*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.*

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

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

Neha
October 10, 2018

Very useful article for increasing the volume of cake and what pan size to use.<br /><br />I would appreciate if you could also tell how to decrease a recipe to fit a smaller pan<br />For example an 8 x 2” pan using 6 eggs And 2 cups almond flour.<br />To halve the recipe what pan size will work best?<br />Thank you in advance for your advice<br />[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!

Adele
July 26, 2018

Hello, Just to make sure I get this right...if I have a recipe for an 8 or 9 inch cheesecake...what do I do if I want to use a 6 inch pan? Thanks!

Jerrie
July 22, 2018

Hi, my query is about baking in 3in deep pans. A couple of sites suggest x number of cups per pan using a 3in deep pan but the volumes differ significantly. Do you have a suggestion on the volume required for a 6x3in, 8x3in and 10x3in deep pan? I want to avoid underfilling as I've read this inhibits rising and overfilling where the cake dries out from taking too long to set or doesn't set snd sinks in the middle. <br /><br />Thanks

Lissa J.
July 18, 2018

Thanks for replying. I have a favorite chocolate cake that uses 2, 8 inch pans and other cakes that use 9 inch pans. My 6 inch pan is round and 2 1/2 inches deep.

Lissa J.
July 17, 2018

Hi This is very good information. However, I am now cooking for one, after losing my husband. I love desserts and would like to know how to reduce the size of a cake to a 1 layer 6 inch pan. Thanks

Don B.
July 18, 2018

Very sorry about the loss of your husband. However, you haven't provided enough info to answer your question. Do you have a current recipe you'd like to reduce? What type and size pan is it he current recipe? Is the new 6” pan circular, square , or ?? Etc.

Denise M.
July 13, 2018

In reference to my question:<br />1/3 cup - whites of 2 large eggs<br />3/4 cup - whites of 4 large eggs<br />Just need conversion from large egg white amounts to 7 JUMBO egg whites.<br /><br />

Denise M.
July 13, 2018

If I have a cake recipe that calls for 7 Jumbo Egg Whites.<br />How many cups of egg beater egg whites do I need? They are considered large in the container.<br />

Denise M.
June 29, 2018

Carrot Cake<br />2 ½ cups all-purpose flour<br />1 ¼ tsp. baking powder<br />1 tsp. baking soda<br />½ tsp. table salt<br />1 ¾ tsp. ground cinnamon<br />½ tsp. ground nutmeg<br />⅛ tsp. ground cloves<br />1 lb. peeled carrots, (about 6 to 7 carrots)<br />1 ½ cups granulated sugar<br />½ cup packed light brown sugar<br />4 large eggs<br />1 ½ cups vegetable oil <br /><br />For the Cream Cheese Frosting:<br />10 Tbsp. unsalted butter, softened to room temperature<br />3 cups confectioners' sugar, sift if lumpy<br />1 ½ tsp. vanilla extract<br />¼ teaspoon salt<br />2 Tbsp. sour cream (optional, but adds a tangier taste and creamier texture)<br />1 lb. COLD cream cheese, (brick-style cut into 1-inch pieces<br /><br />This recipe is mainly for (3) 8 inch round layers or (2) 9 inch round layers---the depth pans are 2 <br />inches.<br /><br />Can you convert this recipe for me to (3) 9 inch round layers-depth pans are 2 inches.? I really appreciate your help with this.....<br /><br />

Don B.
June 30, 2018

If this recipe works for either 3 8" round layers or 2 9" layers, then to get 3 9" layers of the same depth, just multiply the recipe for the carrot cake by 1.5 (i.e., increase it by 50%). As for the frosting, assuming the entire top and sides are frosted, and assuming there is frosting between the layers, do the same - just add 50% to the recipe.

Lola
June 18, 2018

I have a recipe that calls for a 9x13 square pan, however I would like to use a 9inch round tin to bake a cheesecake. Would I need to cut my recipe in half? What would be your best advice for this?<br /><br />Thank you!

Don B.
June 19, 2018

Roughly, yes, cut your recipe in half. (The actual amount is 54% of your original pan.)

