Álvaro Ramírez points out that Emacs has the built-in capability to calculate the number of days between two dates. It’s easy to do; the tl;dr is:
M-x calendar <mark the region between the two dates (inclusive)> M-= (or M-x calendar-count-days-region)
Ramírez has some animated screen shots that show how it works and also a shortcut for going to the endpoints of the date range.
It’s a nice trick and it’s all already there. Read the post and try it out.