Why pan size changes recipe quantity
A recipe written for one pan shape and size assumes a certain batter footprint and usually a certain depth. If you switch to a wider pan, the batter spreads thinner. If you switch to a smaller or deeper pan, the mixture sits thicker and the same quantity may overfill the pan.
That is why recipe scaling starts with geometry. Round pans scale from circle area, rectangular pans scale from width multiplied by length, and a full volume comparison multiplies that footprint by batter depth when the depth changes too.
Round area = π × r²
Used for circular cake tins and springform pans.
Rectangular area = Width × Length
Used for trays, roasting tins, and sheet-style pans.
Scaling factor = Target area or volume ÷ Original area or volume
The multiplier applied to the ingredient list when comparing the two pans.