Cake

June 22, 2015

Every week, baking expert Alice Medrich will be going rogue on Food52—with shortcuts, hacks, and game-changing recipes.

Today: Alice Medrich's famous brownies are made in an 8-inch pan, but you'll want to make a sheet pan-worth. Here's how you can make that happen with just a little math.

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The brownie recipe you want to make calls for an 8-inch square pan, but your only square pan is a 9-inch. Should you risk it? Maybe you want to double or triple a recipe but you aren’t sure which pan to use, or maybe you have a specific large pan but don’t know how many times to multiply your recipe in order to fill it.

The answers to these and similar questions (asked endlessly in cooking classes!) do not involve rocket science, but just enough elementary school math to calculate the area of a square, rectangle, or circle. I love the math (and I’ve included a little math review below if you want to brush up), but I’m sharing my chart in case you don’t have my thing for math.

The handy list below (or some basic math, also explained below) will tell you the surface area of your pan. Once you know the area of any pan, you can compare it to the area of another pan to see how much bigger or smaller it is. You can divide the area of a large pan by the area of a small pan to figure out how many times to multiply a recipe to fill the larger pan with the same depth of batter (more on that later).

Handy list (with the numbers rounded up to the nearest inch):

Area of square/rectangle pans:

• 6 x 6 = 36 square inches
• 7 x 7 = 49 square inches
• 8 x 8 = 64 square inches
• 9 x 9 = 81 square inches
• 9 x 13 = 117 square inches
• 12 x 16 (half-sheet pan) = 192 square inches

Area of round pans:

• 5 inch = 20 square inches
• 6 inch = 29 square inches
• 7 inch = 39 square inches
• 8 inch = 50 square inches
• 9 inch = 64 square inches
• 10 inch = 79 square inches
• 12 inch = 113 square inches

Geometry review:

I don’t always have the chart at hand; I often just do the math!

For squares and rectangles: The area of a square or rectangular pan is calculated by multiplying one side times the other side. The area of an 8-inch square is 64 square inches because 8 x 8 = 64; the area of a 9 x 13-inch pan is 117 square inches because 9 x 13 = 117. Easy.

For rounds: The area of a circle equals π times the radius squared. In case you don’t remember, π = 3.14; the radius of a circle is half of its diameter; and squaring means multiplying a number by itself. Ready? To calculate the area of an 8-inch round pan, multiply 3.14 (π) by 4 (because it’s half of 8) times 4. Thus, the area of an 8-inch circle is 3.14 x 4 x 4, approximately 50 square inches. Not so hard!

Just by glancing at the two pans, you might think that a 9-inch pan is very close in size to an 8-inch pan of the same shape, thus making it a reasonable substitute. But if you check the chart, you’ll find that a 9-inch square pan is more than 25% larger than an 8-inch square pan. (The relationship between a 9-inch and 8-inch round pan is similar.) Such a considerable difference will result in a 9-inch batch of very thin brownies that may be over-baked by the time you check them for doneness (because thin brownies bake faster than thick ones). Knowing this beforehand, you can increase the recipe by 25% for results as thick than the original recipe intended. If you want brownies that are even a tad thicker than the original recipe, you can even increase the recipe by 33%.

Let's try an example: How many times should you multiply an 8-inch brownie recipe to fill a 9- x 13-inch pan or a 12- x 16-inch half sheet? To figure this out, divide the area of the larger pan by the area of the 8-inch pan.

• For the 9- x 13-inch pan: 117 divided by 64 = 1.82, which is close enough to 2 that you can confidently double the recipe for the larger pan.
• For the half sheet: 192 divided by 64 is exactly 3, so you can multiply the recipe times 3.

Using similar math, you can calculate how many times to multiply the recipe for a round cake to make a large rectangular sheet cake. And don’t forget that you don’t always have to multiply recipes by whole numbers—it’s perfectly fine to multiply a recipe by 1 1/2 or 2 2/3.

About now, you might be wondering about eggs. It’s nice if you can increase recipes so that you don’t have to deal with fractions of eggs—by increasing a 2-egg batter by 1 1/2 or a 3-egg batter by 1/3 or 2/3, for example—but it is not essential.

Here’s what to do if you multiply a recipe and end up needing part of an egg: Set aside any whole eggs you need. Next, whisk the other egg to blend the white and yolk; weigh it (preferably in grams); then weigh out the fraction of the egg that you need for the recipe and add that to the whole eggs. If you need 40% of a 50-gram egg, that’s 20 grams of the whisked egg. When egg whites and yolks are used separately, weigh and measure them in the same way, but separately. Add leftover egg parts to your morning scramble. See, no waste and still no rocket science!

