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classical music from Western culture, an augmented third ( ) is an Play ( · help ) info interval of five semitones. It may be produced by widening a major third by a chromatic semitone.  For instance, the interval from C to E is a major third, four semitones wide, and both the intervals from C  to E, and from C to E ♭ are augmented thirds, spanning five semitones. Being augmented, it is considered a ♯ dissonant interval. 
inversion is the diminished sixth, and its enharmonic equivalent is the perfect fourth.
The just augmented third, E#, is 456.99 cents or 125:96.
The Pythagorean augmented third, E Play ( · help ) info ♯ + + +, is 521.51 cents or 177147:131072, eleven just perfect fifths.
Play ( · help ) info
^ a b Benward & Saker (2003).
Music: In Theory and Practice, Vol. I, p.54. ISBN 978-0-07-294262-0.
^ Haluska, Jan (2003).
The Mathematical Theory of Tone Systems, p.xxvi. ISBN 0-8247-4714-3. Classic augmented third.
^ Hoffmann, F.A. (1881).
Music: Its Theory & Practice, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007. Archaically: superfluous third.
^ Benward & Saker (2003), p.92.