Novices can sometimes be intimidated by baking, because it has a reputation for requiring close and careful accuracy of measurement and technique. That's true up to a point, and baked goods rely on chemistry to arrive at a good outcome, but often baking requires judgement and common sense as much as scientific precision. For example, if you're baking your cake in a different-sized pan you need to know your pan's volume and the depth of the batter; but you'll still need to judge whether other adjustments are required.
Read your recipe to find the recommended pan size, then look up the volume of that pan in an online chart or in a cookbook. If you don't have any easy way to look up the pan's volume, fill it to the 2/3 mark with water. Measure the water into a cup, to arrive at the volume of your baking pan.
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Follow the same process to calculate the volume of the pan you'll be using. If the pans hold comparable quantities of batter, you shouldn't have to make any further adjustments. For example, two 8-inch round pans hold the same amount of batter as a 9-inch square pan. That same quantity of batter can fit in an 8-inch square pan, but will be deeper.
Measure the depth of the batter if your pan is larger or smaller than the volume of the original pan. If you've reduced the depth of your batter, it will bake more quickly. You'll need to increase the oven's temperature by 5 to 10 degrees for it to brown properly. If you've increased the depth of the batter, it will bake more slowly. Extend the baking time by 5 to 8 minutes, and be prepared to reduce your oven temperature if the cake browns too quickly.
Maintain the same temperature if you've moved from a small pan to a sheet pan, but still have the same depth of batter. Large sheet pans can take slightly longer to bake in the middle, but you can counter this by using one or two heating cores to conduct heat into the middle section. They're commonly available from baking-supply shops.
Look up the recommended baking times for your pan, if you make a drastic change such as transferring your batter to a Bundt pan. The Bundt pan's ring shape speeds baking, but it still often requires longer baking time or a lower temperature.
Things You'll Need
Heating cores (optional)
There's a great deal of imprecision with this type of substitution, because all cakes are not created equal. Light and frothy sponge cakes tend to bake more rapidly than dense butter cakes, and will be more affected by changes in pan size. You'll need to judge when the cake is properly baked. Some bakers use visual indicators such as the cake shrinking from the sides of its pan, while others tap it gently to assess its firmness. If you prick the cake with a skewer to test doneness, a few moist crumbs are ideal but wet batter indicates it's not done.
All pans are not created equal, either. Dark pans transfer heat more effectively than light-colored pans, so if your new pan is darker than the old one you'll need to reduce the temperature to compensate for that. Ideally, try to substitute a pan of equal weight and color.