The chart (or your ability to do the math) is extremely valuable: Use it but don’t be a slave to it. When I make brownies in a large quantity, I like them to be about the same thickness as they are in a small batch, so I stay close to the chart. But, when I increase the dimensions of a birthday cake, I often make it a bit taller than the original (in other words, I round up when multiplying) because the proportions are visually more pleasing. For example, if I am making a 12-inch round cake using a recipe meant for an 8-inch pan, I divide the area of the 12-inch round pan (113) by the area of the 8-inch round (50 inches) and get 2.26. But instead of multiplying the recipe by just 2.26, I might multiply it by 3 so that the cake will turn out tall and lofty. See: Love the chart, but don’t let it bully you!

When you round things up like that, don’t go overboard: Pans should not be filled more than about 2/3 full or batter may overflow. If you do end up with too much batter, scrape the excess into cupcake molds or a mini cake pan—bonus cakes never go uneaten!

When you increase recipes and bake in larger pans, you should anticipate longer baking—anywhere from a little longer if the pans are filled to the same level as the original recipe to considerably longer if you are making the cake taller by filling the pan a bit more. If you are making a smaller amount of the recipe, check earlier than you think you need. And always use a cake tester to check to see if the cake is finished.

Pick up a copy of Alice's new book Flavor Flours, which includes nearly 125 recipes -- from Double Oatmeal Cookies to Buckwheat Gingerbread -- made with wheat flour alternatives like rice flour, oat flour, corn flour, sorghum flour, and teff (not only because they're gluten-free, but for an extra dimension of flavor, too).

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See what other Food52 readers are saying.

GBChelle May 25, 2019
Hi! I found Ina Garten’s recipe for brownies that makes a sheetpan (12x18). But I love my brownies thick. Do you think it would work to make them in a 9x13 pan and just bake them longer? Or will that just be too much batter and the weight of all of that better would cause them to sink in the middle and not cook properly?

Sara May 3, 2019
Hello,
This post is extremely helpful. Especially the chart. However, I’m having some uncertainty with scaling down, which seems to be what I need to do based on the volumes. I’m trying to determine how to scale the recipe/ingredients of three 8” rounds to one 9x13. Please help!
Thank you!
Sara

Don B. May 4, 2019
simple question, but it can be a little tricky. your original recipe for three 8" rounds has a surface area of about 151 square inches, whereas your 9"x13" pan has a surface area of 117 square inches. therefore, to fill your rectangular pan to the same depth as the three round pans, you'll need about 22% less batter (that's (151-117)/151 = .22 ). so, for example, if your recipe calls for 5 cups of flour, you'll actually need about 3.9 cups of flour.

Sara May 4, 2019
Oh boy, that’s a bit tricky. Thank you very much for the reply.

Sara May 4, 2019
I actually just thought of a clever solution! Make the recipe as is, weigh the finished batter, and remove about 1/4 (or as close to 22% I can get) of it, and use that for a few cupcakes. You’re reply was very helpful. Now I truly understand how to scale a recipe down with your example and calculations. Thank you again!

Don B. May 4, 2019
great idea. let me know when I can come over for a cupcake :)

Lorie P. April 30, 2019
So I did the conversion also using another method and using this method and another method my answer comes to roughly 1.8, my question is, is this the same factor you use if using multiple Cake layers? Recipe I’m using calls for 6, 6 inch rounds however I’m using 6, 8 inch rounds?

Don B. April 30, 2019
Yup. going from a 6" round to an 8" round of the same depth means you need to multiply your recipe by 1.8, which is (8/6)^2 .

