Growing out of this discussion: Official Calibre PPA?, here are some simple scripts to update calibre on different platforms.

Note: This can also perform the first-time install, since the version check returns the same failure for out-of-date as it does if there is no calibre installed.

Thanks to aleyx for working out the version checking!

To install the script on linux, run the following command:

sudo -v && wget -nv -O- https://github.com/eli-schwartz/calibre-installer/raw/master/linux/calibre-installer.sh | sudo sh -

To install the script on OSX, run the following command:

sudo -v && wget -nv -O- https://github.com/eli-schwartz/calibre-installer/raw/master/osx/calibre-installer.sh | sudo sh -