Cake Pans


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Hello,

Is there a way to determine what pan size to use if I love a cake recipe meant for say 3, 8 x 2 pan. How do I scale up or down, irrespective of shape of pan (round/square)? Can I use the,area of s circle/square/rectangle to get it right? Is there a way to calculate for that, where the depth of the pan is 2/3 inches? In effect how can I scale up or down the batter without any leftover?

Thanks
 
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Hello,

Is there a way to determine what pan size to use if I love a cake recipe meant for say 3, 8 x 2 pan. How do I scale up or down, irrespective of shape of pan (round/square)? Can I use the,area of s circle/square/rectangle to get it right? Is there a way to calculate for that, where the depth of the pan is 2/3 inches? In effect how can I scale up or down the batter without any leftover?

Thanks
There’s two ways to do it.
bakers percentages. He would only use this if you were in large scale production.

The second way is to use the area of each pan. I’ll post later with a demonstration of each later.
 
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Btw, You don’t have to bake cakes in traditional cake pans. I frequently don’t even use cake pans, and a lot of pastry chefs don’t use them either.

instead I bake in a rimmed baking sheet. I get a nice 1” layer cake. I use cake rings to cut the size layers need.

Any leftover cake is then cut into small rings With a biscuit cutter and frozen. These are later made it into little individual cakes. So I have dessert on hand since I don’t run a business out of my home kitchen.

But for a business they can be used for wedding/event cake tastings for potential customers. Some event cake bakers will charge a nominal fee for the tastings; then apply the fee toward the purchase if they order a cake. But it kills two birds with one stone. It gives you the flexibility to cut whatever size layers you need. And it provide you with a number of samples.
 
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SQUARE and RECTANGLE PANS


Square and rectangle pans are easy. Just find the area of each pan.

STEP 1: FIND AREA OF THE PANS

Multiply the width by the length

7 x 7 = 49

9 x 9 = 81


STEP 2: DIVIDE THE AREA OF THE LARGER PAN INTO THE AREA OF THE SMALER PAN

81 ÷ 49 = 1.65

The quotient 1.65 is used as the multiplier



STEP 3: MULTIPLY EACH INGREDIENT BY THE MULTIPLIER

To scale up to a 10” pan, multiple each ingredient by 1.65


From the example chocolate chiffon cake recipe:
  • water 51.8 x 1.65 = 85.47 ml
  • semi sweet chocolate 64.5 x 1.65 = 106.42 g
  • egg yolk 51.6 x 1.65 = 85.14 ml
  • canola oil 46.44 x 1.65= 76.62 ml


examples of rectangle pans

Find the area of the pans
7 x 11 = 77

9 x 13 = 117

Divide the area of the larger pan into the area of the smaller pan
117 ÷ 77 = 1.51



multiplier is 1.51



SCALE DOWN

If you want to scale down from a 9 x 13 to a 7 x 11, then just do the opposite


Divide the AREA of SMALLER PAN into the AREA of the LARGER PAN


77 ÷ 117 = .65


to scale down from a 9 x 13 to a 7 x 11 use .65 as the multiplier.

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



STEP 1: FIND AREA OF THE PANS

r² • π = AREA

(radius squared x pi = area)

Radius is 1/2 of the diameter. 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 SMALER PAN


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

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

NOTE: to scale DOWN from 10” to 8”

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


50.35 ÷ 78.5 = 0.64


0.64 is the multiplier to scale from a 10” pan to 8” pan. This recipe is not scaled for a 10” pan, but if it were you would multiple each ingredient with 0.64.


  • 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


example 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
 
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Scaling a cake recipe to a deeper pan is not an exact science. It’s more an estimate because when the depth of the pan changes, you have to calculate the volume of a cylinder. But you don’t full a cake pan to capacity, so you have to figure out how much of that cylinder you want to use.

I will use 8” x 2” and 10”x 4” in this example

pi x radius² x height = volume

  • Find the radius: 8 ÷ 2= 4
  • Square the radius: 4 x 4 = 16
  • Multiply radius by pi: 16 x 3.14 = 50.24
  • Multiply the area by height: 50.25 x 2 = 100.48
  • Volume of an 2” x 8” pan is 100.48


BUT we don’t fill the cake pan to capacity. So use 75% of the volume to figure out the multiplier


100.48 x .75 = 75.36

volume of 8” cake = 75.36


Now repeat the steps for the 10" cake pan.

  • Find the radius: 10 ÷ 2 = 5
  • Square the radius: 5 x 5 = 25
  • Multiply the radius by pi: 25 x 3.14 = 78.5
  • Multiply the area by height: 78.5 x 4 = 314

The volume capability of the 10" x 4" pan is 314

  • Calculate 75% of the volume


314 x .75 = 235.5

  1. Calculate the difference in volume between the original 8" pan and the 10" pan. Divide the larger size pan into the small size pan
  2. 235.5 ÷ 75.36 = 3.125

3.125 is the multiplier.

  • Water 51.6 x 3.125 = 161.25 ml
  • semi sweet chocolate 64.5 x 3.125 = 201.56 g
  • egg yolk 51.6 x 3.125 = 161.25 ml
  • canola oil 46.44 x 3.125 = 145.12 ml

REMEMBER when scaling for pans of SAME height, do not factor in pan heights. Just calculate area. Area = pi x radius² .



Keep in mind volume calculations are for maximum capacity of the pan. Cake pans are never filled to maximum capacity to allow room for the batter to rise. The assumption is the original recipe has been scaled to allow for the appropriate rise. So when you make conversations, the are based on proportions and the rise of the original recipe.



