Any chord can be played with a note other than its root in the bass. When the third is lowest the chord is in first inversion, when the fifth is lowest it is in second inversion, and a seventh chord with the seventh in the bass is in third inversion. Inversions keep the chord’s identity but change its colour and, above all, the bass line: they let you move smoothly between chords, as in C – G/B – Am.
Two notations describe inversions. Pop and jazz charts use slash chords (C/E means a C chord with E in the bass). Classical theory uses figured bass, which lists the intervals above the bass: a first-inversion triad is a “6” chord, a second-inversion triad a “6/4”, and seventh chords are 6/5, 4/3 and 4/2 for their three inversions. Roman numeral analysis attaches these figures to the chord’s degree, e.g. V6/5.
The calculator shows both notations and the voicing from the bass up, highlights it on a keyboard, and lists all inversions of the chord at once for practice.
How to use the Chord Inversion Calculator
- Chord root (key)
- Chord type
- Inversion
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The chord is spelled from its root. For inversion k, its k-th note becomes the bass and the remaining notes are placed above in order, each in the next octave where needed. Intervals above the bass are measured with letter names, so the figures match the written music.
Worked example
A7 (A, C♯, E, G) in first inversion puts C♯ in the bass: C♯, E, G, A. The intervals above C♯ are a minor third (E), a diminished fifth (G) and a minor sixth (A), so the figured bass is 6/5 and the slash symbol A7/C♯. Second inversion is E, G, A, C♯ (4/3, A7/E) and third inversion G, A, C♯, E (4/2, A7/G).
Inversion figures
| Chord | Bass note | Figured bass | Example in C |
|---|---|---|---|
| Triad, root position | root | 5/3 | C E G |
| Triad, 1st inversion | 3rd | 6 (6/3) | E G C = C/E |
| Triad, 2nd inversion | 5th | 6/4 | G C E = C/G |
| 7th chord, root position | root | 7 | G B D F |
| 7th chord, 1st inversion | 3rd | 6/5 | B D F G = G7/B |
| 7th chord, 2nd inversion | 5th | 4/3 | D F G B = G7/D |
| 7th chord, 3rd inversion | 7th | 4/2 (2) | F G B D = G7/F |
Formula
Inversion k: bass = k-th chord tone, the others stacked above it
Triads: root position 5/3 · 1st inversion 6 · 2nd inversion 6/4
Seventh chords: 7 · 6/5 · 4/3 · 4/2
Worked example
Inputs — Chord root (key): A; Chord type: Dominant 7th (C7); Inversion: First inversion (3rd in the bass).
Results — Inversion notes (bass → top) = C♯, E, G, A; Slash-chord symbol = A7/C♯; Figured bass = 6/5; Bass note = First inversion – C♯ in the bass; Chord notes (root position) = A, C♯, E, G; Intervals above the bass = m3, d5, m6.
Key terms
- Root position
- The root of the chord is the lowest note.
- Inversion
- Any arrangement with a chord tone other than the root in the bass.
- Figured bass
- Numbers giving the intervals above the bass note (6, 6/4, 6/5 …).
- Slash chord
- Chord symbol plus bass note, e.g. G7/B.
Frequently asked questions
What is the first inversion of C major?
E, G, C – E in the bass. As a slash chord it is C/E; in figured bass it is a 6 chord.
What is the second inversion of C major?
G, C, E (C/G), figured 6/4.
What are the notes of G7 in first inversion?
B, D, F, G – written G7/B or V6/5 in the key of C.
How many inversions does a seventh chord have?
Three: with the 3rd, the 5th or the 7th in the bass (6/5, 4/3 and 4/2).
Why use inversions?
They make bass lines move by step and smooth voice leading, e.g. C – G/B – Am instead of jumping from G down to A.
Is the second inversion stable?
Not really – the fourth above the bass makes 6/4 chords sound unstable; they are used in cadences (I6/4–V) and as passing chords.
Does an inversion change the chord’s name?
No. C/E is still a C major chord; only the bass note changes.