Cake Pan Converter

Background.

This converter answers the question every home baker eventually hits: the recipe says one 9 by 13 inch pan, and the cupboard has two 9-inch rounds. It compares the two pans by footprint area and returns the single number you actually need — the factor to multiply every ingredient by — plus the brim capacity of each pan in cups, the depth the unscaled batter would reach in the new pan, and a plain verdict on whether the swap works without scaling anything at all.

It compares by area rather than by volume on purpose, and that choice comes straight from King Arthur Baking's own published method: square and rectangular pans are compared by length times width, round pans by radius squared times pi, and on that basis an 8-inch square pan and a 9-inch round pan can be used interchangeably for cake and bar recipes because both come to roughly 64 square inches. Matching area is what holds batter depth constant, and batter depth — not total volume — is what governs how long the centre takes to set and how much the edges brown. Two pans with the same volume but different footprints bake completely differently.

Three scope limits belong right here, beside the answer, not buried in an accordion. First, the dimensions you enter are treated as inside measurements of a straight-sided pan. Real cake pans usually taper a little, and a tapered pan holds less than area times depth, so measure across the inside of the base rather than the outer rim. Second, the two capacity figures are brim volumes — the pan filled to the very top edge — and not batter capacities. When a manufacturer publishes a capacity in cups it has usually already been reduced by a half or a third, so do not compare their number with this one without knowing which is which. Third, a scale factor is not a recipe: it keeps the ratios right, but leavening, spices and eggs do not always behave linearly across a big change, and the oven still needs a skewer.

The fill verdict bands against the half-to-two-thirds range that Wilton, King Arthur and the pan maker Fat Daddio's all publish independently. Those three sources genuinely disagree about deep pans, and this page does not hide it: Wilton says pans 3 inches deep should be filled only half full, while Fat Daddio's says 3 and 4 inch pans want the batter about two-thirds high. Because they contradict each other, no depth-dependent rule is built into the arithmetic. How full your original pan was is an input you control, defaulted to 60 percent — the middle of the range all three agree on — and the verdict only ever compares against the half and two-thirds limits they share.

Capacities use the exact United States customary cup. The gallon is defined as exactly 231 cubic inches, and a gallon is 16 cups, so one cup is exactly 231 divided by 16, or 14.4375 cubic inches. Nothing in the capacity column is approximated. Round pans use the full value of pi rather than the 3.14 that published pan charts often use, which is why this page reports two 9-inch rounds as 127.2 square inches where a chart may print 128.

What is cake pan converter?

A cake pan converter turns a recipe written for one pan into a recipe for a different pan. It works on the pans' footprint areas: divide the total area of the pans you are going to use by the total area of the pans the recipe specifies, and multiply every ingredient by that ratio. The result keeps the batter at the same depth it was designed for, which is what keeps the bake time, the crumb and the browning close to the original.

The reason area is the right basis, rather than volume, is that batter depth drives the bake. Heat enters a cake through the pan walls and the surface, so a shallower layer sets faster and browns more; a deeper one needs longer and risks a raw centre with a dark rim. Two pans can hold identical volumes and still bake very differently if one is wide and shallow and the other narrow and tall. Matching area holds depth constant and therefore holds the bake constant.

Beyond the scale factor, this page reports each pan's brim capacity in cups, how much batter the recipe actually makes given how full its own pan was, and how deep that batter would sit if you simply poured it into the new pan without scaling. That last figure is what the fit verdict classifies, against the half-to-two-thirds fill range published by Wilton, King Arthur Baking and the pan manufacturer Fat Daddio's.

What it is not: a substitute for testing. It assumes straight-sided pans measured on the inside, it treats every ingredient as scaling linearly, and it cannot know how much your particular batter rises. It is the arithmetic, done exactly; the judgement is still yours.

How to use this calculator.

1. 01Pick the shape of the pan the recipe was written for, then enter its inside dimensions — diameter for round, side length for square, length and width for rectangular.
2. 02Enter that pan's depth and how many of them the recipe uses. A two-layer cake recipe usually means two pans.
3. 03Pick the shape and dimensions of the pan or pans you actually intend to use, with their depth and count.
4. 04Set how full the original pan was. Leave it at 60 percent unless you know better — that is the middle of the half-to-two-thirds range Wilton, King Arthur and Fat Daddio's all publish.
5. 05Read the hero number: multiply every ingredient by it to keep the batter the same depth.
6. 06Check the fit verdict if you would rather not scale at all. If it says the swap sits inside the published fill range, pour the batter straight in.
7. 07Read the bake-time note and then ignore the clock in favour of a skewer — depth changed, so doneness will not arrive when the recipe says it will.

