Chord Calculator — spell any chord, in any inversion

This chord calculator answers a question that comes up constantly for anyone learning harmony, arranging a part or reading a lead sheet: which notes are actually in this chord? Type a root, choose a quality from a plain triad to a thirteenth with an altered ninth, and the tool returns the spelled notes, the interval formula in semitones, the inversion you asked for, and a voicing you can play with the frequency of each pitch.

Arb Digital maintains a free tools library that grew out of the everyday arithmetic our own team kept redoing by hand, and the audio and music corner of it exists because sound is measurable. The tool is deliberately narrow. It spells chords. It does not analyse a progression, suggest what to play next, or generate audio — it gives you the raw material and leaves the musical decisions to you.

What This Chord Calculator Does

A chord is a set of pitches stacked at defined intervals above a root. The calculator takes the root you choose, applies the interval pattern that defines the quality, and reports the result three ways: as note names spelled correctly for that root, as a list of semitone distances, and as an octave-tagged voicing that tells a keyboard player exactly which keys to press.

It handles power chords, all four triad types, both suspended chords, sixths, the five common seventh chords, the minor-major seventh, added and extended ninths, elevenths and thirteenths, and the four everyday alterations of the dominant seventh. Inversions rotate the stack: first inversion puts the third in the bass, second inversion the fifth, third inversion the seventh. If you ask for a third inversion of a triad, which has no seventh, the tool leaves the chord in root position rather than inventing a note.

Here is the boundary with the other music tools on the site, because these questions get run together. The music scale generator produces the notes of a scale or mode — a horizontal set you draw melodies from — whereas this page produces a vertical stack meant to sound at once. The music transposer moves an existing chord or key up and down by an interval; it changes what you already have rather than building it from scratch. The note frequency converter takes a single named pitch to its frequency in hertz, which is the one-note case of what the grid on this page reports for the root.

How to Use It

1. Choose the root and its spelling. If the piece is in E♭ major, choose E♭ rather than D♯ even though they sound the same, so the resulting notes match the key signature.
2. Pick the quality. The list runs from simplest to most extended. Lead sheets abbreviate heavily: a bare letter means a major triad, a lowercase m or a dash means minor, and a bare 7 means a dominant seventh, not a major seventh.
3. Choose the octave. This does not change the notes, only the register the voicing is printed in. C4 is middle C.
4. Select an inversion if you need one. Inversions are what make a chord sequence move smoothly instead of leaping around.
5. Read the result. The hero line gives the notes in playing order, the sub-line gives the voicing with octave numbers, and the grid gives the chord symbol, the interval formula and the root frequency.

The Formula: How Chords Are Actually Built

Chords in Western harmony are built by stacking thirds. Take a scale, start on any degree, and take every other note: the first, third and fifth degrees give a triad, adding the seventh gives a seventh chord, and continuing past the octave gives the ninth, eleventh and thirteenth. The Open Music Theory chapter on triads and seventh chords sets out the four triad qualities and the five common seventh chords in exactly these terms.

Because a third can be major (4 semitones) or minor (3 semitones), four triads are possible. Major is a major third then a minor third: 0, 4, 7. Minor is a minor third then a major third: 0, 3, 7. Diminished stacks two minor thirds: 0, 3, 6. Augmented stacks two major thirds: 0, 4, 8. Every other chord in the list is one of these four with something added or altered.

Worked example. Build a G dominant seventh. The root G sits at semitone 7 in the chromatic set starting from C. The formula for a dominant seventh is 0, 4, 7, 10. Adding those offsets to G gives semitones 7, 11, 14 and 17, which reduce to G, B, D and F. The letter names follow from the stack of thirds: G is the first degree, so the chord uses the first, third, fifth and seventh letters counting from G — G, B, D, F. That letter-first method is what keeps the spelling right, and it is why the tool never prints something like G–B–D–E♯.

Why Spelling Is Not the Same as Sound

On a piano, D♯ and E♭ are one key. On paper they are different notes, and treating them as interchangeable is the single most common source of unreadable notation. The rule the tool follows is that a chord built by stacking thirds must use alternate letters: root, skip a letter, third, skip a letter, fifth. Once the letters are fixed, the accidental on each is whatever is needed to hit the right semitone.

That rule produces some notes that look alarming and are correct. A D♯ major triad is D♯–F♯♯–A♯, with a double sharp, because the letters must be D, F and A. Written as D♯–G–A♯ it would sound identical and be wrong, because G is a fourth above D rather than a third, and a reader looking for a triad would not see one. This is why the root selector offers both spellings of each black key: the correct answer depends on the key you are in, not on the sound.

