An 8-inch pan is not a smaller 9-inch pan

You have the recipe open and the pan you own is the wrong size. Every chart on the internet answers this in one line — a 9-inch round holds about a quarter more than an 8-inch, so multiply everything by 0.79 — and then it leaves.

The ratio is the easy half. It is also not the half that ruins the cake.

Where the batter goes

Pour the same batter into a narrower pan and the volume has to go somewhere. It goes up. An 8-inch round holds 79 percent of what a 9-inch holds, which means the same batter sits 27 percent deeper in it. That is the number no chart prints, and it is the one that decides what comes out of the oven.

Heat enters a cake from the outside and has to travel to the middle. Widen the pan and the journey gets shorter: the center sets sooner, and the edges spend less time drying out while they wait. Deepen it and the journey gets longer, so the outside is well past done by the time the middle stops being batter.

A quarter more depth on a thirty-five minute cake is not a couple of extra minutes. It is somewhere between forty and forty-five — and the edge spends every one of those extra minutes drying out, in the dark, while you wait for a skewer to come clean.

The two directions fail differently, and only one of them tells you

Too deep announces itself. The batter climbs, it spills over the rim onto the oven floor, the middle sinks as it cools because it never set properly, and you know exactly what happened. It is a bad evening and it is an honest one.

Too shallow says nothing at all. The cake comes out level, browned, correct-looking. It is dry. Nothing about it looks like a mistake, so the mistake gets attributed to the recipe, and a perfectly good recipe gets abandoned by somebody who did everything right except own the pan it was written for.

That asymmetry is the reason this is worth thinking about at all. The failure you can see gets fixed. The one you cannot see gets blamed on somebody else.

What to actually do

There are three cases and they are short.

Your pan is smaller than the recipe’s. Make less. Multiply the whole ingredient list by the volume ratio — 79 percent for an 8-inch standing in for a 9-inch — and bake it for the time the recipe says. This is the boring answer and it is the right one. If you would rather keep the recipe whole, split it between two pans, weigh the batter so they are actually even, and start checking a good deal earlier than the recipe says, because each one is now shallower than it was written to be.

Your pan is bigger. You can pour the whole thing in and it will fit. It will also be done well before the timer, and this is the direction people get caught by, because nothing in the oven looks wrong. Start checking at two thirds of the stated time. It will feel absurdly early. Do it anyway.

The two pans are within about six percent. Do nothing. Pour it in, bake it as written, and stop thinking about it.

How full a pan is supposed to be

None of this works without knowing where the batter is meant to stop, and it is not the rim. It depends entirely on what is going in.

A leavened cake stops at about 60 percent of the pan’s height, because half its final height happens in the oven. Brownies and bars go to 75, since they barely rise and you want them thick. Yeast bread stops at 50 — it proofs in the pan and then springs again in the heat. A casserole can take 85, and a cheesecake or a custard 90, because nothing in either of them is going anywhere; leave a thumb of clearance for the water bath and that is all.

Those fractions are why “it fits” and “it works” are different questions. A cake batter that fills an 8-inch pan to 75 percent of its height fits perfectly well, right up until it starts to rise.

The four swaps that need no arithmetic

Most conversion charts bury these under forty rows that do need arithmetic, which is a shame, because these are the ones worth carrying in your head.

• An 8-inch square is a 9-inch round. 128 cubic inches against 127 — within half a percent. This is the single most useful equivalence in baking and almost nobody knows it.
• A 9-inch square is a 10-inch round. Within three percent.
• A 9 by 13 is a half sheet pan. Not approximately — exactly. Both are 234 cubic inches, because 13 by 18 by one inch deep and 9 by 13 by two inches deep happen to land on the same number.
• Two quarter sheets are one half sheet. Same 234, split in two.

And one that gets repeated as though it were true: two 8-inch rounds do not equal a 9 by 13. They are fourteen percent short, which is enough to notice on the plate. Two 9-inch rounds overshoot it by nine percent, which is the closer of the two and still not nothing.

Measure the pan you actually own

Across the inside of the top rim, not the outside. A pan sold as nine inches is frequently eight and three quarters where it counts, and on a round pan that is six percent of the volume gone before you have measured a single ingredient. Depth matters as much and gets checked even less: a 9-inch round two inches deep and the same pan three inches deep are not the same pan, and a springform is usually the deeper one.

The one that is never fine

Do not put a batter meant for a tube pan into a solid one. An angel food or a chiffon is engineered around the hole in the middle. The hole is what lets a very deep, very wet foam cook through before the outside sets, and it is what the cake hangs from while it cools upside down. Without it the center never sets and the whole thing collapses into the pan as it cools.

That is not a deeper cake. It is a different dish, and no amount of adjusting the time will make it one.

The arithmetic, done for you

All of the above is one calculation repeated, so we built it: the Pan Calculator takes the pan the recipe wants and the pan you have, computes both from their actual dimensions, draws where the batter will sit against where it should stop, adjusts the time, and says plainly when the swap is one you should not make. It is free, there is no sign-in, and it will tell you to stop rather than pick a number it cannot stand behind.

If the problem is the number of people rather than the size of the pan, the Scaling Calculator is the one next door — and it will tell you which parts of a recipe emphatically do not multiply.

Part of Kitchen Systems.