The formula.

Footprint area depends on shape only: a round pan is pi times the radius squared, a square pan is its side squared, and a rectangular pan is length times width. Multiply by the number of pans to get total area. The scale factor is new total area divided by original total area, and that is the whole answer for the recipe — multiply flour, sugar, eggs, butter and liquid by it and the batter lands at the same depth in the new pan as it did in the old one.

Capacity is total area times depth, giving cubic inches, converted to cups by dividing by 14.4375. That constant is exact rather than rounded: the United States gallon is defined as exactly 231 cubic inches and contains 16 cups, so a cup is exactly 231 divided by 16. The batter the recipe makes is the original pan's brim volume multiplied by the fill percentage you entered. Poured into the new pan without scaling, that same batter volume spreads over the new total area, so its depth becomes batter volume divided by new total area — and the new fill percentage is that depth as a share of the new pan's height.

Nothing is rounded part-way through. Every quantity is carried at full precision and rounded once, when it is displayed. The two verdicts classify the unrounded values, and both do it by cross-multiplication rather than by dividing: the two-thirds limit is tested as three times the batter volume against twice the pan volume, so an edge that falls exactly on two-thirds is decided exactly instead of being decided by where a repeating decimal happened to be cut off.

Worked through on the default inputs — a 9 by 13 by 2 inch pan at 60 percent full, moving to two 9 by 2 inch rounds — the original area is 117 square inches and the new area is 127.2 square inches, so the factor is 1.087. The recipe makes 9.72 cups of batter, which spreads 1.10 inches deep across the two rounds, filling them to 55.2 percent of their height. That sits inside the published half-to-two-thirds range, so the swap works with no scaling at all, and because the batter is shallower than it was, King Arthur's guidance is to start checking 10 to 15 minutes before the stated time. King Arthur's own article describes this exact substitution the same way: two 9-inch rounds for a 9 by 13 recipe means the batter will be slightly shallower, and a larger pan often bakes more quickly.

Two published figures deliberately differ from what this page returns, and both differences are stated rather than smoothed away. King Arthur's arithmetic uses 3.14 for pi and prints two 9-inch rounds as 128 square inches; the exact value is 127.2, a gap of 0.6 percent. And for a 9-inch square recipe moved to a 9 by 13, the area method gives 117 divided by 81, or 1.444, while the same King Arthur article advises increasing the recipe by 50 percent. This page returns 1.444 because that is what King Arthur's own method produces; their 50 percent is a kitchen-friendly round-up that leaves a slightly deeper cake.

A worked example.

Frequently asked questions.

References& sources.

1. [1]King Arthur Baking Company (2019-04-23). 'The essential alternative baking pan sizes.' Source of the area method — square and rectangular pans compared by length x width, round pans by radius squared x 3.14 — of the 8-inch square and 9-inch round equivalence, of the 117 square inch figure for a 9x13, and of the two-8-inch-round overflow warning.
2. [2]King Arthur Baking Company (2025-08-18). 'Why the size of your baking pan matters so much.' Source of 'fill the pan between half and two-thirds full', of the 8-inch square / 9-inch round volume equivalence (about 128 cubic inches or 8.8 cups), and of the 10-to-15-minute bake-time adjustments in both directions.
3. [3]Wilton Brands LLC. 'Wedding Cake Guide.' Source of 'Fill pans 1/2 to 2/3 full; 3 in. deep pans should be filled only 1/2 full', of the note that its 2-inch batter amounts assume pans two-thirds full, and of the 4 to 5 1/2 cup yield of an average two-layer cake mix.
4. [4]Wilton Brands LLC. 'Cake Bakeware 101: How to Prepare a Cake Pan and More.' Source of 'filling your pans no more than 2/3 full with batter (a little more than half way)'.
5. [5]National Institute of Standards and Technology (2008). 'Guide for the Use of the International System of Units (SI), NIST Special Publication 811', Appendix B.8. The US liquid gallon is exactly 231 cubic inches, so the cup used here is exactly 231/16 = 14.4375 cubic inches.