Converting a 9×13″ pan recipe to a 9×5″ loaf pan
Batter scales with volume, not with width. A 9×13″ pan holds about 14 cups filled to the brim, and a 9×5″ loaf pan holds 8 cups, so you need 43% less batter. Multiply every ingredient — including the eggs, which is the awkward one — by 0.57×.
The number people miss is depth. Two pans can hold the same volume and still bake completely differently, because what matters is how thick the batter sits: volume divided by bake surface. Here that moves from about 1.2″ to 1.7″. Batter sits deeper in the new pan, so the center needs longer to set. Increase bake time roughly 15–25% (an estimate, not a published or tested figure); start testing at the original time.
Because the batter ends up noticeably deeper, our rule of thumb (an estimate, not a published figure) is to drop the oven by 25°F (≈14°C). At the original temperature the outside sets and browns well before the centre is cooked, which is how you get a cake with a dark crust and a raw seam through the middle.
How many pans one batch fills
A 9×13″ pan recipe comes to about 1¾ 9×5″ loaf pans, which doesn't divide neatly. Three honest options: fill two pans and accept that the last comes out shallower; scale the recipe by 0.57× for a single pan; or scale it by 1.14× to fill both properly. Batter left standing while an earlier pan bakes loses its lift, so get them all in the oven together where you can.
A caution worth reading
Volume conversions hold well for cakes, brownies and quick breads — anything poured. They hold less well for recipes where structure comes from the pan itself: a delicate chiffon or angel food climbs the ungreased side of a tube pan, and a loaf's shape is part of how it bakes. For those, scale the ingredients by all means, but expect the texture to shift, and use the skewer rather than the recipe's clock.