*- Apparently, this post contains some metamathematical errors. I’ve since updated and simplified the formula. You can find the new, updated (and correct!) formula here. – *

Welcome to Thesis-Land! The land of academic despair and self-doubt! Look to your left and you’ll see the Marshes of Hours Lost and on your left rises the Paper Mountain of Discarded Ideas!

No, I’m just kidding. The work on my thesis is actually going pretty well. Sure, I’m a bit stuck on Norbert Elias and his theories on sociogenesis (socio-what-the-sis???) at the moment, but I’ve also found another great book which is being shipped to me as we speak! So, all in all, I’m pretty happy! Plus, I’ve learned a valuable lesson from my daily tear off block calendar today. I’ll share it with you. Because I’m *that* kind of person. Here’s how it goes:

*Happiness never decreases by being shared. *

Isn’t that beautiful? It’s from Buddha! There’s also a part about candles and the life-expectancy of candles in general, but I will not bore you with that. I didn’t really get that part, anyway… But hey! What I’m really trying to say is this: I’m happy and I want you (yes, you!) to be happy too! So I came up with something interesting that will completely change the way you look at your (round) cake pans! Sounds exciting, right?

### Where is my 7-inch cake pan? Do I even* have* a 7-inch cake pan???

First, imagine being in the kitchen. If you’re anything like me, you have too much cake pans. If you don’t, imagine yourself having a lot of cake pans. Again, you’re in your kitchen, and your getting ready to bake a cake. Say the recipe you want to make calls for an 8-inch springform pan, and all you have is a 9-inch springform pan. Or, even worse, you don’t even *have* a springform pan and all you have is a regular round 9-inch cake pan. Or, you have an 8-inch cake pan, a 10-inch cake pan and even a 12-inch cake pan, but not a 7-inch cake pan!

It’s the worst! Especially if you’re halfway through a recipe…

So, second lesson today: always read through the entire recipe before you start baking. It’s not by Buddha. It’s by the Eternal Forces of the Universe. Which means, um, me… Not that I always follow that advice, but it’s great advice nonetheless. Believe me, it’s better for your sanity… And truth be told, I really* try* not to skip this whole read-the-recipe-before-you-start-step. But what can I say, I have the patience of a two-year-old…

But aaaaaanyway, I’m here to make you happy. Not by learning you about life, but by learning you about pans. Cake pans. Round cake pans to be exact! Sometimes you need a particular size cake pan. A size that you just don’t have, no matter how many times you rummage through your cake pan cupboard. At times like that, you may find yourself surfing the world wide web in order to find out if you can use one of your other pans. Usually, what you’ll find is something like this:

Pan Size | Volume | or… | Pan Size | Volume |
---|---|---|---|---|

6 x 2 inches | 4 cups | 18 x 5 centimeters | 1280 mls | |

8 x 2 inches | 6 cups | 20 x 5 centimeters | 1570 mls | |

9 x 2 inches | 8 cups | 22 x 5 centimeters | 1900 mls |

Yeah… So not helpful! I don’t need to know how much water goes into a 6-inch pan! I need to know if I can use one of the pans I already have instead of the pan the recipe calls for!

Enter: the Round Cake Pan Conversion Formula!

### Why You Need The Round Cake Pan Conversion Formula

Let’s say that you find yourself in a situation where all you have is a 22-cm/9-inch cake pan, while the recipe you want to make calls for a 25-cm/10-inch cake pan. If you were to use your smaller cake pan, you would quickly find out that the amount of batter the recipe makes is too much for your smaller pan. Best case scenario? You realize this before the pan is in the oven and decide to not pour all the batter in. That could happen.

