I have a 16 GB SD card, but apparently I am already out of space! I ran
ncdu / and apparently I am only using 2.5 GB. How is this possible? There is no way that the OS (Raspbian) is taking up the remaining 13.5 gigs.
It sounds like you have not expanded the install to fill the entire SD card capacity, running
raspi-config and choosing the "Expand Filesystem" option should do the trick.