pastries.^{[1]}^{[2]}^{[3]}^{[4]} It is also referred to as baker's math,^{[5]}^{[6]} or otherwise contextually indicated by a phrase such as based on flour weight.^{[1]}^{[7]} It is sometimes called formula percentage,^{[1]} a phrase that refers to the sum of a set of bakers' percentages.^{[note 1]} Baker's percentage expresses each ingredient in parts per hundred as a ratio of the ingredient's mass to the total flour's mass (that is, the unit mass):^{[12]}^{[13]}^{[10]}
 <math>baker's\ percentage_{ingredient} = 100\% \times \frac{mass_{ingredient}}{mass_{flour}}</math>
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 mass of flour rather than with respect to the mass of all ingredients, the total sum of these percentages always exceeds 100%.
Flourbased recipes are more precisely conceived as baker's percentages, and more accurately measured using mass instead of volume. The uncertainty in using volume measurements follows from the fact that flour settles in storage and therefore does not have a constant density.^{[14]}^{[15]}
Contents
Baker percentages
A yeastdough 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 percentages
To derive the ingredient weights when any weight of flour (W_{f}) is chosen:^{[note 2]}
 <math>\begin{array}{rcl}weight_{ingredient} &=& \frac{weight_{flour}\ \times \ baker's\ percentage_{ingredient}}{100\%}\\ &=& {weight_{flour} \times baker's\ percentage_{ingredient}}\\\end{array}</math>
Baker's
percentageweights
^{[note 3]}ingredient % method 1 method 2 flour 100% W_{f} * 1.00 W_{f} * 100% water 35% W_{f} * 0.35 W_{f} * 35% milk 35% W_{f} * 0.35 W_{f} * 35% fresh yeast 4% W_{f} * 0.04 W_{f} * 4% salt 1.8% W_{f} * 0.018 W_{f} * 1.8%
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:
Baker's
percentageweights 2 lb 10 kg ingredient % lb oz kg g flour 100% 2 32 10 10000 water 35% 0.7 11.2 3.5 3500 milk 35% 0.7 11.2 3.5 3500 fresh yeast 4% 0.08 1.28 0.4 400 salt 1.8% 0.036 0.576 0.18 180
Creating baker's percentages
The baker has determined how much a recipe's ingredients weigh, and uses uniform decimal 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:
ingredient weight ^{ingredient mass}⁄_{flour mass} × 100% flour 10 kg 10 kg÷ 10kg= 1.000= 100% water 3.5 kg 3.5 kg÷ 10kg= 0.350= 35% milk 3.5 kg 3.5 kg÷ 10kg= 0.350= 35% fresh yeast 0.4 kg 0.4 kg÷ 10kg= 0.040= 4% salt 0.18 kg 0.18 kg÷ 10kg= 0.018= 1.8%
Due to the canceling of uniform weight units, the baker may employ any desired system of measurement (metric or avoirdupois,^{[16]} 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
Ingredient
^{[note 4]}baker's
%true
%flour 100% 56.88% water 35% 19.91% milk 35% 19.91% fresh yeast 4% 2.28% salt 1.8% 1.02% Total 175.8% 100%
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:^{[11]}
 <math>\begin{array}{rcl}formula\ mass & = & mass_{flour} \times formula\ percentage\\ \frac{formula\ mass}{formula\ percentage} & = & mass_{flour}\\\end{array}</math>
 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:
 <math>
\begin{array}{rcl} mass_{ingredient} & = & formula\ mass \times true\ percentage_{ingredient} \\ true\ percentage_{ingredient} & = & \frac{baker's\ percentage_{ingredient}}{formula\ percentage} \times 100\% \\ mass_{ingredient} & = & formula\ mass \times \frac{baker's\ percentage_{ingredient}}{formula\ percentage} \\ & = & \frac{formula\ mass \ \times\ baker's\ percentage_{ingredient}}{formula\ percentage} \end{array} </math>
 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:
 <math>
\begin{array}{rcl} mass_{ingredient} & = & \frac{formula\ mass}{formula\ percentage} \times baker's\ percentage_{ingredient}\\ & = & mass_{flour} \times baker's\ percentage_{ingredient}\end{array}</math>
 The two methods of calculating the mass of an ingredient are equivalent:
 <math> formula\ mass \ \times \ true\ percentage_{ingredient} \ = \ mass_{flour}\ \times\ baker's\ percentage_{ingredient}</math>
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 (g) for weight, the liter (L) for volume, the meter (m) for length, and degrees Celsius (°C) for temperature; multiples and submultiples are indicated by prefixes, two commonly used metric cooking prefixes are milli (m) and kilo (k).^{[17]} Intrametric conversions involve moving the decimal point.^{[18]}
Common avoirdupois and metric weight equivalences:^{[19]}
 1 pound (lb) = 16 ounces (oz)
 1 kilogram (kg) = 1,000 grams (g) = 2.20462262 lb ^{[note 5]}
 1 lb = 453.59237 g = 0.45359237 kg
 1 oz = 28.3495231 g.
