The landscape form factor, in my experience, is less likely to get in the way of my book or paper than a portrait form factor. Probably because we write left to write then top to bottom, and read the same way, and so a landscape form factor overlaps fewer lines than the same area in portrait form factor.

A phone calculator in landscape mode is not as good for a couple reasons. First, phones tend to turn off when idle for a bit. It gets annoying to have to keep unlocking the thing.

Second, without physical buttons it is a lot harder to operate without looking.

This later problem could be addressed if you made a physical overlay that you could put over you phone screen, which covers the key section of the phone calculator, and has a hole over each key. Make the overlay thick enough that it is easy to feel where the holes are. That should provide enough feedback to let you use the calculator without looking.

(Fancier would be to make an overlay that actually has physical buttons. Make the buttons out of something that conducts touch, so that when you press it the button touches the screen).