UPDATE
Automatic compilation is available from version 6.0 with the function "File watchers":
Although you can find the same answer in a question that is suggested as a duplicate, I will post it here again with minor corrections for the latest version of WebStorm:
The latest version of WebStorm has an action to compile CoffeeScript, but it just displays a window with the result without writing any files ( Help | Find Action | Preview the compiled Coffeescript file or bind it to a keyboard shortcut in Settings | Keymap ).
The same action is available in the context menu of the editor.
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