Cooking, Baking & Brewing Recipe Scaling & Kitchen Conversions Pan area scaling

Baking Pan Size Conversion Calculator

Swapping a 9×13 for two 8-inch rounds is not a guess — it is a ratio of two areas. This calculator works out the baking surface of your original pan and your replacement pan, gives you the exact factor to multiply every batter ingredient by, and tells you how deep the batter will sit if you pour the same batch into a different pan. Because bake time follows batter depth rather than pan width, it also returns a check-time window instead of a single false-precision number.

Calculator

This calculator runs in your browser. Enable JavaScript for live results — the inputs, formula and worked example below remain fully readable without it.

Inputs this calculator takes, with typical values
InputWhat to enterExample
Original pan shapePick the shape the recipe was written for. Springform pans count as round.Rectangular or square
Original pan diameter or lengthMeasure across the top inside edge — pans are sold by their nominal size, not their real one.13 in
Original pan width (or tube hole diameter)For a rectangle, the short side. For a tube or bundt, the diameter of the centre hole.9 in
New pan shapeThe pan you actually own and intend to bake in.Round (or springform)
New pan diameter or lengthMeasured the same way as the original — across the top inside edge.9 in
New pan width (or tube hole diameter)Leave as is for a square pan; enter the hole diameter for a bundt.9 in
What do you want to keep the same?Scaling the recipe keeps the bake behaving the same; keeping the batch changes how deep the batter sits.Batter depth — scale the recipe
Batter depth in the original panHow deep the raw batter sits before baking — usually about half to two-thirds of the pan's height.1.5 in
Original bake timeThe time the recipe gives for the original pan, at the recipe's stated temperature.35 min

It returns

  • Multiply every ingredient by — Applies to the whole batter. In batch mode this is 1 because you are not changing the recipe.
  • Original pan baking area — Multiply by 6.4516 for square centimetres.
  • New pan baking area
  • Batter depth in the new pan
  • Batter volume needed
  • Start checking at
  • Do not expect it done after

The formula

S=AnewAold
hnew=Aold⁢holdAnew

In plain text: S = A_new / A_old, A_round = πd² / 4, A_rect = L × W, A_tube = π(D² − d²) / 4

  • SScale factor applied to every batter ingredient (×)
  • ABaking surface area of a pan (in²)
  • DOutside diameter of a round or tube pan (in)
  • dCentre-hole diameter of a tube or bundt pan (in)
  • L × WInside length and width of a rectangular pan (in)
  • kDepth ratio: new batter depth ÷ original batter depth (ratio)

Pan area scaling holds batter depth constant, which is what keeps the bake behaving the same. Pan height does not enter the scale factor at all — only the depth the batter actually reaches.

Updated Category Recipe Scaling & Kitchen Conversions Verified against published test cases Reading time 12 min

Why pan area, not pan size, is the number that matters

A cake bakes from the outside in. Heat enters through the bottom, the sides and the surface, and the centre is the last part to reach the temperature at which the starch gelatinises and the egg proteins set. What controls how long that takes is not how wide the pan is — it is how far the heat has to travel, which is the depth of the batter.

That single fact organises everything on this page. If you keep the batter depth the same when you change pans, the bake behaves almost identically: same temperature, same time, same crumb. To keep the depth the same you have to change the amount of batter in proportion to the pan's baking area — the flat footprint the batter covers. Area, not diameter, not volume, not the number printed on the pan.

Diameter is the trap. An inch of extra diameter sounds trivial, but area goes with the square of the diameter, so a 9-inch round pan holds 26% more batter than an 8-inch one at the same depth (63.6 in² against 50.3 in²). Bakers who pour an 8-inch recipe into a 9-inch pan and wonder why the layer came out thin and dry have met that 26% the hard way.

Pan volume, the figure manufacturers stamp on the box, is the wrong tool as well. It measures capacity to the brim, and no one fills a cake pan to the brim. Two pans with identical volume — a shallow wide one and a tall narrow one — bake completely differently.

The three area formulas and the one ratio

You only ever need three area formulas, and the calculator picks the right one from the shape you select.

