Converting between pan sizes by surface area
When you swap one pan for another, what has to stay constant is batter depth — that's what keeps bake time and texture roughly the same. Depth stays constant when you scale the recipe by the ratio of the pans' surface areas, not their linear dimensions. This trips people up: a 10-inch round isn't a little bigger than an 8-inch round, it's 56% bigger, because area grows with the square of the radius.
The area of a round pan is π × radius², a square or rectangle is length × width. To move a recipe from pan A to pan B, compute both areas and multiply every ingredient by area B ÷ area A. Going from a 9-inch round (about 64 in²) to a 9×13 rectangle (117 in²) means scaling up by roughly 1.83 — nearly double. Skip the area math and use the diameters directly and you'll end up with a thin, over-baked layer or a pan that overflows.
Two practical notes. First, keep the same depth of pan; this method assumes you're not also changing how tall the sides are. Second, treat the scaled bake time as a starting point, not gospel — a wider, shallower bake usually finishes a touch faster, a deeper one slower. Set a timer for the original time, then judge doneness by the usual cues rather than the clock.
If you'd rather not measure dimensions at all, you can compare pans by the water they hold: fill each to the brim, and the ratio of volumes is the factor you want. It's a quick check when a pan is an odd shape — a bundt or a springform — that doesn't reduce neatly to a circle or rectangle.
Worked example
Moving a recipe from an 8-inch round pan to a 9-inch round pan.
- Area of 8" round = π × 4² ≈ 50.3 in²
- Area of 9" round = π × 4.5² ≈ 63.6 in²
- Factor = 63.6 ÷ 50.3 ≈ 1.27
→ Multiply every ingredient by 1.27 to keep the same batter depth.