In four different Englishlanguage countries of recipe and measuringutensil markets, approximate cup volumes range from 236.59 to 284.1 milliliters (mL). Adaptation of volumetric recipes can be made with density approximations:
Volume to mass conversions for some common cooking ingredients ingredient density
g/mL
^{[note 6]}metric cup
250 mLimperial cup
≈284 mLU.S. customary cup
≈237 mL^{[note 7]}g oz g oz g oz water^{[note 8]} 1^{[note 9]} 249–250 8.8 283–284 10 236–237 8.3^{[note 10]} granulated sugar 0.8^{[20]} 200 7.0 230 8.0 190 6.7 wheat flour 0.5–0.6^{[20]} 120–150 4.4–5.3 140–170 5.0–6.0 120–140 4.2–5.0 table salt 1.2^{[20]} 300 10.6 340 12.0 280 10.0
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 of some kind occurs.
Drawbacks
Baker's percentages do not accurately reflect the impact of the amount of glutenforming 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.^{[21]} Manipulation of known flourprotein levels can be calculated with a Pearson square.^{[22]}^{[23]}
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.
Advantages
Baker's percentages enable the user to:
 compare recipes more easily (i.e., which are drier, saltier, sweeter, etc.).
 spot a bad recipe, or predict its baked characteristics.^{[3]}
 alter or add a singleingredient percentage without changing the other ingredients' percentages.^{[2]}^{[10]}
 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^{[24]} 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 bagels and pretzels, and medium hydration levels (58–65%) are typical for breads and rolls.^{[25]} Higher hydration levels are used to produce more and larger holes, as is common in artisan breads such as baguettes or Ciabatta. Doughs are also often classified by the terms stiff, firm, soft, and slack.^{[26]} Batters are more liquid doughs. Muffins are a type of drop batter while pancakes are a type of pour batter.
Doughs
^{[25]}^{[26]}Very stiff < 57% Stiff to firm 5765% Soft 6570% Soft to slack 7080% Batters
^{[note 11]}Drop 95% Pour 190%
Errata
 ^{†} Except for creams and custards,^{[27]} when the formula includes milk,^{[28]} bakers almost always use highheat NFDM (nonfat dry milk).^{[27]}^{[29]}^{[30]}^{[31]}^{[32]} In breads the usage is typically within a range of 5%12%; fresh whole milk is 3.5% milk fat, 88% water, and 8.5% milk solids.^{[29]}
 ^{††} A yeast flavor in the baked bread is generally not noticeable when the bakers' percent of added yeast is less than 2.5%.^{[7]}
Notes
 ^ There is some ambiguity regarding the use of the phrase "formula percentage" in the literature. From the published date of 2004^{[8]} to the date 2007,^{[9]} Hui's definitions have changed slightly. In 2004 "formula percent" was defined by "total weight of all ingredients"; however by the latter date's usage, the preference was to use the prefix "true" in the phrase "True formula percent (true percent)" when referring to "total weight of all ingredients." In 2005, Ramaswamy & Marcotte used the phrase "typical formula" in reference to a "baker's %" series of ingredients, then drew the semantic and mathematic distinctions that "actual percentage" was one based upon "total mass", which they labeled "% flour", "% water", etc.^{[10]} In 2010, Figoni said that "baker's percentage" was "sometimes called formula percentage...."^{[1]} In 1939, the phrase formula percentage was said to commonly refer to the sum of the particular percentages that would later be called bakers' percentages.^{[11]}
 ^ Derived algebraically from Gisslen's formula.
 ^ W_{f} denotes a flour weight. In method 1 the percentage was divided by 100%. Method 2 works well when using a calculator. When using a spreadsheet, formatting the cell as percentage versus number automatically handles the percent portion of the calculation.
 ^ True percentage values have been rounded and are approximate.
 ^ It's worth noting the multiplicative inverse of 2.20462262.
