In music theory, an augmented fifth is an interval that has height half steps 
The augmented fifth requires that:
- The interval must be a fifth interval (five note names between the first and the last).
- The interval must have height half steps.
What does an augmented fifth look like?
Here is an example of a melodic augmented fifth (two music notes in a melody) and a harmonic augmented fifth (in a chord):
How to recognize an augmented fifth?
Rule of music theory: All intervals in a major scale starting with the tonic (degree I) are either major or perfect, and only unison, octave, fourth and fifth are perfect (the others are major).
Example with the interval A♭ / E♮:
Let's take the A flat major scale to have A♭ as the tonic:
From the rule stated above, the interval A♭ / E♭ is a perfect fifth, so the interval A♭ / E♮ is an augmented fifth.
Inversion of the augmented fifth
The inversion of the augmented fifth is the diminished fourth.
Here is an example of a diminished fourth:
Musical examples of augmented fifth
Interval identification game
You will find this interval in my Intervals identification game:
