Hi Keith, I am actually working on pan conversion charts (and some other charts that I am hoping to release later this month), so I am literally working on a spreadsheet of pan conversions right now, so good timing!

OK, so you want to convert a recipe for an 8x2" round pan to an 8x3" round pan. According to my spreadsheet, the 8x2" round pan (assuming straight edges) has a volume of 7 cups, whereas an 8x3" round pan has a volume of 10 cups (we are rounding these numbers a little for the sake of sanity, but that's okay). So this would be like you say 1.4-1.5x the cake batter recipe. And you are saying you multiplied all your ingredients by 1.5 and then when you filled the 8x3" pan, it only filled it halfway. That is odd! And doesn't really make sense to me. Are you sure the first pan is 2" height and the other pan is really 3" height and that both pans are truly the same diameter? Other thought: are the edges slanted, because then we need to calculate the volume of a truncated cone, LOL! Oh, the math...

We must be forgetting to factor a key piece of information in our logic. Let me think on it a little!

Using an actual bake, I baked a Walnut/Honey/Prune Cake, using the above conversions. My handy-dandy spreadsheet I created (it will convert the ingredients for any pan size that is either 2" or 3" deep by just entering diameter and the depth) predicted that I would get 1.5 times the batter of the proven 2" x8"--10.5 cups, 84 ounces--42 oz. per pan. I did! Issue? The quantity did not quite fill the pan to 2/3 of its volume as expected. It was just a smidge above halfway. Notwithstanding, the cake was delicious!
SO, if my post did not give you a headache (haha), perhaps there is something missing that you could point out?

Anyway, thank you for these realizations regarding measures, I totally agree with you.
Sincerely,
Keith Peterson
Everett, WA

Oh and to answer your specific question about 2.5 eggs, I'd weigh out 25 grams of a whisked egg to count as the 0.5 eggs and then add 2 eggs to that!

Hi! This is a great question. Scaling up or down a recipe can be tricky because of the eggs. First of all, I'd convert the number of eggs to a weight. Assuming a recipe has one large egg and we know it's 50 grams of egg per cracked large egg, if I want a half recipe, I'd need 25 grams of egg. Then what I do is I crack an egg into a small bowl and whisk it with a pinch of salt to try to break up the protein globs and to better combine the white and yolk. Then I'd weigh out 25 grams of that whisked mixture. I find the salt helps get a more even mix of the white and yolk, but it's optional. Hope that helps and thanks for commenting!