 ^ One gram per millilitre is very close to one avoirdupois ounce per fluid ounce: 1 g/mL ≈ 1.002 av oz/imp fl oz
This is not a numerical coincidence, but comes from the original definition of the kilogram as the mass of one litre of water, and the imperial gallon as the volume occupied by ten avoirdupois pounds of water. The slight difference is due to water at Script error: No such module "convert". being used for the kilogram, and at Script error: No such module "convert". for the imperial gallon. The U.S. fluid ounce is slightly larger.
 1 g/mL ≈ 1.043 av oz/U.S. fl oz
 ^ From cup (unit). Note the similarity of cup mL to water weight or mass as g. This density relationship can also be useful for determining unknown volumes.
 ^ 1 g/mL is a good rough guide for waterbased liquids such as milk (the density of milk is about 1.03–1.04 g/mL).
 ^ The density of water ranges from about 0.96 to 1.00 g/mL dependent on temperature and pressure. The table above assumes a temperature range Script error: No such module "convert".. The variation is too small to make any difference in cooking.
 ^ Since an imperial cup of water weighs approximately 10 avoirdupois ounces and five imperial cups are approximately equal to six U.S. cups, one U.S. cup of water weighs approximately 8⅓ avoirdupois ounces.
 ^ Mathematically converted from liquidtodry volumetric ratios on quick bread. 1 cup water weighs 237 g, 1 cup all purpose flour, 125 g, rounding applied. It is worth noting that if the liquid is whole milk of 3.25% milkfat, which is somewhat common in pancake recipes, the actual water content or hydration is about 88% of that value per the USDA National Nutrient database, thus pancake hydrations may be as low as, or lower than, 167% or thereabouts (190% * 88%).
References
 ^ ^{a} ^{b} ^{c} ^{d} Paula I. Figoni (2010). How Baking Works: Exploring the Fundamentals of Baking Science. New York: Wiley. pp. 9–11. ISBN 0470392673. Retrieved 20101206.
Baker's percentage—sometimes called formula percentage or indicated as "on flour weight basis"—is different from the percentages commonly taught in math classes.
 ^ ^{a} ^{b} Griffin, Mary Annarose; Gisslen, Wayne (2005). Professional baking (4th ed.). New York: John Wiley. p. 10. ISBN 0471464279. Retrieved 20110101.
 ^ ^{a} ^{b} Corriher, Shirley (2008). BakeWise: The Hows and Whys of Successful Baking with Over 200 Magnificent Recipes. New York: Scribner. p. 32. ISBN 1416560785. Retrieved 20101209.
 ^ Hui, Yiu H. (2006). Handbook of food science, technology, and engineering. Washington, DC: Taylor & Francis. p. 166. ISBN 0849398495. Retrieved 20101209.
 ^ Laura Halpin Rinsky; Glenn Rinsky (2009). The pastry chef's companion: a comprehensive resource guide for the baking and pastry professional. Chichester: John Wiley & Sons. p. 19. ISBN 0470009551. Retrieved 20101209.
 ^ Daniel T. DiMuzio (2009). Bread Baking: An Artisan's Perspective. New York: Wiley. p. 31. ISBN 0470138823. Retrieved 20101211.
 ^ ^{a} ^{b} Cauvain, Stanley P. (2003). Bread making: improving quality. Boca Raton: CRC Press. p. 475. ISBN 1855735539. Retrieved 20101208.
Generally the taste of yeast itself is not detectable in bread unless the amount of yeast used is greater than 2.5% based on the weight of flour.
 ^ J. Scott Smith, Yiu H. Hui, ed. (2004). Food processing: principles and applications. Cambridge, MA: Blackwell Pub. p. 178. ISBN 0813819423. Retrieved 20101229.
Formula—term used instead of "recipe," by the baking industry; the weight of each ingredient is determined based on the weight of flour at 100%.
Formula percent—term used by the baking industry to describe the amount of each ingredient by weight for a "recipe" or formula compared to the weight of all ingredients.  ^ Yiu H. Hui, ed. (2007). Handbook of food products manufacturing. New York: Wiley. p. 302. ISBN 0470125241. Retrieved 20101229.
True formula percent (true percent): Term used by the baking industry to describe the amount of each ingredient by weight for a "recipe" or formula compared with the total weight of all ingredients.
 ^ ^{a} ^{b} ^{c} Michele Marcotte; Hosahalli Ramaswamy (2005). Food Processing: Principles and Applications. Boca Raton: CRC. pp. 14–15. ISBN 1587160080. Retrieved 20101225.
