Dough quantity scales with the square of the pan diameter, not the diameter itself, because what fits in the pan is determined by the area of its base, not the length of its side. When adapting a recipe written for a 20-centimeter pan to a 24-centimeter pan, multiply the ingredients by 1.44. Although the diameter increases by only one-fifth, the area increases by nearly half, so the same recipe turns out very differently in the two pans.
The amount of batter a pan can hold is determined by the area of its base, not the length of its side. The base area of a round pan is proportional to the square of its radius; since the radius is half the diameter, the area also grows with the square of the diameter. That is why increasing the diameter a little increases the area much more. In the kitchen, this is where your eyes can be misleading: when two pans are placed side by side, the difference looks like a few centimeters, but the difference in how much batter they hold is much greater, and the recipe will not forgive that difference.
The calculation fits on one line: area equals the square of the radius multiplied by pi. A pan with a diameter of 20 centimeters has a radius of 10 centimeters and an area of about 314 square centimeters. At 22 centimeters, the area is 380; at 24, it is 452; and at 26, it is 531 square centimeters. These four numbers do not need to be memorized; what you need is the ratio between them, which you find each time by division. Measure the pan’s diameter on the pan itself, not from the manufacturer’s label, because the label often gives the top diameter, and if the sides are sloped, the base is narrower.
To find the ratio, divide the area of the new pan by that of the old one. Going from 20 to 22, 380 divided by 314 gives 1.21; going from 20 to 24, 452 divided by 314 gives 1.44. Apply the resulting multiplier separately to every ingredient in the recipe: flour, sugar, eggs, milk, fat, and leavener are all multiplied by the same number. Applying the multiplier to some ingredients but not others throws off the recipe’s internal balance, because the batter works when the ingredients are in proportion to one another.
For ingredients that cannot be divided, such as eggs, the multiplier produces a fraction, and there are two ways to handle it. First, beat and weigh the egg, then measure out the required portion; this is preferred for delicate cake and pastry batters. Second, adjust the multiplier to one that rounds the egg count: if multiplying a 3-egg recipe by 1.44 brings it to 4 eggs, use 1.33 as the multiplier and multiply all the ingredients by that number. The important thing is to choose one multiplier and apply it to the entire list.
After scaling, one final check remains. If the new pan is wider and the batter is the same depth as before, the baking time stays almost the same; check doneness with a toothpick or by checking the center. If the depth changes, the baking time changes too, and the multiplier alone is not enough. If the pan’s sides are sloped, the calculated area will be greater than the actual area; for a pan like this, the most reliable approach is to measure the 2 pans with water, compare the volumes they hold, and calculate the multiplier from those 2 values.
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