Lolly April 17, 2019
Hi

I just found the most perfect cake recipe which may sound strange to most people but I am allergic to eggs, milk and have celiacs disease so cannot have wheat either. I haven’t had cake for a lot of years now well not without being ill :-/ The recipe I found is the first one to not have odd stuff in like a lot have chickpea flour which does not appeal to me and other various odd things.... whole other story... Anyhoo the recipe calls for a 9 inch round cake tin and says cook for 30-35 mins. I only have 8 inch cake tins which I do love and I have had a go at using which it looked absolutely perfect consistency when I was putting into the tins before it went into the oven.... I checked at 35 mins (not thinking of the relevance of the size) and it looked pretty good but wasn’t done (so gave another 5 and checked then another 5) looked really good and squewer came out clean... obviously out of practice at making cakes and forgot the whole opening the door who ha so collapse situation.. tastes good though! Do you think the time was right in total so next time if I did for 45 without opening the oven it would be ok or any theories on maths with the time for the smaller tin. Please let me know. May just have to suck it up and go buy 2x 9inch ones! Many thanks x

Martha April 1, 2019
Our household is down to two and I plan to start baking deserts in a six-inch round cake pan. I have a good sense from this article about how to cut down the ingredients. Is there a general rule of thumb about how to translate cooking times (many recipes call for an 8 or 9 inch round cake pan, same depth). Apologies if I have missed that herein!

Sabrennah March 24, 2019
What if you wanted to do the opposite? Such as scaling down a recipe. I want to take my cake recipe, that calls for a 9 inch round and make 6 inch rounds with it...not sure how to cut the recipe in halve correctly? Thanks for any help!

Don B. March 25, 2019
the math works the same scaling down as scaling up. One 6" round will use about 44% of the recipe of one 9" round. (44% is close enough to half as should make no difference.) So your recipe for a 9" round should make enough cake for two 6" rounds. (Or you could just halve the ingredients and make one 6" round.)

Jeff February 1, 2019
How do I calculate from 8 round to cupcakes? Would the area math work for cupcakes and if so, is their a standard size for a cupcake?

Xan January 28, 2019
I'm baking brownies and the recipe calls for an 8x8 pan but i want to bake it in a 9x9 pan. I followed your computation and end up to 1.50. How can i double my recipe?

Salma January 20, 2019
I want to halve a recipe that calls for a 9 inch springform pan. What size pan should I use instead?

Don B. January 21, 2019
To fill the pan to the same depth, you'll want to use a pan that's 6.3” in diameter (or as close as you can get) - that's 9” divided by the square root of 2 (0.707).

Annie January 19, 2019
I’m making cornbread and have a 9” square pan, not the 8” a square pan called for in the recipe. How do I adjust the cooking time?

Lori December 29, 2018
I am making a Strawberry dessert with pretzel crust that requires a 9 by 13 pan. I would like to make one and a half times that amount do not want to completely double the recipe what size pan would I use?

Don B. December 29, 2018
many possibilities. how about a 13" x 13" square pan. that will be close to your 1 1/2 times amount.

Alexine B. December 19, 2018
Im making a 1/8 in cake, what size cake pan do I use?

Don B. December 19, 2018
what do you mean by 1/8 in? do you really mean it's 1/8 inch thick?

Diana December 18, 2018
Sorry. I have a recipe for spice bars that calls for a 17x11x1-1/2 baking pan. Can someone please give a substitution. I can't find this size pan anywhere. I think it is from way back. Please help. I asked for help but put the wrong size. It is a 17x11x1-1/2 pan substitution I'm looking for. Help

Don B. December 19, 2018
you don't say what size baking you want to use. assuming it's a standard size, say 9" x 13", then you'll need about 2/3 (actually about 62.5%) of your current recipe.

Diana December 18, 2018
please help me. I have a TBI but, want to make a recipe for spice bars which uses a 17x111x1-1/2 inch pan that is measured from the inside. I don't have this size pan so what can I substitute? Cab somebody help?

Shelley K. December 5, 2018
Im working in a camp with over 200 people and we need to bake with the large industrial sheet pans.. for things like nanaimo bars date aquares etc..how many times would i double the recipe?? 4 or 5?? Plz help. Shelley

Neha October 10, 2018
Very useful article for increasing the volume of cake and what pan size to use.

I would appreciate if you could also tell how to decrease a recipe to fit a smaller pan
For example an 8 x 2” pan using 6 eggs And 2 cups almond flour.
To halve the recipe what pan size will work best?
[email protected]

Emily J. September 12, 2018
So I have a chocolate cake recipe that makes 3 8" rounds. I want to make a rectangle cake and I have a 9x13 pan. So would 1 batch of cake be enough? If I split it between two 9x13 pans, I'd have thinner layers to stack?

Siv September 1, 2018
Hi! I am hoping you can help me! I have a carrot cake receipt that calls for 2 9 inch round pans. I am trying to convert it to a 3 tier cake. Pan sizes: 3x2, 5x2, 7x2. How do I convert that? Thank you!