Baker percentage

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Baker's percentage is a baker's notation method indicating the flour-relative proportion of ingredients 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 mass (that is, the unit mass).

baker's percent(ingredient) = 100 × ingredient mass⁄flour mass[10][12]

For example, if a recipe calls for 10 pounds of flour and 5 pounds of water, the corresponding bakers' percentages will be 100% and 50%. Because of the way these percentages are stated, as a percent of flour mass rather than of all ingredients, the total will always exceed 100%.

Flour-based recipes are more precisely conceived as baker's percentage, 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.[13][14]

Contents

[edit] Baker percentages

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

flour  100% 
water 35%
milk† 35%
fresh yeast  4%††
salt 1.8%

[edit] Conversions

There are several main conversions that are used with baker percentages. Converting baker percentages to ingredient weights is one, or using them. Converting known ingredient weights to baker percentages is another, or creating them. Conversion to true percentages, or based on total weight, is helpful to calculate an unknown flour weight from a desired total or formula weight.

[edit] Using baker percentages

To derive the ingredient weights when any weight of flour is chosen:

ingredient weight = flour weight × baker's percent(ingredient)⁄100[note 2]
ingredient   % weights
[note 3]
flour  100%  X * 1.00
water 35% X * 0.35
milk 35% X * 0.35
fresh yeast 4% X * 0.04
salt 1.8%  X * 0.018 

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:

Bakers'
percentage		 weights
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

[edit] Creating baker 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 for baker's percentage:

ingredient   weight   ingredient mass⁄flour mass  × 100
flour 10 kg 10 kg ÷ 10 kg = 1.000 ⟹ 100%
water 3.5 kg 3.5 kg ÷ 10 kg = 0.350 ⟹ 35%
milk 3.5 kg 3.5 kg ÷ 10 kg = 0.350 ⟹ 35%
fresh yeast 0.4 kg 0.4 kg ÷ 10 kg = 0.040 ⟹ 4%
salt 0.18 kg 0.18 kg ÷ 10 kg = 0.018 ⟹ 1.8%

Due to the canceling of uniform weight units, the baker may assign any desired system, metric or avoirdupois[15] or other customary, to the flour weight when scaling and using bakers' percentages. Generally, the baker will find it easiest to use their balances' or scales' weight system.

[edit] Formula percentage and total weight

Ingredient
[note 4]		 bakers'
%		 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 bakers' percentages is called the formula percentage. The sum of the ingredient weights is called the formula weight. The flour weight times the formula percentage also equals formula weight.[11]

When each ingredient's bakers' percent is divided by the formula percentage, its multiplicative inverse, and all are expressed as percentages, their resulting sum equals 100%. When removing an ingredient from the list or adding one to it, or increasing or decreasing a bakers' percentage, the formula percentage changes. If it changes, the true percentages require recalculation.

A desired formula weight times the true percent of each ingredient equals the ingredients' respective weights. A desired formula weight times each ingredients' bakers' percent divided by the formula percentage also equals the ingredients' respective weights. Thus, it is not necessary to pre-calculate the true percentages, only the formula percentage.

[edit] 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 sub-multiples are indicated by prefixes, two commonly used metric cooking prefixes are milli- (m-) and kilo- (k-).[16] Intra-metric conversions involve moving the decimal point.[17]

Common avoirdupois and metric weight equivalences:[18]

1 pound (lb) = 16 ounces (oz)
1 kilogram (kg) = 1000 grams (g) = 2.20462262 lb [note 5]
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 approximations:

Main article: Cup (unit)#Using volume measures to estimate mass
Volume to mass conversions for some common cooking ingredients
ingredient density
g/mL
[note 6]		 metric cup
250 mL		 imperial cup
≈284 mL		 U.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[19] 200 7.0 230 8.0 190 6.7
wheat flour 0.5–0.6[19] 120–150 4.4–5.3 140–170 5.0–6.0 120–140 4.2–5.0
table salt 1.2[19] 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.

[edit] 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.[20] Manipulation of known flour-protein levels can be calculated with a Pearson square.[21][22]

In home baking, the amounts of ingredients such as salt or yeast expressed by weight 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. Many breadmaking books targeted to home bakers will provide both percentages and volumes for common batch sizes, for this reason.

Besides the need for appropriate scales, a kitchen calculator is helpful when working directly from baker's percentage.

[edit] Advantages

Baker's percentage enables the user to:

  • more accurately compare recipes (i.e. which is drier, saltier, sweeter, etc.);
  • spot bad recipes or predict their baked characteristics;[3]
  • alter or add a single-ingredient percentage without changing the other ingredients' percentages;[10][2]
  • uniformly measure ingredients such as eggs, commonly used in baking, where the quantity per unit may vary;
  • accurately and easily scale for different batch sizes.

[edit] Common Formulations

Common formulations for bread[23] include 100% flour, 60% water/liquid, 1% yeast, 2% salt and 1% oil, lard or butter. The amount of water, expressed as a percentage of the weight of flour, is referred to as the "hydration" and is indicative of the stickiness of the dough and the "crumb", or internal texture, of the bread. Higher hydration levels produce more and larger holes, as is common in artisan breads such as baguettes or Ciabatta.

