Interval Numbers
An interval's number indicates how many scale degrees are between the two notes.
To determine the number, count the letters from the lower note to the higher note, starting at 1 and including both notes.
Interval numbers are dictated by letter names and not affected by the presence of accidentals. So where C to E is a 3rd, so too is C to Eb. The following examples don't use accidentals.
Examples
C to DCount the letters from C to D.C - DThere are 2 -- it's a 2nd!
C to ECount the letters from C to E.C - D - EThere are 3 -- it's a 3rd!
C to FCount the letters.C - D - E - FThere are 4 -- it's a 4th!
C to GCount the letters.C - D - E - F - GThere are 5 -- it's a 5th!
C to ACount the letters.C - D - E - F - G - AThere are 6 -- it's a 6th!
C to BCount the letters.C - D - E - F - G - A - BThere are 7 -- it's a 7th!
C to CCount the letters.C - D - E - F - G - A - B - CThere are 8 -- it's an octave!
Once again...
Interval numbers are dictated by letter names and not affected by the presence of accidentals. So where C to G is a 5th, so too is C to G#.