A rectangular or square pan is L × W, using the inside dimensions across the top. A 9 × 13 is 117 in²; an 8 × 8 is 64 in². A round pan is πd²/4 — a 9-inch round is π × 81 ÷ 4 = 63.62 in². A tube or bundt pan is a ring, so you subtract the hole: π(D² − d²)/4. A 10-inch tube with a 4-inch centre column gives π(100 − 16)/4 = 65.97 in², barely more than a 9-inch round, which is why a bundt recipe so often fits a single deep round layer.

The scale factor is then just the ratio S = Anew ÷ Aold. Multiply every batter ingredient by S — flour, sugar, eggs, butter, liquid, leavening, salt, all of it, by the same number. Baking is a system of ratios, so scaling the whole formula uniformly preserves it. This is the same logic that runs the baker's percentage calculator, where every ingredient is quoted against flour weight for exactly this reason.

If instead you keep the batch and change the pan, the batter simply redistributes: depthnew = Aold × depthold ÷ Anew. Volume is conserved; only the shape of the slab changes.

Bake time then follows the depth ratio k. Two defensible bounds bracket it. Heat has to cross a longer path, so time cannot fall below a linear scaling t × k; and for pure conduction into a slab the time to reach a given centre temperature goes with the square of the thickness, giving t × k². Real baking sits between them because evaporation and crust formation intervene. The calculator reports both, smallest first, and you check at the earlier one.

Worked example: a 9 × 13 sheet cake moved into a 9-inch round

Your recipe fills a 9 × 13 pan with batter 1.5 inches deep and bakes for 35 minutes. You only own 9-inch round pans. Work it both ways.

  1. Original area. 13 × 9 = 117 in².
  2. New area. π × 9² ÷ 4 = 3.14159 × 81 ÷ 4 = 63.62 in².
  3. Scale factor. 63.62 ÷ 117 = 0.544. So a batter using 400 g flour becomes 400 × 0.544 = 218 g; 3 eggs becomes 1.63 eggs, which in practice means weighing your eggs and using 1.63 × 50 g = 82 g of beaten egg.
  4. Batter needed. 63.62 in² × 1.5 in = 95.4 in³, and at 14.4375 in³ per US cup that is 6.61 cups of batter.
  5. Bake time. The depth is unchanged, so k = 1 and both bounds land on 35 minutes. Start testing at 30 anyway, because a round pan of half the area heats through its edges a little faster.

Now the other way — you refuse to scale and pour the entire 9 × 13 batch into one 9-inch round.

  1. Batter volume. 117 in² × 1.5 in = 175.5 in³ = 12.16 cups.
  2. New depth. 175.5 ÷ 63.62 = 2.76 inches, nearly twice as deep.
  3. Depth ratio. k = 2.76 ÷ 1.5 = 1.839.
  4. Time bounds. Linear: 35 × 1.839 = 64 min. Squared: 35 × 1.839² = 118 min. So you are looking at somewhere between 64 and 118 minutes — and you should also drop the oven by 25 °F, because at that depth the edges will be dark before the middle is set.

The second version is legal but not good baking. A 9-inch pan is typically 2 inches tall, so 2.76 inches of batter does not fit at all: it overflows. That is the real answer, and the calculator's depth warning is the thing to act on.

How to read the scale factor and the depth

Judge the scale factor first. As a rule of thumb, a factor near 1 — say within a quarter either way — is a comfortable swap: you can round awkward quantities and nothing bad happens. Further from 1 than that, convert the recipe to weights before you scale, because a factor of 0.54 applied to "3 eggs" or "1½ teaspoons baking powder" produces quantities you cannot measure with cups and spoons. The ingredient weight to volume calculator converts a cup-based recipe to grams so the multiplication becomes trivial.

Then judge the depth. For cakes and brownies, batter between about 1 and 2 inches deep is the well-behaved range that virtually every published recipe is written inside. Under an inch you are effectively baking a thin sheet: fast, easy to overbake, and best checked several minutes early. Over about 2.5 inches you need to lower the oven temperature and extend the time, because the surface will set and dome long before the centre is done.