Another thing that could happen is: you pour all the batter in your cake pan only to find out that, once it’s time to pull the cake out of the oven, it isn’t done yet. You decide to give the cake another few minutes in the oven, which eventually leads to a done cake with a burned top. Not ideal…

And the worst case scenario? You pour all the batter in, place the cake in the oven and go about your business. Forty minutes later you’re scraping blackened bits of cake from the bottom of your oven, because the batter has spilled over the edges of your cake pan…

Truth be told, using a smaller cake pan isn’t the end of the world, especially if you know what you’re doing. I make larger batches of cake batter all the time and use them to make smaller cakes. After all, experienced bakers know to only fill a cake pan halfway to two-thirds of the way up with batter. And having some leftover batter usually isn’t a problem. Not in this house, anyway… No, it gets tricky when you only have a slightly larger pan at your disposal. Sure, you could double the recipe, but usually that means that you will have a lot of leftover batter. And while I like a little leftover cake batter, I don’t like having an entire bowl of the stuff… I can’t just throw it away, but eating it all seems a little excessive… So does eating an entire batch of cupcakes made with leftover batter…

### The Round Cake Pan Conversion Formula in Centimeters and Inches

So, what I’ve come up with is a basic conversion formula that tells you by which factor you should multiply the ingredients the original recipe calls for. This way, you end up with a cake that is either smaller or larger in diameter (depending on the cake pan you decide to use) than the cake you would have ended up with if you had followed the recipe’s instructions to the T, but which also happens to be just as tall as the cake the original recipe would have yielded. For example, if a recipe yields a 22-cm/9-inch cake that is 5-cm/2-inches tall, and you use these formulas to turn it into a 13-cm/5-inch cake, you will end up with a 5-cm/2-inches tall 13-cm/5-inch cake.

Aka: these formulas mess with the cake’s diameter, not with its height!

And be warned, there’s math involved. Some of you math-haters may think it’s not worth the trouble. Because math sucks. Yeah, I know! But this method really isn’t that hard! Honestly, I use these formulas all the time! It’s easy and once you learn how to use them you can make batches of batter that actually fit your cake pans and you don’t ever have to throw anything away anymore! Well, except maybe half an egg or something…

So just give it a go, all right? Just think ‘cake’!

Oh, and by the way, since most cake pans are either 5-cm/2-inches or 9-cm/3-inches high, I usually use one of those numbers for the height of the pan… However, if you’re using a pan that has very low sides, remember not to overfill it!

**Start by calculating the volume of the pan the recipe calls for:
**Step 1: (diameter of cake pan in centimeters or inches / 2 = radius

Step 2: radius x π = bottom of the cake pan in square centimeters or inches

Step 3: bottom x height in centimeters or inches = volume in cubic centimeters or inches!

So, for a 22-cm cake pan:

22 / 2 = 11

11 x π = 34.5575

34.5575 x 9 = 311.017 cubic centimeters!

And for a 9-inch cake pan:

9 / 2 = 4.5

4.5 x π = 14.1371

14.1371 x 3 = 42.4115 cubic inches!

**Now that you know the volume of the pan the recipe calls for, calculate the volume of the pan you have with the same three-step-formula:
**Let’s say I have a 18-cm:

18 / 2 = 9

9 x π = 28.2743

28.2743 x 9 = 254.4690 cubic centimeters

or a 7-inch pan:

7 / 2 = 3.5

3.5 x π = 10.9955

10.9955 x 3 = 32.986 cubic inches

**Next, calculate the factor by which you should multiply the recipe’s ingredients:
**volume of your pan in cubic centimeters or inches / volume of the pan the recipe calls for in cubic centimeters or inches = factor

So, in centimeters:

254.4690 / 311.017 = 0.81

And in inches:

32.986 / 42.4115 = 0.777

**Once you’ve calculated the factor by which you should multiply the ingredients, calculate the amount of ingredient’s you’ll need:**

The recipe may call for the following ingredients:

– 4 eggs

– 200g (or 1 cup) of sugar

– 1 teaspoon of vanilla extract

– 480ml (or 2 cups) of milk

For centimeters:

