Cake pan converter
Swap a 9-inch round for an 8-inch square, with the batter-depth warning you actually need.
Most cake recipes fill to about 2 inches
Close enough to use the recipe as written
At 2 in deep
At 2 in deep
Comfortable
How it works
Pans are compared by the volume of batter they hold, and for a given batter depth that is just their footprint area. So the swap comes down to comparing two areas.
round area = π × (diameter ÷ 2)²
square / rectangle area = length × width
scale factor = new area ÷ old area The classic case
A 9-inch round has an area of 63.6 in²; an 8-inch square has 64 in². They are within 1% of each other, which is why that swap is the one every baking book endorses without adjustment. A 9-inch square, at 81 in², is 27% larger — same recipe, noticeably thinner cake, and a shorter bake.
Bundt and tube pans
The centre tube removes volume that this footprint estimate does not account for, so treat bundt figures as an upper bound. The reliable method is to measure: fill the pan with water a cup at a time until it reaches the fill line.
Bake time does not scale with the recipe
Heat travels inward from the surface, so what governs the bake is depth, not total volume. A thinner layer bakes faster at the same temperature; a deeper one needs a lower oven so the edges do not overcook while the centre catches up. Start checking at two-thirds of the original time.