Finally, use the check-time window as a window, not a prediction. Set a timer for the lower figure and test then — a skewer into the centre, or an instant-read thermometer showing 200–210 °F (93–99 °C) for most butter and sponge cakes. Whatever the calculator says, the doneness test is the authority.

Pan material shifts things too. Dark, non-stick and anodised pans absorb more radiant heat and typically bake faster and darker at the edges; glass conducts poorly but stores heat, so it lags at the start and keeps cooking after you pull it out. Neither effect is in the arithmetic, and neither is large enough to change the scale factor — only the time.

Baking area of the pans in a normal kitchen

Areas from the nominal top-inside dimensions. Divide two areas to get the scale factor between any pair — a 9 × 13 to two 9-inch rounds is 127.2 ÷ 117 = 1.09, so the recipe scales up by 9%.
PanArea (in²)Area (cm²)Batter at 1.5 in deep (cups)
8 in round50.33245.22
9 in round63.64106.61
10 in round78.55078.16
8 × 8 in square64.04136.65
9 × 9 in square81.05238.42
9 × 13 in rectangle117.075512.16
8.5 × 4.5 in loaf38.32473.97
9 × 5 in loaf45.02904.68
10 in tube, 4 in hole66.04266.85
13 × 18 in half sheet234.0151024.31

Square centimetres are the in² figure × 6.4516. Cups are area × 1.5 in ÷ 14.4375 in³ per US cup.

Where pan conversions go wrong

  • Scaling by diameter instead of area. Going 8 in to 10 in is not a 25% increase, it is 56% — area follows the square of the diameter.
  • Using the pan's stated volume. Manufacturers quote brim capacity. You are never filling to the brim, and two pans of equal volume with different footprints bake nothing alike.
  • Measuring the outside of the pan. Sloped sides and a thick rim can cost you half an inch. Measure across the top inside edge.
  • Forgetting the bundt hole. Treating a 10-inch tube pan as a 10-inch round overstates its area by 19% (78.5 in² against 66.0 in²) and you will overfill it.
  • Scaling everything except the eggs. Eggs are an ingredient like any other. Weigh them — a large US egg is about 50 g out of the shell — and use the fraction.
  • Keeping the temperature when the depth changes a lot. A much deeper batter needs a lower oven, not just a longer timer, or the outside burns while the middle stays wet.
  • Assuming the time scales with the area. It does not. If the depth is unchanged, the time is essentially unchanged no matter how much wider the pan is.

This does not work for everything you bake

Pan area scaling is written for batters that pour and set: cakes, brownies, blondies, bar cookies, cornbread, quick breads, cheesecakes and baked custards. It is reliable for those.

It is unreliable for anything whose structure depends on the pan geometry rather than on depth. A chiffon or angel food cake climbs the ungreased sides of its tube pan, so it cannot be moved to a greased round. Yeasted breads proof to fill a pan and are governed by dough weight per unit of pan volume, not by batter depth — use the pizza dough ball calculator or a dough-weight rule instead. Pastry crusts, soufflés and anything relying on a specific climb up the side should be baked in the pan the recipe names.

Where this fits with the other adjustments

A pan swap is one of four independent adjustments, and they compose in a fixed order. First scale the batter by area — that is this page. Then, if you also changed the number of servings, apply the yield factor from the recipe scaling calculator; the two multipliers simply multiply together. Then convert the oven setting if the recipe came from another market, with the oven temperature conversion calculator. Finally, if you are baking in a fan oven, apply the convection correction with the convection oven conversion calculator — and apply it to the time you got from here, not to the recipe's original time.

One caution about stacking corrections: each of them is an approximation, and stacking three approximations widens the uncertainty rather than cancelling it. If you have changed the pan, the yield and the oven all at once, treat the first bake as a test bake, write down the actual time, and use your own number from then on. That is what a test kitchen does, and it is why published times are trustworthy for the pan they were developed in and nowhere else.

The one number worth recording is the batter depth. A recipe archive that lists depth alongside pan size is portable to any pan you will ever own; one that lists only "9 × 13" is not.