Lola
June 19, 2018

Thanks Don!<br /><br />So would be it best to them use an 8inch, so the measurements are exactly half? What cooking time would you recommend?

Don B.
June 19, 2018

Lola,<br />If you mean an 8" square pan, then it is still approximately 55% of the original 9" x 13" pan. If you mean an 8" round pan, it is only about 43% of the 9" x 13" pan. So you're better off with either the 9" round pan or the 8" square pan to be close to your 50% estimate. (The difference of 4% or 5% from 50% isn't enough to matter, so you can just make half the original recipe. But none of them are *exactly* 50% of the original recipe.)<br /><br />As for cooking time, I think the new cooking time should be pretty close to time in the original recipe since the heat will mainly enter from the bottom and top. By cutting the recipe in half for the 8" square or 9" round pan, the depth of the batter will be about the same as in the original 9" x 13" pan, so the cooking time should be roughly the same. To be safe, I'd probably starting checking for doneness at around 80-90% of the original cooking time. Good luck. Let me know how it turns out.<br />Don

Lola
July 2, 2018

Hey Don,<br /><br />The recipe came out delicious!! I halved the recipe and baked it for the same amount of time. My cheesecake cracked pretty bad (which has never happened before) but I think that had to do with using a fan-forced oven and not realizing I had to adjust the temperature. <br />Thanks for your help! I will try making this again and adjusting the temperature.

Don B.
July 2, 2018

yes, a forced-fan (convection) oven will heat the cake more quickly, so lower the temp by 25 degrees or so. (or just turn off the convection feature.)

Sara
June 15, 2018

Hi, <br /><br />just a quick question. I want to change a brownie batter that is for a 16cm*16cm square tin, to at 16 cm round tin. Ive done the calculations, and i take every ingredient*0,78 and i think this is correct. However, i am stuck with the baking time. The original recipe calls for 25 minutes baking at 175 degrees celsius. Would i change the baking time? I am so afraid to get a dry brownie

Don B.
June 16, 2018

Hmm. You're right about the change in the batter amount, but the cooking time is not so clear. Since the perimeter of the round tin is less than that of the square, and the distance from the edge to the center is also mostly less than that for the square tin, I'd think the cooking time will be less as well, but not by a lot, especially since most of the heat enters from the top and bottom; that distance should be the same for both tins. Nonetheless, I'd start checking with a toothpick at around 20 minutes (which you should probably do even if staying with the original tin).

Samantha H.
May 30, 2018

Hi there! This is very helpful. Just curious about chemical leavener. If you're scaling up in pan size, let's say you're going from a 6 x 2 to a 10 x 2, is the baking powder converted in the same proportions as the rest of the ingredients, or should it be treated differently/reduced? And if it should be reduced, is there a set amount to lower it by?

Lilaloa
May 24, 2018

I have a recipe for a 9" round cake that I need to convert into a 10" SQUARE cake. 😫 If my calculations are right, the 1.56 can be safely rounded up to 2?<br />Here is the recipe:<br />1&1/4 cup cake flour<br />1&1/4 tsp baking p<br />1/2 tsp baking s<br />1/2 tsp salt<br />3/4 cup sug<br />1/2 cup oil<br />1/2 cup buttermilk<br />1&1/2tsp v extract<br />I feel like my math is wrong & that this will be a disaster.

Don B.
May 24, 2018

Yes, you can round the 1.57 up to 2 (i.e., double all the ingredients), but you will have an extra 27% in depth, so adjust your cooking time accordingly. alternatively, use only 3/4 of the batter your recipe yields to fill the 10" pan to the same depth as the 9" pan. finally, be sure to check the doneness of the cake frequently after the time the original recipe says it should be done, since the cooking time will be different ( a bit longer) for the 10" pan.

