How scaling a recipe to another pan works
Multiply every ingredient by the ratio between the two pans' volumes, then adjust the bake for the new depth. Volume is geometry: π r² h for a round tin, width × length × depth for a rectangular one. Depth is the part the ratio does not cover — a deeper batter needs longer at a lower temperature, and a shallower one the reverse.
What happens to your recipe
1.Measure both pans
A round tin is π r² h; a rectangular one is width × length × depth. An 8-inch round two inches deep holds 100.5 cubic inches. A 9×13 holds 234. Neither number comes from a chart — both are computed from the tin's own dimensions, which is what makes the ratio between them exact.
2.Multiply every ingredient by the ratio
234 ÷ 128 is 1.83, so an 8-inch square recipe baked in a 9×13 needs 1.83× of everything. That is the whole of the arithmetic, and it is the part a calculator already does well.
3.Round to something you can measure
This is where most conversions fail. 3 eggs × 1.83 is 5.48, and nobody owns half an egg. Quantities land on whole eggs, quarter-sticks of butter — the wrapper is printed in quarters — and the ⅓ and ⅔ markings a measuring cup actually has.
4.Adjust the bake for the new depth
The ratio says nothing about depth, and depth is what changes the bake. The same batter poured deeper needs longer, usually at a slightly lower temperature so the outside does not set before the middle. Spread thinner, it cooks faster and dries out sooner.
What does it not do?
It does not rewrite your recipe, and it does not invent quantities. The text you paste is stored exactly as typed and shown beside the scaled version. A line with no number in it — a pinch of salt, butter for the tin — is carried through untouched, because 1.8 pinches is not an instruction.
Why is there no Bundt pan?
Because its volume would have to be invented. A round or rectangular tin has a formula; a fluted mould displaces an amount that depends on the mould, and no formula covers it. Every pan in the catalogue has a volume derived from its own dimensions, and a measured tin is worth more than a confident guess.
Questions people actually ask
Why not just use a cups-per-pan chart?
Because published charts each assume a fill level — half full, two-thirds full — and the assumption is rarely stated. Mix two charts and the ratio between them is wrong. Computing both volumes from the pans' own dimensions is self-consistent, and a ratio between two geometric volumes is exact no matter how full you fill them.
Do eggs and leavening scale linearly?
Not really. Ingredients that make a batter rise or set behave differently at the edges of a big scale-up, and eggs only come in whole units anyway. The quantities are scaled by volume and rounded to what you can measure; the baking notes call out the ones worth watching.
Why does bake time change at all?
Because heat reaches the middle of a thicker batter more slowly. The same mixture spread thinner cooks faster and can dry out; poured deeper it needs longer, usually at a slightly lower temperature so the outside does not set before the centre does.