Converting a 9×13″ pan recipe to a 10″ Bundt pan
Batter scales with volume, not with width. A 9×13″ pan holds about 14 cups filled to the brim, and a 10″ Bundt pan holds 12 cups, so you need 14% less batter. Multiply every ingredient — including the eggs, which is the awkward one — by 0.86×.
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 1.6″. 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. (Bundt and tube depths are approximate: their ring-shaped bake area isn't published, so we estimate it.)
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 a little over one 10″ Bundt — about 1.2 pans' worth — so a single pan would be overfilled. Scale the recipe by 0.86× to fill one pan to two-thirds, or bake the extra batter separately as a few cupcakes.
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.