The same logic gives diminished seventh chords their double flats. A C diminished seventh is C–E♭–G♭–B♭♭, because the seventh must be a B of some kind and the pitch required is a whole tone below C. Every professional engraver spells it that way, and every reader parses it instantly.

Inversions and Why They Matter More Than Beginners Expect

An inversion moves the lowest note of a chord up an octave, which changes which note is in the bass without changing the chord's identity. C–E–G, E–G–C and G–C–E are all C major. Lead sheets write inversions with a slash: C/E means a C major chord with E in the bass.

The reason to care is voice leading. If you play C major then F major in root position, every finger jumps. Play C major in root position and then F major in second inversion — C–F–A — and the top hand barely moves. Smooth motion between chords is most of what separates a progression that sounds arranged from one that sounds like a beginner reading symbols. When you are working out an accompaniment, build each chord here in the inversion whose notes sit closest to the chord before it.

Inversion also changes weight. A root-position chord sounds settled because the bass reinforces the root's own overtone series. A second-inversion triad, with the fifth in the bass, sounds unstable and tends to want to resolve, which is precisely why it is used at cadences to build tension before the final chord.

Reading Chord Symbols Without Guessing

Chord symbols are compressed to the point of ambiguity, and a few conventions cause most of the confusion. A bare number 7 means a dominant seventh — a major triad with a minor seventh — not a major seventh, which is written maj7 or with a triangle. A 6 chord adds a sixth to a triad and is not an inversion of anything. Sus chords replace the third rather than adding to it, so a Csus4 has no E in it at all; that is why the tool's sus2 and sus4 formulas contain no third.

Extended chords are the loosest area. In practice an eleventh chord usually omits the third, because the eleventh sits a semitone above it and the clash is harsh, and a thirteenth chord usually omits the eleventh for the same reason. This calculator prints the full theoretical stack so you can see the whole structure, and it is normal for a player to leave notes out. The notes that must survive any omission are the root, the third and the seventh — those three carry the chord's identity, and everything else is colour.

Where the Frequencies Come From

The frequency shown for the root uses twelve-tone equal temperament, in which each semitone is the twelfth root of two — about 1.05946 — times the one below it. From a reference pitch, the frequency of any note is the reference multiplied by that ratio raised to the number of semitones between them. Twelve semitones multiply out to exactly 2, which is why an octave doubles the frequency.

The reference is A above middle C, and ISO 16, the international standard for musical pitch, sets it at 440 Hz. Not everyone follows it: many European orchestras tune to 442 or 443 Hz for a brighter sound, and historical performance often uses 415 Hz. The tuning field lets you set the reference, and every printed frequency scales with it. If you need to convert a series of pitches rather than one chord root, the frequency converter handles the unit side and the note frequency converter handles named pitches.

One consequence of equal temperament worth knowing: none of the intervals except the octave is acoustically pure. The equal-tempered major third is about 14 cents wider than the pure 5:4 ratio, which is why sustained major triads on a keyboard beat slightly and why a barbershop quartet, free to adjust, sounds smoother than a piano playing the same chord.

Common Mistakes to Avoid

• Reading a bare 7 as a major seventh — C7 is C–E–G–B♭. The major seventh chord is Cmaj7 and contains B natural.
• Spelling a chord with the wrong letters — a triad must use alternate letters. If two adjacent letters appear, the spelling is wrong even when the sound is right.
• Adding a third to a sus chord — sus2 and sus4 replace the third. Playing a Csus4 with an E in it defeats the whole point of the suspension.
• Playing every note of an eleventh or thirteenth — the full stack is theory. In practice the eleventh clashes with the third and one of them is dropped.
• Assuming inversions change the chord — C/E is still C major. What changes is the bass line and the smoothness of the movement, not the harmony's name.

Related Free Tools From Arb Digital

Use the music scale generator for the scale a chord is drawn from, the music transposer to move a whole chart into a different key, the note frequency converter for the hertz value of a single named pitch, the frequency converter for unit conversion across the audio range, and the delay and reverb time calculator when you are setting time-based effects to a tempo. Everything else is in the free online tools hub.

Frequently Asked Questions

This tool spells chords using standard Western theory conventions. Notation practice varies between styles and publishers, and the arrangement you are reading may use different abbreviations or omit notes deliberately.