Major and minor chords in a given scale are represented by different types of Roman numerals. Major chords are represented by upper-case while minor chords are represented by lower-case. The chords in a scale are numbered 1 through 7. For example, the first note in a major chord is numbered I while the second note in a minor chord is numbered ii.
Augmented and diminished chords are also represented by upper and lower-case Roman numerals, but they have an additional symbol added for clarity. Augmented chords are represented by upper-case with a plus sign added. An augmented chord that is third in a scale is represented as III+. Diminished chords are represented as lower-case followed by a small circle. A diminished chord that is seventh in a scale is represented as vii°.
Less common chords in a scale are represented in different ways. For example, a half-diminished chord is written as a diminished chord but with a slash through the circle and a number indicating the level. Extended chords are written as either major or minor with a number noting the extension, like IV9. Altered chords are written with the sharp or flat for the alteration noted either before the Roman numeral or between that and the number, like #v or ii#7.
The chord is numbered according to where its root is in the scale. A chord that is in the fifth position on the scale gets a number V if it is major or augmented and v if it is minor or diminished. The ability to read and understand Roman numeral notation is important for analyzing music and understanding the chords that make up a given passage.