Enter the root note of the chord and the inversion number into the calculator to determine the chord inversion value; this calculator can also evaluate the root note or inversion number, given the chord inversion value is known.

Chord Inversion Formula

The following formula is used to calculate the chord inversion:

 CI = (N + I) * P12


  • CI is the chord inversion
  • N is the root note of the chord (represented as a number from 0 to 11, where 0 represents C and 11 represents B)
  • I is the inversion number (represented as a number from 0 to 2, where 0 represents the root position, 1 represents the first inversion, and 2 represents the second inversion)

To calculate the chord inversion, add the root note of the chord to the inversion number, and then take the modulus of the sum with 12. This will give you the chord inversion value.

What is a Chord Inversion?

A chord inversion is a rearrangement of the notes within a chord in which the note in the bass (the lowest note) is not the root of the chord. In other words, it is a chord that has been rearranged so that a note other than the root is the lowest note. This is typically done to create a different sound or to facilitate smoother transitions between chords. For example, in a C major chord (C-E-G), the root is C. If we rearrange the chord so that E is the lowest note (E-G-C), we have the first inversion. If we rearrange it so that G is the lowest note (G-C-E), we have the second inversion. Each inversion creates a different voicing, or arrangement of the chord’s notes, which can give the chord a different sound or character.

How to Calculate Chord Inversion?

The following steps outline how to calculate a Chord Inversion:

  1. First, determine the chord you want to invert.
  2. Next, identify the root note of the chord.
  3. Next, determine the intervals between the root note and the other notes in the chord.
  4. Choose the inversion you want to create (e.g., root position, first inversion, second inversion).
  5. Rearrange the notes of the chord to create the desired inversion.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Chord: C major

Root note: C

Intervals: C – E – G

Inversion: First inversion

Rearranged notes: E – G – C