Key terms

Baking area
The flat footprint of the pan that the batter covers, measured across the top inside edge. This is the quantity that scales a recipe.
Batter depth
How deep the raw batter sits before baking. The variable that actually controls bake time.
Scale factor
The ratio of the new pan's area to the old pan's area. Multiply every ingredient by it.
Annulus
The ring shape of a tube or bundt pan's floor. Its area is the outer circle minus the centre hole.
Brim capacity
The volume a pan holds filled to the very top — the figure printed on the box, and not a useful baking number.

Frequently asked questions

Can I bake a 9 × 13 recipe in two 9-inch round pans?

Yes, and it is one of the cleanest swaps there is. Two 9-inch rounds give 2 × 63.6 = 127.2 in² against the 9 × 13's 117 in², a scale factor of 1.09. You can bake the batch unchanged and the layers will simply be about 8% shallower, which shortens the bake by a few minutes. Start checking around five minutes before the recipe's stated time.

How do I convert an 8 × 8 recipe to a 9 × 13?

Multiply everything by 117 ÷ 64 = 1.83. In practice most bakers double the recipe instead, which gives 128 in² of batter spread over 117 in² — about 9% deeper than the original and completely acceptable. Add five to ten minutes and test with a skewer. Going the other way, a 9 × 13 into an 8 × 8 is 64 ÷ 117 = 0.55, so a little over half.

Does a deeper pan need a longer bake time?

Only if the batter is deeper. Pan height is irrelevant on its own — a 3-inch-tall pan holding 1.5 inches of batter bakes exactly like a 2-inch-tall pan holding 1.5 inches of batter. What changes the time is the distance heat must travel to the centre. That is why this calculator asks for batter depth rather than pan depth.

Why is the bake time given as a range?

Because the true relationship between depth and time sits between two limits and no simple formula pins it down. Time cannot scale less than in proportion to depth, and pure conduction into a slab would scale with depth squared. Crust formation and moisture loss put the real answer in between, and where exactly depends on your oven, the pan material and the batter. Treat the lower figure as when to start testing.

Do I scale the baking powder and salt too?

Yes — scale every ingredient by the same factor. Leavening works on the ratio of gas produced to batter mass, so halving the batter and keeping the baking powder gives you a cake that rises hard and collapses. The one place bakers legitimately deviate is very large scale-ups, where salt and strong spices are sometimes held back slightly and adjusted by taste, which does not apply to batters that go straight into the oven.

How full should I fill a cake pan?

Between half and two-thirds of the pan's height for a standard butter or sponge cake, which leaves room for the rise. Cheesecakes and dense brownies rise very little and can go higher; anything heavily leavened should stay nearer half. If the calculator's depth output exceeds two-thirds of your pan's height, split the batter between two pans.

What is a springform pan's area?

The same as any round pan of that diameter: πd²/4. A 9-inch springform is 63.6 in², identical to a 9-inch cake pan. Springforms are usually taller, around 2.75 to 3 inches, which is what makes them suitable for the deep batters — cheesecakes especially — that would overflow a standard round.

How do I measure a pan that has sloped sides?

Measure across the top inside edge and use that. The batter's surface is what matters most for heat transfer and the top is where it sits at its widest. Sloped pans hold slightly less than the calculation suggests, so if a pan is noticeably tapered, expect the real batter depth to come out a fraction higher than the figure shown.

Can I use this for a casserole or a lasagne?

The area scaling works fine for anything layered in a dish — the amount of food scales with the footprint, and the cooking time follows the depth just as it does for a cake. The time bounds are less reliable, because a covered casserole cooks partly by steam rather than by conduction alone. Use the scale factor with confidence and treat the time as a starting point.

References

  • On Food and Cooking: The Science and Lore of the Kitchen, 2nd ed. — Scribner (Harold McGee)
  • Modernist Bread, Volume 3: Techniques and Equipment — The Cooking Lab
  • Fundamentals of Heat and Mass Transfer, 7th ed. — transient conduction in a plane wall — John Wiley & Sons (Incropera, DeWitt, Bergman & Lavine)
  • NIST Handbook 44, Appendix C — General Tables of Units of Measurement — National Institute of Standards and Technology
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