What the numeral tells you
The number gives the chord’s root as a scale degree. In C major, C is degree 1, D is degree 2 and G is degree 5, so C, D minor and G are labelled I, ii and V.
I · ii · iii · IV · V · vi · vii°
Uppercase, lowercase and diminished
Uppercase numerals indicate major chords and lowercase numerals indicate minor chords. A small degree symbol marks a diminished chord. The numeral therefore carries two pieces of information at once: the root’s position in the scale and the chord quality.
In a major key, the diatonic triads always follow I–ii–iii–IV–V–vi–vii°. The pattern stays the same when the key changes, even though every chord name changes.
Why musicians use numbers
Chord names describe absolute notes; Roman numerals describe relationships. C–Am–F–G in C major and G–Em–C–D in G major are both I–vi–IV–V. That makes the progression easier to transpose, compare and remember.
In G: G–Em–C–D
Seventh chords and inversions
Add 7 to show a seventh chord: V7 means a dominant seventh built on degree 5, while ii7 means a minor seventh on degree 2. Figured-bass symbols can show inversions, but start by becoming fluent with root-position triads and sevenths.
Roman numerals are key-relative
A chord can receive a different numeral when the tonal centre changes. D major is II in C major if treated as a chromatic chord, but V in G major. Always identify the key before assigning the numeral.