Scaling Recipes: Help with Math for Perfect Portions

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Trying to scale a two-layer cake, 9" layers, to fit two 7" pans. The way I am figuring it: The original recipe is approx. 40 ounces of batter. I am multiplying 40 x 7 and dividing by 9, coming up with approximately 31 ounces batter for the 7 inch layers. Is this the correct formula to scale recipes, taking the diameter of the pan (or area in the case of square/rectangular pans) and the ingredient amount, and cross multiply/divide? On paper it would look like this: 40/9 and 31/7. Cross multiply top (40) to bottom (7) and divide by the other diameter (9) to come up with 31 ounces for the 7" pans. If there is a better way to scale recipes, please share! Thank you!!
 
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To scale properly, your recipe needs to be in weight measurements.


Scale round cake pan



ROUND I will use 8” & 10” pans for this example

STEP 1: FIND AREA OF THE TWO PANS

r² • π = AREA
(radius squared x pi = area)

Radius is 1/2 of the diameter of the pan
pi = 3.14
  • Find the radius: 8 ÷ 2= 4
  • Square the radius: 4 x 4 = 16
  • Multiply radius by pi: 16 x 3.14 = 50.24
  • Area of 8” round pan: 50.24

  • Find the radius: 10 ÷ 2 = 5
  • Square the radius: 5 x 5 = 25
  • Multiply radius by pi: 25 x 3.14 = 78.5
  • Area of 10” round pan: 78.5

STEP 2: DIVIDE THE AREA OF THE LARGER PAN INTO THE AREA OF THE SMALLER PAN TO SCALE UP

  • Area of 8” round pan: 50.24
  • Area of 10” round pan: 78.5
78.5 ÷ 50.25 = 1.56

The quotient 1.56 is used as the multiplier



STEP 3: MULTIPLY EACH INGREDIENT BY THE MULTIPLIER


To scale up to a 10” pan, multiple each ingredient by 1.56.
  • water 51.6 x 1.56 = 80.49 ml
  • semi-sweet chocolate 64.5 x 1.56 = 100.62 g
  • egg yolk 51.6 x 1.56 = 80.49 ml
  • canola oil 46.44 x 1.56 = 72.44

chocolate chiffon cake
5 - 8” cakesbaker’s percentages1 - 8” cake
water258 ml60.0051.8
semi sweet chocolate322.5 g75.0064.5
egg yolk258 g60.0051.6
canola oil232.2 ml54.0046.44
vanilla extract8.6 ml2.001.72
cake flour, sifted430 g100.0086
baking powder20 g4.653.99
baking soda5.71 g1.331.14
granulated sugar #1516 g120.00103.2
Egg whites455.8 ml106.0091.16
granulated sugar #2240.8 g56.0048.16
cream of tartar3.87 g0.0090.77
Total Batter WeightTotal Baker’s PercentagesTotal Batter Weight
2751.48 g638.99550.28
550g per 8” pan


=======================================
=======================================



To scale DOWN from 10” to 8” Step 2 changes as follows:



STEP 2: To Scale Down: Divide the AREA of the smaller pan into the area of the larger pan

50.35 ÷ 78.5 = 0.64

0.64 is the multiplier

Step 3 stays the same - multiply each ingredient by the multiplier.

0.64 is the multiplier
  • Water 51.6 x 0.64 = 33.0 ml
  • semi-sweet chocolate 64.5 x 0.64 = 41.28
  • egg yolk 51.6 x 0.64 = 33.0 ml
  • canola oil 46.44 x 0.64 = 29.72
 
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Thank you so much, Norcal Baker. The recipe I am using is from Ruth Levy Beranbaum, and she has metric values listed, so it will be easy to convert. Now I have to figure out the teaspoon amounts for some of the ingredients. I normally weigh my ingredients save for the teaspoon/tablespoon measurements. I don't work in metric, I should really get used to doing that!
 
