We can compare a C Major chord with Caug and Caug7:
C: C – E – G
Caug: C – E – G#
Caug7: C – E – G# - A#
The only difference between C major and C augmented is that the fifth is raised, or augmented, one semi-step. The augmented seventh chord adds a minor seventh. However, it is not as common to write these chords aug7 as +7 or 7#5.
Formula and steps
The formula for the aug chord is 1 - 3 - #5. There is four half steps to the 2nd note and four half steps to the 3rd.
Alternative chord symbols
Besides the aug chord symbol that is presented on this site, you may find the alternative plus symbol (+), as in C+, also being used occasionally. A third symbol that occurs less commonly is C(#5) instead for Caug (the reason for "#5" is that the fifth is sharpened).