Converting a 10″ Bundt recipe to a 9″ square pan
Batter scales with volume, not with width. A 10″ Bundt pan holds about 12 cups filled to the brim, and a 9″ square pan holds 10 cups, so you need 17% less batter. Multiply every ingredient — including the eggs, which is the awkward one — by 0.83×.
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 1.6″ to 1.2″. Batter sits shallower in the new pan. Check 10–15% earlier than the recipe states (an estimate) — shallower batter bakes faster. (Bundt and tube depths are approximate: their ring-shaped bake area isn't published, so we estimate it.)
Coming out of a Bundt is easier than going in. A Bundt's central column lets heat through the middle of the batter, so a plain round pan of the same capacity bakes more slowly at the centre. Give it a little longer and test in the thickest part.
How many pans one batch fills
A 10″ Bundt recipe comes to a little over one 9″ square — about 1.2 pans' worth — so a single pan would be overfilled. Scale the recipe by 0.83× 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.