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
 
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If you are in production, and you know how much batter your different cake pans hold, then you can simply use baker’s percentages to mix the amount of batter you want. It’s late here, so I will try to post the BP’s tomorrow.
 
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Just a very small thing to add, but for people who find the calculations a bit confusion, for round pans, you'll note that the pi technically cancels out. So you really only need to deal with the radius squared of each pan.

Example: Converting an 8" pan to a 10" pan, assuming equal heights
  1. Radius squared of 8" pan = 4*4 = 16
  2. Radius squared of 10" pan = 5*5 = 25
  3. Multiplier = 25/16 = 1.56
And you can simplify the calculation even further by just dividing the radiuses then squaring that.
  1. Divide the radiuses: 5/4 = 0.8
  2. Multiplier = 0.8*0.8 = 1.56
It's not much of a simplification, but I've noticed that some people are just intimidated or confused by having to use pi and memorizing these equations, so figured it might help someone to provide a shortcut that simplifies it as much as possible.
 
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Just a very small thing to add, but for people who find the calculations a bit confusion, for round pans, you'll note that the pi technically cancels out. So you really only need to deal with the radius squared of each pan.

Example: Converting an 8" pan to a 10" pan, assuming equal heights
  1. Radius squared of 8" pan = 4*4 = 16
  2. Radius squared of 10" pan = 5*5 = 25
  3. Multiplier = 25/16 = 1.56
And you can simplify the calculation even further by just dividing the radiuses then squaring that.
  1. Divide the radiuses: 5/4 = 0.8
  2. Multiplier = 0.8*0.8 = 1.56
It's not much of a simplification, but I've noticed that some people are just intimidated or confused by having to use pi and memorizing these equations, so figured it might help someone to provide a shortcut that simplifies it as much as possible.
shortcuts are great. But the problem a shortcut is if you forget how to to it then how do you look it up?

The formula for an area (And volume) is a fundamental formula. So you can always look up the formula.

r² • π = AREA

Math is used in baking to ensure consistency and uniformity. And you can always look up the math formulas like area and volume to see how to calculate it.
 
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Akos, when a baker usually knows the amount of batter they use per cake for their various pans. In production the flow of business changes daily. So production is adjusted accordingly. And bakeries will often cakes in a couple of sizes. So baker’s percentages allow for easy scaling on a larger scale.

As a home base baker, you can also use baker’s percentages to mix specific amounts of batter—assuming of course you know how much batter you want.

Step 1: calculate the amount of batter you need

  • six 4” cakes 275 g batter each
  • 6 x 275 = 1650 g total batter needed


Step 2: calculate 1% of the baker’s percentage

  • Divide the total weight of the batter you need (1650 g) by the total baker’s percentage (638.99 see example recipe)
  • 1650 ÷ 638.99 = 2.58
the quotient is the multiplier


Step 3: Multiply each ingredient with the multiplier

to make six 4” cakes 275 g batter each

  • Water 258 x 2.58 = 665.64
  • Semi sweet chocolate 322.5 x 2.58 = 832.05
  • egg yolk 258 x 2.58 = 665.64
  • canola oil 232.2 x 2.58 = 599.07


It doesn’t matter how much batter you need, just apply the steps and the ratios will stay the same

five cakes with 650 g batter each

  • 5 x 650 = 3250

divide the total amount of batter needed with the total baker’s percentage

  • 3250 ÷ 638.99 = 5.08

5.08 is the multiplier.
  • Water 258 x 5.08 = 1310.64
  • Semi sweet chocolate 322.5 x 5.08 = 1638.3
  • egg yolk 258 x 5.08= 1310.64
  • canola oil 232.2 x 5.08 = 1179.57


example 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
 
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Hello hello Cate,

OMG! Words have escaped me. Thank you so very much. Wow. When it comes to the knowledge of the science of baking, you're awesome; and now the math. Wow.

I have read 3 articles about the topic I posted but didn't understand the way you have explained to me in detail. Thank you. I will prefer to use the second option of using the area of the pan. From this explanation, I can work with different pans eg 8"round to 10" square, and also pans with different heights. Thanks so much. I really appreciate. I'm going to make it practical and send feedback. Thank you once again. This is a reply to all your answers to my post. Please write a book.
 
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Hello hello Cate,

OMG! Words have escaped me. Thank you so very much. Wow. When it comes to the knowledge of the science of baking, you're awesome; and now the math. Wow.

I have read 3 articles about the topic I posted but didn't understand the way you have explained to me in detail. Thank you. I will prefer to use the second option of using the area of the pan. From this explanation, I can work with different pans eg 8"round to 10" square, and also pans with different heights. Thanks so much. I really appreciate. I'm going to make it practical and send feedback. Thank you once again. This is a reply to all your answers to my post. Please write a book.
you are welcome Akos. I posted them separately in hopes they would be less confusing. It seems like an overwhelming amount of information. But when you put it to use, it becomes familiar and simple.

I do want to write a cookbook. The books on the market leave much to be desired.
 
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Hello,

Is there a way to determine what pan size to use if I love a cake recipe meant for say 3, 8 x 2 pan. How do I scale up or down, irrespective of shape of pan (round/square)? Can I use the,area of s circle/square/rectangle to get it right? Is there a way to calculate for that, where the depth of the pan is 2/3 inches? In effect how can I scale up or down the batter without any leftover?

Thanks
easiest method is just fill the pan with water and measure it.
 

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