 ^ ^{a} ^{b} Quartermaster Corps, ed. (1939). Army baker. Washington: U.S. Government Printing Office. pp. 38–41. Training Manual No. 2100151. Retrieved 20120207.
The sum of the percentages of ingredients used in any dough is commonly referred to as the formula percentage (168 percent in example in b above). The sum of the weights of ingredients used in a dough is commonly referred to as formula weight (462 pounds in example in c above).
 ^ Gisslen, Wayne (2007). Professional cooking (Sixth ed.). New York: John Wiley. p. 893. ISBN 047166376X. Retrieved 20101225.
 ^ Gisslen, Wayne (2009). Professional baking. New York: John Wiley. p. 24. ISBN 0471783498.
 ^ Stanley P Cauvain (2009). Stanley P. Cauvain & Linda S. Young, ed. The ICC Handbook of Cereals, Flour, Dough & Product Testing: Methods and Applications. BakeTran, High Wycombe, Buckinghamshire, UK. Lancaster, Pennsylvania: DEStech Publications, Inc. p. 69. ISBN 1932078991. Retrieved 20101226.
Using Cereal Testing at Mill Intake" > "The Bulk Density of Grain (Hectolitre Mass, Bushel Mass, Test Weight, Specific Weight)
 ^ Wihlfahrt, Julius Emil (1913) [1905]. A treatise on flour, yeast, fermentation and baking, together with recipes for bread and cakes. THE FLEISCHMANN CO. p. 25. Retrieved 20100122.
 ^ Rees, Nicole; Amendola, Joseph (2003). The baker's manual: 150 master formulas for baking. London: J. Wiley. p. 11. ISBN 0471405256. Retrieved 20101206.
 ^ "The Metric Kitchen". Retrieved 20101130.
 ^ "Intrametric Conversions" (DOC). Retrieved 20110215.
 ^ Google Calculator, retrieved 20101218
 ^ ^{a} ^{b} ^{c} L. Fulton, E. Matthews, C. Davis: Average weight of a measured cup of various foods. Home Economics Research Report No. 41, Agricultural Research Service, United States Department of Agriculture, Washington, DC, 1977.
 ^ "KitchenSavvy: Flour Power?". Retrieved 20101209.
 ^ Hosahalli Ramaswamy; Amalendu Chakraverty; Mujumdar, Arun S.; Vijaya Raghavan (2003). Handbook of postharvest technology: cereals, fruits, vegetables, tea, and spices. New York, N.Y: Marcel Dekker. p. 263. ISBN 0824705149. Retrieved 20100107.
 ^ Van Loon, Dirk (1976). The family cow. Charlotte, Vt: Garden Way Pub. p. 152. ISBN 0882660667.
 ^ Reinhart, Peter (2009). Peter Reinhart's Artisan Breads Every Day. Berkeley, Calif: Ten Speed Press. pp. 207–209. ISBN 1580089984. Retrieved 20101209.
 ^ ^{a} ^{b} http://www.stellaculinary.com/scs20
 ^ ^{a} ^{b} "Bakers Percentages  Revised" (HTML). Retrieved 20141128.
 ^ ^{a} ^{b} Paula I. Figoni (2010). How Baking Works: Exploring the Fundamentals of Baking Science. New York: Wiley. p. 360. ISBN 0470392673. Retrieved 20101208.
 ^ Schieberle, Peter (2009). Food Chemistry. Berlin: Springer. p. 716. ISBN 3540699333. Retrieved 20101211.
 ^ ^{a} ^{b} Hui, Yiu H. (2006). Handbook of food science, technology, and engineering. Washington, DC: Taylor & Francis. p. 14826. ISBN 0849398495. Retrieved 20101208.
 ^ Mark Keeney; Jenness, Robert; Marth, Elmer H.; Noble P. Wong (1988). Fundamentals of Dairy Chemistry. Berlin: Springer. p. 760. ISBN 0834213605. Retrieved 20101208.
 ^ Daniel T. DiMuzio (2009). Bread Baking: An Artisan's Perspective. New York: Wiley. p. 24. ISBN 0470138823. Retrieved 20101211.
 ^ Paula I. Figoni (2010). How Baking Works: Exploring the Fundamentals of Baking Science. New York: Wiley. p. 150. ISBN 0470392673. Retrieved 20101211.
External links
 Baker's percentage
 Sample recipe
 Understanding The Baker's Percentage  Video A video that explains in detail the baker's percentage, its benefits, and best uses.