4 (eggs) x 0.81 = 3.24 eggs

200 (grams of sugar) x 0.81 = 162 grams of sugar

1 teaspoon (vanilla extract) x 0.81 = 0.81 teaspoon of vanilla extract

480 (ml of milk) x 0.81 = 388 ml of milk

For inches, bearing in mind that 1 cup equals 240ml:

4 (eggs) x 0.77 = 3 eggs

240ml (of sugar) x 0.77 = 185 ml of sugar, or ¾ cup + 1 teaspoon

5 (ml vanilla extract) x 0.77 = 3.75 ml, or ¾ teaspoon

480 (ml of milk) x 0.81 = 388 ml, or 1½ cups + 2 tablespoons of milk

That’s it! Isn’t that easy??? This way, you can turn a recipe that makes a tiny 13-cm/5-inch cake into a huge wedding cake! Just calculate the factor by which you need to multiply the ingredients! And don’t worry too much if the amount of ingredients you need is a bit odd, like 388ml or something. Trust me, 390ml will do fine!

Oh, and the best part? This method works for regular cake pans and springform pans! Just don’t forget to use your head before pouring a batter into a springform pan. The batter can’t be too runny! Oh, and baking a cheesecake in a regular cake pan doesn’t sound like a good idea to me either, but apart from that, this method works beautifully!

### No, wait! I didn’t understand any of it!

Relax. Don’t worry. Breathe! Not everyone can be a math genius. Trust me, I know that from experience. I’m *not* a math genius, you know. Not at all! Far from it, actually… Just ask my high school friends. I was notoriously bad at math. Yet I have no trouble using this great formula! And if a math retard like me can do this, so can you! Just grab a calculator, a piece of paper and a pen and start messing around with those numbers. You will be fine! And it really is a lot easier than having to throw delicious cake batter away or having to eat more batter than your precious digestive tract can handle…

So go make the mother of all cakes. Or a tiny baby cake! I’m heading back to Thesis-Land!

Kathi @ laughingspatula.com says

Ha Ha – Loved this article! I am a cake fanatic and have tucked this information away – I know I will need it one day!

Happy 4th!

Kathi

Nila says

Thanks Kathi! I love to use this formula when I’m developing new recipes. Or if I’m making a big birthday cake from a smaller recipe… But you’re a cake fanatic, so you know what I mean, right?

Happy 4th to you too

Boelo Meijer says

Hi Nila

Just read this article and you know what? It’s exactly the way I do it (somehow I like math).

But I think you have one mistake in here:

You say: “Step 2: radius x π = bottom of the cake pan in square centimeters or inches”

But isn’t the bottom calculated: radius x radius x π ?

So for a 22cm pan it would be:

11 x 11 x π = 380 square cm

380 x 9 = 3150 cubic cm

Hope this doesn’t mess up your calculations.

Please keep writing, love your blog

Love

Boelo

Arielle says

Boelo is right – the formula for the area of the bottom of the cake pan is pi*r*r, not pi*r. Also, if you are assuming you want the same height (eg. a 9-inch 2-inch-tall cake instead of a 10-inch 2-inch-tall cake) you can leave the height out, since you will just be multiplying by it and dividing by the same thing. Truthfully, you can leave out pi also, because you are just multiplying by it in one step and then dividing by it in the next step. All you need to do is r*r of the pan the recipe is written for / r*r of the pan you’re using.

Arielle says

Sorry, the fraction is the other way round – r*r of the pan you’re using / r*r of the pan the recipe is written for.

The Tough Cookie says

Thanks Arielle! Like I said, I’m not really a math genius

Kirsten says

So.. My recipe calls for three nine inch. When I’m doing this equation, is it accounting for there being three pans? Or do I have to the multiply by how many pans I’m going to be using? I’m using two 12 inch.

The Tough Cookie says

Hi Kirsten, good question. I wish I knew how to answer it… I’ll try asking a math genius for you! In the meantime, sorry I can’t be of more help, but math really isn’t my forte

nifemi says

I want to use 12inch of pan.so give me the recipe

The Tough Cookie says

Sorry, I’m not a calculator….