Free Chord Inversion Calculator

Understanding Chord Inversions

A chord inversion occurs whenever a note other than the root occupies the lowest voice (the bass). This simple shift completely alters the harmonic character of a chord while the collection of pitches stays the same. Whether you’re exploring piano chord inversions, analysing a figured bass line, or trying to decode a slash chord symbol, a clear grasp of inversions is essential for both composition and improvisation.

The Chord Inversion Calculator (part of the broader Chord Notes Finder family) removes the guesswork: choose a key, pick a chord type (triads, sevenths, ninths, and beyond), and select an inversion. The tool instantly shows you the note names in order and the corresponding figured bass or slash chord label. In just a few clicks you can test any voicing idea.

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What Is an Inversion?

Take any chord, move one of its notes to the bass line, and you’ve created an inversion. The number of possible inversions equals the number of notes in the chord—each note can become the bass. Using C major (pitches C‑E‑G) as a demonstration:

• Root position – root stays as bass: C‑E‑G
• First inversion – the third is placed in the bass: E‑G‑C
• Second inversion – the fifth becomes the bass: G‑C‑E

The same logic extends to larger chords. For G dominant seventh (G‑B‑D‑F) the third inversion puts the seventh in the bass: F‑G‑B‑D. For D minor ninth (D‑F‑A‑C‑E) the fourth inversion sounds with the ninth as the lowest note: E‑F‑A‑C‑D.

Inversions for Triads and Seventh Chords

The following tables summarize the standard inversions, the interval pattern (from the bass note upward), and the conventional figured‑bass symbol.

Triads

Inversion	Note order (C major)	Intervals from bass	Figured‑bass symbol
Root position	C‑E‑G	$3 + 5$	$\text{I}^{5}_{3}$ (often $\text{I}$)
First inversion	E‑G‑C	$3 + 6$	$\text{I}^{6}_{3}$ (usually $\text{I}^{6}$)
Second inversion	G‑C‑E	$4 + 6$	$\text{I}^{6}_{4}$

Seventh Chords

Inversion	Note order (G⁷)	Intervals from bass	Figured‑bass symbol
Root position	G‑B‑D‑F	$3 + 5 + 7$	$\text{V}^{7}_{5}$ (simplified $\text{V}^{7}$)
First inversion	B‑D‑F‑G	$3 + 5 + 6$	$\text{V}^{6}_{5}$
Second inversion	D‑F‑G‑B	$3 + 4 + 6$	$\text{V}^{4}_{3}$
Third inversion	F‑G‑B‑D	$2 + 4 + 6$	$\text{V}^{4}_{2}$

Notice that the absolute order of the upper voices can be changed without affecting the inversion label—that’s the realm of voicing, a separate but related concept.

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Two Ways to Notate an Inversion

Figured Bass (Classical Style)

Figured bass uses Roman numerals to indicate the chord’s degree within the current key, while numbers stacked below the numeral show the intervals above the bass note.

Example in C major, chord IV (F‑A‑C):

• Root position: $\text{C:IV}^{5}_{3}$ (usually abbreviated to $\text{C:IV}$).
• First inversion (A‑C‑F): $\text{C:IV}^{6}_{3}$ ($\text{C:IV}^{6}$).
• Second inversion (C‑F‑A): $\text{C:IV}^{6}_{4}$.

For seventh chords the pattern is similar but uses three intervals. In the key of G major, the dominant seventh (D‑F♯‑A‑C) in second inversion would be written $\text{G:V}^{4}_{3}$.

Figured bass works beautifully for strict four‑part chorale writing. It becomes unwieldy when ninths, suspended notes, or altered extensions appear, which is why modern harmonic analysis often prefers the slash‑chord system.

Slash Chords (Modern & Pop)

A slash chord consists of the chord name (e.g., Cmaj, G⁷, Dmin⁹) followed by a slash and the intended bass note.

• C major first inversion → C/E (C major chord with E in the bass).
• G dominant seventh third inversion → G⁷/F.
• D minor seventh with G in the bass (not an inversion but a chord with a non‑chord bass tone) → Dmin⁷/G.

Slash chords are unambiguous about the chord quality and the bass pitch but omit the key‑context information that figured bass provides.

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A Practical Illustration: Bach’s Prelude in C (BWV 846)

The opening measures of Bach’s prelude can be annotated using both systems. Figured bass clearly shows the home key (“C”), the modulation to G major, and each chord’s degree within that key. Slash chords give a note‑by‑note mapping that is easier to read at a glance but require the performer to understand the underlying harmonic function. Trying to label the entire prelude with both methods is an excellent exercise for anyone serious about music theory—our Music Theory Calculator can help verify your results as you go.

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When Chords Become Complex

Figured‑bass notation breaks down when chords contain more than four distinct notes. A ninth chord, for instance, introduces a sixth interval (the ninth) that conflicts with the standard inversion numbers. Slash chords remain perfectly clear: Fmaj⁹/E leaves no doubt about the notes (E‑F‑A‑C‑G) and the bass note. The Chord Inversion Calculator handles any combination up to five‑note structures, so you can experiment with extended harmonies without getting lost in notation.