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Thank you so much, Norcal Baker. The recipe I am using is from Ruth Levy Beranbaum, and she has metric values listed, so it will be easy to convert. Now I have to figure out the teaspoon amounts for some of the ingredients. I normally weigh my ingredients save for the teaspoon/tablespoon measurements. I don't work in metric, I should really get used to doing that!

Baking by weight is the most accurate. Once you convert to weight measurement, you won’t go back. There are too many benefits (scaling recipes; consist results; being able to analyze a recipe based on its baker’s percentages).

These are the common weights used in AMERICAN recipes. I emphasize American recipes because the standards for measurements are different with European recipes (UK liquid cup is 250 mL v. US 236 mL; US 1 oz = 29.57mL v. UK 1 oz = 28.41mL; US 1 pint = 16 oz = 473.18mL v. UK 1 pint = 20 oz = 568.28mL, etc.)


Salt weight varies by brand. This is due to grain size and shape. Diamond Crystal kosher salt is the preferred salt for pastry chefs.



Diamond crystal kosher 4 g/teaspoon

Morton kosher 4 g/ teaspoon

Table salt 7 g/teaspoon
Baking powder 5g/teaspoon

Baking soda 6/teaspoon

Sugar 200 g/cup


AP Flour 120 g - 145 g/cup depending on the recipe developer's method for filling a volume up. Spoon and level is around 120 g/cup (King Arthur Flour; most modest

Scoop and Level 145 g/cup (America’s Test Kitchen; most Serious Eats; some Stella Parks; Milk Street; Cook’s Country; Ina Garten; vintage recipes as this was the standard method until the 1990s)

Dorie Greenspan's recipes are about 136g/cup. Anna Olsen is a whopping 150g/cup for most recipes.


Cake flour (bleached flour) 113 g/cup

Vanilla extract 5 g/teaspoon

Large egg approximately 50 g

Milk 236 g/ cup

Cocoa powder 85 g/cup
 
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Baking by weight is the most accurate. Once you convert to weight measurement, you won’t go back. There are too many benefits (scaling recipes; consist results; being able to analyze a recipe based on its baker’s percentages).

These are the common weights used in AMERICAN recipes. I emphasize American recipes because the standards for measurements are different with European recipes (UK liquid cup is 250 mL v. US 236 mL; US 1 oz = 29.57mL v. UK 1 oz = 28.41mL; US 1 pint = 16 oz = 473.18mL v. UK 1 pint = 20 oz = 568.28mL, etc.)


Salt weight varies by brand. This is due to grain size and shape. Diamond Crystal kosher salt is the preferred salt for pastry chefs.



Diamond crystal kosher 4 g/teaspoon

Morton kosher 4 g/ teaspoon

Table salt 7 g/teaspoon
Baking powder 5g/teaspoon

Baking soda 6/teaspoon

Sugar 200 g/cup


AP Flour 120 g - 145 g/cup depending on the recipe developer's method for filling a volume up. Spoon and level is around 120 g/cup (King Arthur Flour; most modest

Scoop and Level 145 g/cup (America’s Test Kitchen; most Serious Eats; some Stella Parks; Milk Street; Cook’s Country; Ina Garten; vintage recipes as this was the standard method until the 1990s)

Dorie Greenspan's recipes are about 136g/cup. Anna Olsen is a whopping 150g/cup for most recipes.


Cake flour (bleached flour) 113 g/cup

Vanilla extract 5 g/teaspoon

Large egg approximately 50 g

Milk 236 g/ cup

Cocoa powder 85 g/cup
I agree with you, different chefs use different weight for flour, and there is a tremendous difference. The metric multiplier formula is very helpful for me to scale the major weight ingredients, I can then scale down the table/teaspoon items accordingly after I figure the main ingredients' weights. And since I started weighing ingredients many years back, everything is consistent now each time something is baked, no guesswork, no worrying about the humidity affecting ingredients. It's also nice to see recipe authors are beginning to put weight as well as cup amounts in their cookbooks.
 

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