Totally get that, doing things by hand forces you to actually think through each step. Found the same thing checking a duct layout last month, the software had a fitting loss totally wrong. Spent an hour with the manual and a calculator, proved it was off. That stuff is boring but it saves your butt lol. The computer just does what it's told, even if the input is garbage.
Read an old engineering textbook that said to do calculations by hand first. It explained you can't trust software until you know what it's doing. That basic understanding is how you find mistakes.