How to launch the Calculator through Terminal

Try to type:

gnome-calculator

Or for Older version (Ubuntu 12.04 and before):

gcalctool

Always when you have such a question in mind, ie, you don't know the name of the tool to invoke it in command line, find it from the terminal itself:

man -k <keyword>

It will search the manual page names and descriptions for the keyword you specified and prints the titles. In your case, it would be:

man -k calculator

As an illustration, if you want to invoke the webcam tool you can type something like:

man -k camera

man -k is equivalent to apropos.

The command is gnome-calculator