[edit] Errata

† Except for creams and custards,[24] when the formula includes milk,[25] bakers almost always use high-heat NFDM (non-fat dry milk).[26][27][24][28][29] 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.[26]
†† A yeast flavor in the baked bread is generally not noticeable when the bakers' percent of added yeast is less than 2.5%.[7]

[edit] Notes

  1. ^ 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 labelled "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]
  2. ^ Derived algebraically from Gisslen's formula.
  3. ^ X denotes a flour weight. When using a calculator, pressing the "%" key usually divides by 100. When using a spreadsheet, formatting the cell as percentage versus number automatically handles the per-cent portion of the calculation. When calculating by hand, the per-cent 100 factor must be accounted for. In this table the percentage was divided by 100.
  4. ^ True percent values have been rounded and are approximate.
  5. ^ It's worth noting the multiplicative inverse of 2.20462262.
  6. ^ 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 4 °C (39 °F) being used for the kilogram, and at 62 °F (17 °C) for the imperial gallon. The U.S. fluid ounce is slightly larger.
    1 g/mL ≈ 1.043 av oz/U.S. fl oz
  7. ^ 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.
  8. ^ 1 g/mL is a good rough guide for water-based liquids such as milk (the density of milk is about 1.03–1.04 g/mL).
  9. ^ 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 0–30 °C (32–86 °F). The variation is too small to make any difference in cooking.
  10. ^ 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.

