Chord Inversion Calculator (notes of every inversion, slash chord & figured bass)

Understanding the chord inversion calculator — concept and principle

This calculator shows the notes of a chord in any inversion, lowest note first, together with the slash-chord symbol, the figured-bass numbers and which chord tone is in the bass. Use it for harmony homework, for writing smooth bass lines, or for finding new voicings on keyboard or guitar.

How it is calculated

1. The chord is spelled from its root: count letters for each degree, then add ♯ or ♭ to reach the right number of semitones.
2. For inversion k, the list of chord tones is rotated so tone k comes first: root position starts on the root, first inversion on the 3rd, second on the 5th, third on the 7th.
3. Tones that moved to the top are raised an octave, so the semitone distances above the new bass are all positive.
4. Slash symbol = chord name + "/" + bass note.
5. Figured bass: triads 5/3, 6, 6/4; seventh chords 7, 6/5, 4/3, 4/2. Sus chords get no figure. Triads have only three positions.

The principle

An inversion keeps the same notes but changes which one is lowest. The bass note strongly affects how stable a chord sounds, so inversions let a composer keep the harmony while giving the bass line a smoother path. Figured bass, from the Baroque era, names a chord by the intervals above the bass. In a first-inversion seventh chord the root sits a 6th above the bass and the 5th a 5th above, hence 6/5. The figures describe the stack above whatever note is lowest, so they identify the inversion without naming the root.

Worked example

Default inputs: root C, Dominant 7th, First inversion.

1. C7 spelled from the root: C, E, G, B♭ (semitones 0, 4, 7, 10).
2. First inversion starts on the 3rd: E – G – B♭ – C; bass note E.
3. Moved C goes up an octave (12). Distances above E (4): 7 − 4 = 3, 10 − 4 = 6, 12 − 4 = 8, giving 3 – 6 – 8.
4. Symbol C7/E; figured bass 6/5; chord tone in the bass: the 3rd; 4 notes.

How to read the result

The note list is a close voicing above the bass; you can spread the upper notes as you like as long as the bass stays the same. Root position sounds most stable. First inversion is softer and is often used to pass between chords. Second inversion triads (6/4) sound unsettled and usually appear in set patterns such as the cadential 6/4. For seventh chords, third inversion (4/2) places the 7th in the bass, which normally steps down.

Common mistakes

• Confusing inversion with voicing; only the bass note decides the inversion.
• Writing figured bass for sus chords, which are not built in thirds.
• Asking for a third inversion of a triad, which does not exist.
• Reading 6/4 as "sixth chord"; it means the 5th is in the bass.

Frequently asked questions

What is the first inversion of C major?

E – G – C, with E in the bass. It is written C/E on a lead sheet and I6 in Roman-numeral analysis.

What does 6/5 mean?

A seventh chord in first inversion: the 3rd is in the bass, with intervals of a 6th and a 5th above it.

Sources: M. Gotham et al., Open Music Theory, 2nd ed. (VIVA Pressbooks), chapters on chord inversion and figured bass