Lilaloa
May 24, 2018

BLESS YOU. THANK YOU. I should state that the batter is always thin for the 9" round (its supposed to be), and because of that I have to pour 1 batch into 1 pan, then repeat for the second . Bake time is 25 min.<br />***Bc it's thin, I've never been able to split it b/w two pans and I doubt I'll be able to for the 10" sq, despite it being doubled. 😫 (Or can I 😲🤔)<br /><br />So since I'll have to double, I'm guessing 35-45m bake time @350° is safe? I'll also likely have to double ingr-whisking time....

contessa W.
April 12, 2018

i have a recipe that is for 2-8 inch round cake tins. i want to make a wedding cake that is a three tier 6'', 9'', and a 12'' how can i convert that?

Don B.
April 13, 2018

assuming you want each of the 3 tiers in your desired cake to be the same thickness as one of your 8" cake tins, you will need a little over twice as much of the recipe. The total volume of the 2 8" cake pans is 100.5 x h, where h is the height of the cake pan; so if the 8" cake pans are 2" deep, they have a total volume of 201 cubic inches. The 3 tiers, each of height h, will have a volume of 205 x h; so, for h = 2", the 3 tiers have a volume of 410 cubic inches, or a little over twice the recipe for the 2 8" cake pans.

Colin
April 10, 2018

Thank you for this! Extremely useful. I’m just wondering if the oven temperature would need to change when scaling up a recipe?

Carla S.
March 7, 2018

I have a recipe that calls for 2, 8" round cake pans. I would like to make 2, 9x13 pans instead. By your math, I should be able to do 1 double batch per 9x13 pan - right? Thank you!

Don B.
March 8, 2018

I'm not quite sure what you mean by a "double batch per pan", but your 2 8" round pans have a total area of about 100 square inches, while your 2 9"x13" pans have a total area of 234 square inches. So your recipe which fills the 2 round cake pans would not quite fill one of the rectangular pans. Hope this answers your question.

Denise M.
March 7, 2018

need help converting cake recipe from (3) 9" round layers to (3) 10" round layers<br /><br />Cake (3-9inch layers)<br />2 box White cake mix<br />16 oz sour cream<br />½ c Vegetable oil<br />6 eggs<br />15 oz can Cream of Coconut (such as Coco López)<br /><br />Frosting<br />16 oz cream cheese<br />4 Tbsp. milk<br />2 lbs. Powdered Sugar<br />2 tsp. Vanilla<br />4 bags (about 24 oz.) Fresh Frozen Coconut<br /><br />Please help...need it today ([email protected])<br />

Don B.
March 7, 2018

Assuming you want the same thickness layers in the 10" layers as in the 9" layers, your new cake will have almost 25% (actually 23.4%) more volume in it. Therefore, you will need about 25% more ingredients, which computes as (for the cake): 2 1/2 boxes white cake mix; 20 ox sour cream; 5/8 c (5 oz) vgetable oil; 7 1/2 eggs; and 19 oz Cream of Coconut. The amount of frosting depends on the surface area, not the volume, of the cake. The relative surface area of the two cakes depends on both the diameter of the cakes as well as the heights (thicknesses) of the cakes. Without knowing the different thicknesses, it's impossible to determine exactly the amount of increase in the frosting recipe. However, let's make an assumption that both cakes are both 8" high (including all three layers). Then the 9" cake has an area of about 707 square inches, and the 10" cake has an area of about 817 square inches, so you will need about 15% more frosting. (This assumes that there is no frosting between the layers. If there is a half inch of frosting between the layers - which means two layers of frosting plus the top surface, then you'll need about 18% more frosting total for the 10" cake as opposed to the 9" cake.)

JuJu
March 1, 2018

Nothing beats the math, especially when one may have an irregular-sized pan, and the article above is great in explaining area and circumference.<br /><br />For folks, however, who shy away from the math and want to know the capacity of common-sized baking pans, enter in your browser, the search phrase, "baking pans volume or capacity," to see a few other sites that provide a list for other common sizes and capacities in addition to the ones above.<br /><br />You'll still need to do a bit of math if comparing capacities, as ecplained in the article, but this may help folks with cup capacity when comparing.<br /><br />Don't forget that regardless of capacity, fill only 2/3 full as this article states, to prevent over-flow.

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