Baking pan size:
match the area, then watch the depth

Why area, not diameter, is the number to compare

A recipe written for an 8-inch round cake pan and baked in a 9-inch one looks like a one-inch difference. In fact the 9-inch pan has 26.6% more floor area, and a floor is what the batter spreads across. Spread the same batter over it and the cake will be noticeably thinner and will bake faster.

Diameters mislead because area grows with the square of the measurement. Every inch added to a round pan adds more floor than the inch before it. That is why a recipe for one pan size rarely stretches to another without adjusting the quantities.

The 8-inch versus 9-inch calculation

That 1.27 factor applies to every ingredient, not just the flour. A recipe calling for 200 g of flour, 150 g of sugar and 3 eggs becomes 253 g of flour, 190 g of sugar and 3.8 eggs. Since a fractional egg is awkward, many bakers whisk an extra egg and add roughly four-fifths of it by weight.

The reverse conversion works too. Moving from a 9-inch recipe to an 8-inch pan, multiply by 1 ÷ 1.2656 = 0.79, so a recipe with 400 g of flour needs about 316 g.

Squares, rectangles and metric pans

The useful result is the first row: an 8-inch square holds almost exactly what a 9-inch round does, so the two can be exchanged with no change to quantities. A 9 × 13 inch pan needs roughly 1.84 times a 9-inch recipe, or 2.33 times an 8-inch round one.

Metric sizes are close to the imperial ones. A 20 cm round is the equivalent of the 8-inch (20.3 cm), and a 23 cm round of the 9-inch (22.9 cm), so you can usually treat them as interchangeable.

Depth, bake time and why area is only half the story

Area tells you how thick the batter will be. Depth tells you whether it fits. If the same batter spreads over 26.6% more floor, its depth drops to about 79% of what it was; a 4 cm layer becomes about 3.2 cm. Thinner cakes cook faster, so begin testing for doneness when the clock has run to about 75 to 80% of the original time.

Going the other way, a cake poured into a smaller pan will be deeper and may need more time at a slightly lower temperature, so that the edges do not set before the centre. A pan that is too shallow also risks overflow: fill batter to no more than about two-thirds of the pan's height for a cake that rises.

Matching by volume when the depth differs

When pans have different heights, compare volume instead of area. Volume is area times depth, and what matters is the volume of batter against the volume of the pan. A 9 × 13 inch pan 2 inches deep holds 117 × 2 = 234 cubic inches, while a 9-inch round of the same depth holds 127 cubic inches.

An easy check: fill your intended pan with water, measure it in a jug, and compare with the pan named in the recipe. Cakes, which rise, are best at roughly half to two-thirds full, while brownies and bars, which barely rise, can fill closer to the rim.

• Loaf pans: 9 × 5 inch holds about 6 to 8 cups of water, and is not interchangeable with a round pan by area alone.
• Bundt and tube pans: compare by volume in cups, since the centre tube changes the geometry.
• Muffin tins: a recipe for one 8-inch cake makes about 10 to 12 standard cupcakes.

Scaling leavening, layers and bake time with the area

Everything that goes into the batter scales with area, including the raising agent. A cake that uses 6 g of baking powder for the 8-inch pan needs about 7.6 g for a 9-inch one. Small quantities are hard to measure, so round to the nearest practical spoon and avoid doubling the raising agent when scaling up by a fraction, since an excess of leavening gives a dome that cracks and then sinks.

Layer cakes follow the same logic. A recipe that makes two 8-inch layers has about 100.5 sq in of floor in total. Poured into one 9 × 13 inch pan with 117 sq in, it covers the pan to about 86% of the area, so add roughly 16% more batter for an even depth, or accept a slightly thinner cake that needs a shorter bake.

Frosting, fillings and toppings are scaled by surface area as well. A 9-inch cake has about 26.6% more top and, for a layered cake, the side surface grows by the ratio of the circumferences, 28.3 against 25.1 inches, about 12.5%. The top grows faster than the sides, so a recipe for a thick coat on the sides will stretch a little further than one for a generous top.

When a swap will not work well

Delicate recipes, such as sponge cakes that rely on a precise rise, or cheesecakes and custards that set by gentle heat, are the least forgiving of changes in depth. Treat the substitution as a plan and watch the first attempt closely.

A baking pan size calculator makes the arithmetic quick when you are juggling several pans, but the principle is easy to carry: find the area of the pan the recipe names, find the area of yours, divide, and multiply the ingredients by that ratio. Then shorten the bake and check early.