A recipe fits a 20 centimetre round pan, your kitchen holds a 25 centimetre square one, and the cake either overflows or comes out thin and dry. The fix is not to guess the batter: it is to scale by pan area. A pan holds batter in proportion to its base area, and area grows with the square of the size, not in step with it. This converter compares your two pans, gives the exact multiplier for every ingredient, and estimates how the baking time shifts, so a recipe written for one pan works in the pan you actually own.
The maths is the part most bakers get wrong. A 20 centimetre round pan has an area of about 314 square centimetres, while a 25 centimetre round pan has about 491, which is 56 percent more, even though the diameter grew only 25 percent. A 20 centimetre square pan is 400 square centimetres, which is already larger than the 20 centimetre round pan. The converter uses the true area formulas: pi times radius squared for round pans, side squared for square pans, and length times width for rectangles. Multiply every ingredient, including eggs, by the scale factor it gives.
Here is a worked example. Your recipe is written for a 20 centimetre round pan, area 314 square centimetres, and you want to use a 25 centimetre round pan, area 491. The scale factor is 491 divided by 314, which is 1.56. A recipe with 200 grams of flour needs 312 grams, 150 grams of sugar needs 234 grams, and 3 eggs become 4.7 eggs, which you round to 5 small eggs or 4 large ones plus a yolk. Rounding eggs is fine: a small difference in egg will not ruin a cake, but a big difference in flour will.
Baking time does not scale with batter, and this is where many conversions fail. A larger cake bakes more slowly because heat must reach the middle, but not in proportion to the batter: doubling the batter does not double the time. As a guide, the time multiplier is roughly the square root of the scale factor, so a 1.56 scale means about 1.25 times the original time. A 30 minute cake becomes about 38 minutes. Treat this as a starting point only, and test with a skewer: it should come out clean or with a few moist crumbs, never wet batter.
Batter depth is the hidden variable. If the new pan gives a much shallower layer, the cake will bake faster and can dry out, even with the scaled time. If it gives a much deeper layer, the middle can stay raw while the edges overbake. The safest conversions keep the depth within about a third of the original. When the depth changes a lot, change your plan instead: bake in two pans, or accept a thinner cake and reduce the time. A pan that is too small is the worst case, because overflowing batter burns onto the oven floor.
A few practical checks finish the job. Grease and line the new pan the same way, because a scaled recipe still sticks to an unlined pan. Fill pans no more than two thirds full, so rising batter has room. Put the pan on the middle shelf, and do not open the oven in the first two thirds of the bake, because the rush of cool air can sink a rising cake. Write the scaled amounts on the recipe card once a conversion works, so the next bake in that pan needs no maths at all.
Pan material also changes the result, and it is worth noting when you convert. Dark metal pans absorb more heat and brown the edges faster, so a cake in a dark pan may need the oven five degrees lower or a few minutes less. Glass pans hold heat longer and keep baking after they leave the oven, so a glass cake can overbake on the tray if you do not turn it out promptly. Silicone pans insulate more and brown less, which suits pale cakes but can leave a soft crust. When you convert a recipe to a new pan, keep the material in mind alongside the size, and check the cake early the first time you use the combination.