Pan Size Conversion

TLDR; Converting between different baking pans is a routine and ongoing need. I have detailed below my ways of thinking when I want to convert between baking pan sizes, to increase or decrease the quantities, and everything written here is my mere suggestion and recommendation to follow. There are plenty of baking pan size conversion calculators available online- a quick google search will yield great results (just a quick example is available at OmniCalculator’s website).

– End TLDR;

Pan Size Conversions

I have debated a lot with myself whether to include this part, regarding pan size conversion. After all, I am not even sure many people at home indeed weigh or measure their baked items or baking pans. Regardless, I’ve decided that this topic is important enough to discuss, because after all – not everyone has the same baking pans at their disposal.
I too, find myself very often making calculations whenever I am testing for new recipes, scaling up or down recipes, etc.
I rely on a single principle in my calculations, which is “the volume principle“.

Baking pans are 3D shapes. Meaning, they have length (l), width (w) and height (h). This means you can quite easily calculate their volume. At least when we’re dealing with common, symmetrical geometric shapes such as a cylinder or a cube.

I’d like to include here some basic geometry formulas that we had long forgotten, since middle school:

Cube Volume = length (l) x width (w) x height (h)

Cylinder Volume = π (Pi) x r² (radius squared) x height (h)

Radius = 1/2 diameter (d)

All of the above formulas are very important when we are trying to convert between the same shape baking pans, that only differ in their height.

One might expect that a cake batter adjusted to be baked in a round baking pan with a diameter of 15cm, would yield a taller cake, rather than if it’d been baked in a round cake that is 24cm in diameter (both are the same height).
If this is true, then in order to successfully convert between same shape baking pans, the height of the pan doesn’t matter. Which brings me to the first principle of pan size conversions:

My first principle for pan size conversions

If a cake is not expected to rise above the height of its cake pan, we can ignore this parameter from the calculation. I.e., we perform the next simple calculation:

To scale up a recipe:

For example, when converting from a round baking pan 15cm (d) to a larger round baking pan 18cm (d), the result is 1.44. Meaning we would need to increase each one of the ingredients in 144% (or, alternatively, multiply the amount of each ingredient by 1.44).

To scale down a recipe:

For example, when converting from a round baking pan 15cm (d) to a smaller round baking pan 12cm (d), the result is 0.64. Meaning we would need to decrease each one of the ingredients in 64% (or, alternatively, multiply the amount of each ingredient by 0.64).

The conversion method listed above is perfectly fine for many cases. However, there would still be some inaccuracies, and we won’t always get the exact cake height we aspire for.  If would only allow us to re-evaluate the quantity of ingredients.

hy would it only “evaluate” and not make a 100% accurate prediction?

Since naturally, different ingredients, have different material densities. The density, is the material quantity per unit of measurement. The density is also the main reason why precision baking does not allow for using measuring cups, even if they are “universal measuring cups”. I’m sure everyone would agree that the density of one cup of peanut butter will be different than the density of one cup of milk. The same exact thing applies when we examine the density of different cake batters.

The first important parameter to measure, is the pre-baked cake batter weight.
 The pre-baked cake batter weight can be considered as its estimated volume. The volume is the benchmark through which I can evaluate by how much I should scale up or down the recipe. Although the measurement unit for volume is cubic meters, for the sake of simplicity I measure the estimated volume in grams.

The second next important parameter to measure (but totally optional – more on that further below), is the height.
At this stage, I do normally pull a ruler out of my pocket and start measuring. Ideally, we want to measure how high a raw cake batter reaches (otherwise, we can make a visual assessment), as well as the height of the fully baked cake. This may require some trial and error but this is actually one of the steps you go through when developing a recipe, and in particular when you want to avoid wasting precious ingredients (in my recipes, I am doing my best efforts to keep the waste of ingredients to a minimum).

My second principle for pan size conversions

We can control the volume of our cakes, by taking notes of the height of the cake batter and the baked cake, as well as the pre-baked cake batter weight, with using the following formulas:

Cube Volume = length (l) x width (w) x height (h)

Cylinder Volume = π (Pi) x r² (radius squared) x height (h)

Assume a cake recipe with an estimated volume of 1604g, which is baked inside a round baking pan sized 24cm (d). After baking (and cooling down), the cake’s height is 5cm.

We are interested to bake the cake in a smaller round cake pan, sized 15cm (d), but also interested for it to be the same final height.  If we plug in all the parameters in the cylinder volume formula, we get a volume of 883g, which is about 50% of the original recipe.

But here’s where it gets a bit tricky- the cake’s behavior during baking.

My third principle for pan size conversions

An additional base assumption, which is also very roughly assumed, is that a cake almost always doubles their size after baking (excluding cheesecakes, which are a whole different entity).
Meaning, even if we prepare half the recipe from the above example, there’s quite a high chance that the cake batter will escape the baking pan (especially if not using a tall baking pan), and make a big mess in the oven.

For this reason, we want to keep the right recipe proportions. In order to do that, we aim for a pre-baked cake batter that would not exceed two-thirds the height of the fully baked cake.
For the above case, we re-calculate for a cake batter height of 3cm, to get a volume of 530g.
And this is how we can control the final height of the cake, almost effortlessly.

If we divide 530 in 1604, we can 0.33: we need to prepare one third of the recipe when converting from a 24cm (d) cake pan to 15cm (d) cake pan.
The bottom line is that the more measurements you take, the better your estimations will be, and you can make your cake the perfect height in accordance to the equipment you have at home.

My fourth principle for pan size conversions

All of the above works very nicely when dealing with scaling up or down recipes, among the same shape baking pans (round, rectangle).

But what happens when you want to convert between baking pans that have different shapes, for example, rectangular pan to an angel food cake pan, or special baking pans with many curves?
Now this requires a lot more trial and error, and there is no fool proof method that works 100% of the time. The more you experiment, you can combine calculations with what is called “a sixth sense for baking”, and your estimations are going to be much more accurate.

Another example I can present is when converting from a round baking pan to a rectangular baking pan, you should recall that there is some “dead area” (in blue stripes) that is not covered by the round baking pan, should the cake had been baked in the rectangular pan. Meaning, if we baked a cake batter that is adjusted for a round 15cm (d) cake pan, inside a squared 15cm cake pan- we can certainly expect the baked cake would turn out shorter, then we may wish to scale up the recipe accordingly. 

Assuming the same cake pan height, the volume differences is about 20%. Therefore, you’d need to scale up the recipe by at least 20% in order to make a successful conversion.

My fifth principle for pan size conversions

One last important point to remember whenever you are converting between different baking pans, is the baking time.
While the baking temperature can virtually remain the same, the baking time will differ in accordance with increasing or decreasing the baking pan size or recipe.

A rule of thumb is that the larger the baking pan is, and/or the deeper the cake batter goes- baking times should be extended, while monitoring the oven, testing with a cake tester that the cake does not burn or gets dry.

In conclusion:

I think I covered everything I had to say on this topic. Or at least most of it. I hope that some of you found it interesting. The more you experiment and measure your baked items, the more accurate your results will become.

I will also conclude by saying that in our days and age, you don’t necessarily need to calculate manually or even by using an excel spreadsheet. Personally, I like calculating things on my own because it gives me a lot of control, and since I always know which height or shape, I plan my cakes to be.

There are plenty of baking pan conversion calculators available online- a quick google search will show outputs of many great and experienced bakers, who have already added their calculators, and I can’t really see the need for re-inventing the wheel here. At least for now lol.

Happy baking!