Quick answer
To move a recipe between pans, scale it by the ratio of the base areas, not by the ratio of the volumes.
Base area decides how deep the batter sits, and depth is what drives bake time. Keep the depth the same and the original time and temperature stay roughly right; change the depth and they do not.
Three swaps worth knowing, all of which this calculator produces from the dimensions rather than from a lookup table:
- An 8-inch square and a 9-inch round are within 1% of each other. Swap them straight across.
- Going from an 8-inch round to a 9-inch round needs about 27% more batter.
- A 9×13 inch pan has about 84% more base area than a single 9-inch round, so a single-layer recipe needs almost doubling.