[edit] References

  1. ^ a b c d Paula I. Figoni (2010). How Baking Works: Exploring the Fundamentals of Baking Science. New York: Wiley. pp. 9–11. ISBN 0-470-39267-3. http://books.google.com/books?id=XqKF7PqV02cC&pg=PA9#v=onepage&q&f=false. Retrieved 2010 Dec 06. "Baker's percentage—sometimes called formula percentage or indicated as "on flour weight basis"—is different from the percentages commonly taught in math classes." 
  2. ^ a b Griffin, Mary Annarose; Gisslen, Wayne (2005). Professional baking (4th ed.). New York: John Wiley. p. 10. ISBN 0-471-46427-9. http://books.google.com/books?id=YrQZi41PqKEC&pg=PA10#v=onepage&q&f=false. Retrieved 2011 Jan 1. 
  3. ^ a b Corriher, Shirley (2008). BakeWise: The Hows and Whys of Successful Baking with Over 200 Magnificent Recipes. New York: Scribner. p. 32. ISBN 1-4165-6078-5. http://books.google.com/books?id=b-iwjIb2RxwC&pg=PA32#v=onepage&q&f=false. Retrieved 2010 Dec 9. 
  4. ^ Hui, Yiu H. (2006). Handbook of food science, technology, and engineering. Washington, DC: Taylor & Francis. p. 16-6. ISBN 0-8493-9849-5. http://books.google.com/books?id=43sA1NhzCWsC&pg=SA16-PA6#v=onepage&q&f=false. Retrieved 2010 Dec 9. 
  5. ^ 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 0-470-00955-1. http://books.google.com/books?id=riDsZRlmmRAC&pg=PA19#v=onepage&q&f=false. Retrieved 2010 Dec 9. 
  6. ^ Daniel T. DiMuzio (2009). Bread Baking: An Artisan's Perspective. New York: Wiley. p. 31. ISBN 0-470-13882-3. http://books.google.com/books?id=kF5uI5uWjEMC&pg=PA31#v=onepage&q&f=false. Retrieved 2010 Dec 11. 
  7. ^ a b Cauvain, Stanley P. (2003). Bread making: improving quality. Boca Raton: CRC Press. p. 475. ISBN 1-85573-553-9. http://books.google.com/books?id=f3Ua43ujjUoC&printsec=frontcover&dq=isbn:1855735539&pg=475#v=onepage&q&f=false. Retrieved 2010 Dec 8. "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." 
  8. ^ J. Scott Smith, Yiu H. Hui, ed. (2004). Food processing: principles and applications. Cambridge, MA: Blackwell Pub. p. 178. ISBN 0-8138-1942-3. http://books.google.com/books?id=QDpi_6VnhegC&pg=PA178#v=onepage&q&f=false. Retrieved 2010 Dec 29. "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."     
  9. ^ Yiu H. Hui, ed. (2007). Handbook of food products manufacturing. New York: Wiley. p. 302. ISBN 0-470-12524-1. http://books.google.com/books?id=mnh6aoI8iF8C&pg=PA302#v=onepage&q&f=false. Retrieved 2010 Dec 29. "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." 
  10. ^ a b c Michele Marcotte; Hosahalli Ramaswamy (2005). Food Processing: Principles and Applications. Boca Raton: CRC. pp. 14–15. ISBN 1-58716-008-0. http://books.google.com/books?id=6Cox1IpjqU0C&pg=PA15#v=onepage&q&f=false. Retrieved 2010 Dec 25. 
  11. ^ a b Quartermaster Corps, ed. (1939). Army baker. Washington: U.S. Government Printing Office. pp. 38-41. Training Manual No. 2100-151. http://babel.hathitrust.org/cgi/pt?view=image;size=75;id=coo.31924105503084;page=root;seq=41;num=39. Retrieved 2012-02-07. "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)." 
  12. ^ Gisslen, Wayne (2007). Professional cooking (Sixth ed.). New York: John Wiley. p. 893. ISBN 0-471-66376-X. http://books.google.com/books?id=i12rMZhl4t0C&pg=PA893#v=onepage&q&f=false. Retrieved 2010 Dec 25. 
  13. ^ 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 1-932078-99-1. http://books.google.com/books?id=F5Yu_eT7-4MC&pg=PA69#v=onepage&q&f=false. Retrieved 2010 Dec 26. "Using Cereal Testing at Mill Intake" > "The Bulk Density of Grain (Hectolitre Mass, Bushel Mass, Test Weight, Specific Weight)" 
  14. ^ 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. http://books.google.com/books?id=m-cqAAAAYAAJ&pg=PA25#v=onepage&q&f=false. Retrieved 2010 Jan 22. 
  15. ^ Rees, Nicole; Amendola, Joseph (2003). The baker's manual: 150 master formulas for baking. London: J. Wiley. p. 11. ISBN 0-471-40525-6. http://books.google.com/books?id=Yz0mF7pXZ38C&pg=PA11#v=onepage&q&f=false. Retrieved 2010 Dec 06. 
  16. ^ "The Metric Kitchen". http://www.jsward.com/cooking/cooking-metric.shtml. Retrieved 2010 Nov 30. 
  17. ^ "Intra-metric Conversions" (Doc). http://teacherweb.ftl.pinecrest.edu/piersog/Regular/Worksheets/WS-Metric%20conversion.doc. Retrieved 2011-Feb-15. 
  18. ^ Google Calculator 
  19. ^ 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.
  20. ^ "KitchenSavvy: Flour Power?". http://www.kitchensavvy.com/journal/2004/12/q_bread_recipes.html. Retrieved 2010 Dec 9. 
  21. ^ 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 0-8247-0514-9. http://books.google.com/books?id=Y4N54Wn618YC&pg=PA263#v=onepage&q&f=false. Retrieved 2010 Jan 7. 
  22. ^ Van Loon, Dirk (1976). The family cow. Charlotte, Vt: Garden Way Pub. p. 152. ISBN 0-88266-066-7. http://books.google.com/books?id=j-efZMh9_WgC&pg=PA152#v=onepage&q&f=false. 
  23. ^ Reinhart, Peter (2009). Peter Reinhart's Artisan Breads Every Day. Berkeley, Calif: Ten Speed Press. pp. 207–209. ISBN 1-58008-998-4. http://books.google.com/books?id=dSarPnb4i6QC&pg=PA207#v=onepage&q&f=false. Retrieved 2010 Dec 9. 
  24. ^ a b Paula I. Figoni (2010). How Baking Works: Exploring the Fundamentals of Baking Science. New York: Wiley. p. 360. ISBN 0-470-39267-3. http://books.google.com/books?id=XqKF7PqV02cC&pg=PA360#v=onepage&q&f=false. Retrieved 2010 Dec 8. 
  25. ^ Schieberle, Peter (2009). Food Chemistry. Berlin: Springer. p. 716. ISBN 3-540-69933-3. http://books.google.com/books?id=xteiARU46SQC&pg=PA716#v=onepage&q&f=false. Retrieved 2010 Dec 11. 
  26. ^ a b Hui, Yiu H. (2006). Handbook of food science, technology, and engineering. Washington, DC: Taylor & Francis. p. 148-26. ISBN 0-8493-9849-5. http://books.google.com/books?id=Ac4D3_GHByEC&pg=PR26&dq#v=onepage&q&f=false. Retrieved 2010 Dec 8. 
  27. ^ Mark Keeney; Jenness, Robert; Marth, Elmer H.; Noble P. Wong (1988). Fundamentals of Dairy Chemistry. Berlin: Springer. p. 760. ISBN 0-8342-1360-5. http://books.google.com/books?id=uP2TYNs3wWoC&pg=PA760#v=onepage&q&f=false. Retrieved 2010 Dec 8. 
  28. ^ Daniel T. DiMuzio (2009). Bread Baking: An Artisan's Perspective. New York: Wiley. p. 24. ISBN 0-470-13882-3. http://books.google.com/books?id=kF5uI5uWjEMC&pg=PA24#v=onepage&q&f=false. Retrieved 2010 Dec 11. 
  29. ^ Paula I. Figoni (2010). How Baking Works: Exploring the Fundamentals of Baking Science. New York: Wiley. p. 150. ISBN 0-470-39267-3. http://books.google.com/books?id=XqKF7PqV02cC&pg=PA150#v=onepage&q&f=false. Retrieved 2010 Dec 11. 
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