Chord Inversion Calculator
Select a root note, chord type, and inversion to see the exact notes in that voicing, the slash chord symbol, the figured bass label, the bass note, and a stability rating. Covers all 12 roots, 17 chord types from major triads to extended 9ths, and up to four inversions. Use the "Show your work" panel to step through the theory behind each result.
What is a chord inversion?
A chord inversion is a rearrangement of a chord's notes so that a pitch other than the root appears in the bass (the lowest voice). Every chord has as many distinct inversions as it has notes: a triad (3 notes) has root position, first inversion, and second inversion; a seventh chord (4 notes) adds a third inversion with the seventh in the bass; a ninth chord (5 notes) can even reach a fourth inversion. The notes above the bass can be voiced in any order without changing the inversion label - only the bass note determines which inversion you are in.
How to name and read inversions
Two notation systems describe inversions. Figured bass, inherited from Baroque practice, uses numbers to show the intervals above the bass: a first-inversion triad is marked "6" (because a sixth and a third appear above the bass), and a second-inversion triad is "6/4". In jazz and pop, slash chord notation is more common: the chord name appears before a forward slash, and the bass note after it (for example, C/E means a C major chord with E in the bass, a first inversion). Root position needs no slash symbol because the chord name already implies the root in the bass.
Why inversions matter in voice leading and harmony
Inversions shape the weight, color, and direction of harmony. Root-position chords sound the most grounded and conclusive, which is why they typically open and close phrases. First inversion lightens the texture and is often used as a passing chord because the bass can move by step between two root-position chords. Second inversion is the most unstable; the classic "cadential six-four" arrives on this inversion before resolving down to a root-position dominant chord, creating the characteristic tension before a final cadence. Third inversion, where the dissonant seventh sits in the bass, has the strongest pull toward resolution and often propels the harmony forward. Understanding inversions lets you write smoother bass lines, connect chords more naturally, and control the degree of tension at any moment in a piece.
How this calculator works
Choose a root note, chord type, and inversion number from the dropdowns. The calculator builds the chord in root position from the standard semitone formula for that chord quality, then rotates the note list so the selected chord tone lands in the bass. It reports the full inverted note stack, the bass note, the slash chord symbol, the figured bass label, and a harmonic stability rating. The "Show your work" panel traces every step, from the interval stack through the rotation to the final notation. All 17 chord types from simple major triads to dominant seventh flat-nine chords are supported, and inversions are clamped to the valid range for the selected chord so you never get a nonsensical result.
Inversion names, figured bass symbols, and stability
| Inversion | Bass note | Figured bass (triad) | Figured bass (7th) | Stability |
|---|---|---|---|---|
| Root position (0) | Root | 5/3 | 7 | Stable |
| First inversion (1) | Third | 6 | 6/5 | Moderately stable |
| Second inversion (2) | Fifth | 6/4 | 4/3 | Unstable (seeks resolution) |
| Third inversion (3) | Seventh | - | 4/2 | Dissonant (strong resolution) |
Standard terminology for triad and seventh-chord inversions used in classical harmony.
Frequently asked questions
What is root position?
Root position means the root of the chord is also the lowest note (the bass). No inversion has taken place; the chord is stacked in its natural order from the root up. A C major chord in root position has C in the bass, followed by E and G above it.
What does first inversion mean?
In first inversion, the third of the chord is the bass note. For C major (C-E-G), first inversion places E in the bass, giving the note order E-G-C from bottom to top. In slash chord notation this is written C/E. The figured bass symbol is "6" because a sixth (C) and a third (G) appear above the bass E.
What does second inversion mean?
Second inversion puts the fifth of the chord in the bass. C major in second inversion has G as the bass note (G-C-E). Slash notation: C/G. Figured bass: "6/4" (a sixth C and a fourth E above bass G). This is the least stable triad inversion and is most often used as a cadential chord that resolves to a root-position dominant.
Can seventh chords have a third inversion?
Yes. A seventh chord has four notes, so it has four inversions: root position, first, second, and third. Third inversion places the seventh in the bass. For a C dominant seventh chord (C-E-G-Bb), third inversion puts Bb in the bass (Bb-C-E-G). The figured bass label is "4/2" and the slash chord is C7/Bb. This inversion has a strong dissonant pull and almost always resolves to the tonic chord.
How do slash chords work?
A slash chord is written as "chord name / bass note". The part before the slash names the chord quality; the part after names the bass note. C/E means play a C major chord but with E as the lowest note - a first inversion. The slash chord notation says nothing about the order of the upper notes; it only pins the bass. It is the dominant notation system in lead sheets, pop charts, and jazz charts.
What is figured bass?
Figured bass is a shorthand from Baroque keyboard practice where numbers beneath a bass note told the keyboard player which intervals to fill in above it. A plain "6" means play a sixth and a third above the bass (first inversion triad). "6/4" means a sixth and a fourth (second inversion triad). For seventh chords, "7" indicates root position, "6/5" first inversion, "4/3" second inversion, and "4/2" or "2" third inversion. Figured bass is still used in classical harmony analysis today.
Does the order of the upper notes change the inversion?
No. Inversion is determined solely by which chord tone is in the bass. The upper notes can be spread across octaves or rearranged in any order (this is called voicing) without changing the inversion label. A C major chord with E in the bass is always first inversion whether the upper notes appear as G-C, C-G, or in some other arrangement.
Why does second inversion sound unstable?
Second inversion places a fourth above the bass (between the bass note and the root). In tonal harmony a fourth above the bass is treated as a dissonance, meaning the ear expects it to resolve. The most common use is the cadential six-four, where a second-inversion tonic chord (I 6/4) appears on a strong beat before a root-position dominant (V), creating the familiar delay before a final cadence. The instability is a feature, not a flaw.