Baking pan conversion calculator

Swapping pans is a volume problem wearing a length disguise, and the disguise is what catches people. A 9 inch round pan is only an eighth wider than an 8 inch one, but it holds 26.6 percent more, because the floor area grows with the square of the diameter. Meanwhile an 8 inch square and a 9 inch round, which sound nothing alike, come out within one percent of each other and King Arthur says to swap them freely. So this tool works in volume: floor area times depth, target against original, and the answer is one factor to multiply the recipe by. What it cannot scale is everything else. Bake time does not follow the factor, because heat travels into the batter from the sides and the bottom and a thinner slab of the same recipe is done sooner. Nor does the depth of the batter, if you decide not to scale at all — so the tool also prints how many times deeper the same batter would stand in your pan, which is the number that decides whether it climbs over the edge.

How it is calculated

factor = (target area × target depth × pans) ÷ (original area × original depth)

Floor area is π times the square of half the diameter for a round pan and length times width for everything else, so a 9 inch round is 63.6 square inches against an 8 inch square's 64. Multiply by depth to get volume in cubic inches, and divide by 231/16 to read it in US cups — a US gallon is exactly 231 cubic inches and holds sixteen cups, so that division is exact rather than rounded. The depth multiplier runs the other way and drops the depths entirely: the same batter spread over a smaller floor stands taller in exact proportion, so it is the original floor area divided by the floor area you are moving it to. That one needs no guess about how full the first pan was.

Source: A pan holds its floor area times its depth, so the factor between two pans is the ratio of those volumes; a square pan of side d therefore holds 4/π times a round pan of diameter d filled to the same depth

Questions people ask

Why does the bake time not scale with the recipe?

Because heat arrives through the surfaces, not through the volume. If you scale a recipe up to a larger pan of the same depth, the batter is the same depth as before and the bake time barely moves. If you pour the same batter into a larger pan without scaling, it is shallower and cooks sooner; King Arthur says to "start checking doneness around 10 to 15 minutes before the bake time called for in the recipe". Going the other way — the same batter in a smaller pan — is the risky direction: "keep an eye on your bake time, which may be 10 to 15 minutes longer", and a butter-based cake given fifteen extra minutes is a dry one. There is no factor that turns one bake time into another, and any calculator that offers you one is guessing.

Will the batter overflow?

The tool will not say, and the reason is worth reading. King Arthur's rule for the smaller pan is to "take care not to fill the pan more than two-thirds full" — that is about the level the batter reaches, and no recipe tells you what level its batter reached in the pan it was written for. Turning that into a confident "it fits" would mean assuming a fill level and then presenting the assumption as arithmetic. What you get instead is the multiplier: tip the same batter into your pan and it stands that many times deeper than it did in the original. A 9 by 13 recipe in one 8 inch round is 2.33 times deeper, which needs no judgement at all. King Arthur calls a 9 inch recipe in an 8 inch pan — 1.27 times deeper — a risk of overflowing, so treat anything much past about 1.2 as the same warning.

Where does the five percent swap window come from?

From us, and it is the one number on this page that is not from a document. King Arthur calls an 8 inch square and a 9 inch round — 0.6 percent apart — interchangeable, and warns off an 8 inch round for a 9 inch recipe at 26.6 percent, but nothing published says where in between the line sits. Five percent is our reading of that gap, and it only decides which sentence appears next to "if you leave the recipe alone". The factor, the capacity and the depth are arithmetic and owe nothing to it.

Why is my Bundt or tube pan missing?

Because its volume is not a disc or a rectangle and there is no honest way to compute it from a diameter. A fluted tube pan has a hole through the middle, sloping sides and a shaped floor, and the capacity printed on the box is usually the brim-full figure rather than what you can bake in. The way to get a real number is to fill it with water a cup at a time up to the level you would actually fill it to, and then treat that figure as the capacity your recipe has to match rather than putting a diameter into this tool.

Do the depths on this page mean anything?

They are yours to type, and they matter more than people expect. Two inches is the usual depth of a cake pan and the depth King Arthur uses when it says an 8 inch square and a 9 inch round match, but springform pans run half an inch to an inch taller and loaf pans vary by maker. The 9 inch round at 2 inches holds about 8.8 cups; the same round at 3 inches holds about 13.2. That is a fifty percent difference from a pan that looks identical from above, so measure yours rather than accepting the default.

What about the pan changing shape as well as size?

The arithmetic does not care — area is area — but the bake does. A loaf pan puts a deep, narrow column of batter a long way from the sides of the oven, so it needs a longer, cooler bake than the same volume spread across a sheet. Moving between shapes of similar area, such as an 8 inch square to a 9 inch round, is safe. Moving the same volume from a sheet into a loaf is a different recipe, not a rescaled one, and the factor of 1.00 this tool would print is telling you about volume alone.

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