The same batter can be baked in a cake pan or in the wells of a muffin pan; what changes is not the total amount but the depth of each piece. To switch pans, divide the cake pan’s capacity by the capacity of one muffin well to find how many wells you need. Because the batter is shallower in the wells, it bakes noticeably faster, so rely on the toothpick test rather than the recipe’s baking time.
The relationship between a muffin pan and a cake pan is not scaling up or down; it is dividing. The total amount of batter is the same in the 2 cases; instead of collecting it in one pan, you distribute it among many smaller wells. That is why you do not apply any multiplier to the ingredients; keep the recipe as written. The only thing that changes is the depth of each piece, and all the results follow from that depth. Batter that sits three finger-widths high in a cake pan rises to less than half that height in a muffin well. This is the only reason the result changes while the rest of the recipe stays the same.
To find how many wells you need, compare the two volumes. Measure the volume of batter in the cake pan, then measure the capacity of one muffin well separately, and divide the first by the second. You can find a well’s capacity using water: fill one well with water from a measuring cup and note the amount. If the result is fractional, round up, because using one extra well is always safer than filling the wells to the brim, and leaving the last one half-full does not spoil the result. Adding water to a half-filled well helps the pan heat more evenly in the oven.
How much room to leave for the batter to rise matters more here than in a cake pan. The wells have low sides, and when the batter rises, any overflow spreads across the top of the pan and joins the neighboring wells; it can also break off from that surface when you remove the muffins. That is why you fill the wells with room for the batter to rise, and the amount of headroom depends on the leavener in the batter. If you note how much space remains in the wells on your first attempt, you can use that record instead of guessing next time. If you use paper liners, measure the headroom from the edge of the well itself, not the edge of the liner.
Expect the baking time to change completely. Heat moves from the surface toward the center, and in a muffin well the center is much closer to the surface; the batter is also surrounded by metal on all sides. These two reasons combine to make baking noticeably faster. Trusting the recipe’s stated time and not opening the oven means the wells may dry out. Start checking early by inserting a toothpick into the center of one muffin; if it comes out clean, remove the entire pan. The muffins around the edges bake before the ones in the middle, so check one in the center.
The reverse direction works the same way. If a recipe written for muffins is poured into one cake pan, the batter is deeper, the center is farther from the surface, and the baking time is longer; lowering the temperature somewhat helps keep the outside from drying out. For the 2 conversion directions, the ingredient ratios stay the same. Signs based on the appearance of the crust no longer apply, because a muffin forms a crust all around while a cake pan forms one only on top; if the recipe calls for checking color, use a center check instead. The center itself is the only reliable sign when changing pans.