How this calculator works
A key signature collects the sharps or flats used by a key and writes them after the clef. Sharps always appear in the order F, C, G, D, A, E, B and flats in the reverse order B, E, A, D, G, C, F, so a reader memorises one sequence rather than each key. Moving up a fifth adds one sharp, which is why G major has one, D major two and A major three. Moving down a fifth adds one flat. The relative minor shares a signature with its major, three semitones below the major tonic, so D major and B minor both have two sharps.
Formula
major keys with sharps follow the circle of fifths: C 0, G 1, D 2, A 3, E 4, B 5, F# 6, C# 7. Major keys with flats run the other way: F 1, Bb 2, Eb 3, Ab 4, Db 5, Gb 6, Cb 7. A minor key shares the signature of the major three semitones above its tonic, so the minor order is A 0, E 1, B 2, F# 3, C# 4, G# 5, D# 6, A# 7 for sharps and D 1, G 2, C 3, F 4, Bb 5, Eb 6, Ab 7 for flats.
Worked example
D major has two sharps, written in the order F# then C#. Its relative minor is B minor, which uses the same two sharps. Eb minor has six flats, written Bb, Eb, Ab, Db, Gb and Cb, and its relative major is Gb major. A signature with three sharps is A major or F# minor depending on the quality you choose.
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Frequently asked questions
How do I read a key signature quickly?
For sharps, the last sharp is one semitone below the tonic, so a signature ending on G# is A major. For flats, the second-to-last flat names the major key, so four flats ending in Db means Ab major. The relative minor is three semitones below the major tonic.
Why do the theoretical keys exist?
C# major with seven sharps and Cb major with seven flats are rare because their enharmonic partners Db major and B major are easier to read. They still appear in modulating passages and in theory exercises. The page lists them so every signature from zero to seven accidentals has a major and a minor answer.
What is the difference between a key signature and an accidental?
A key signature applies to every occurrence of those notes throughout the piece. An accidental is written next to a single note and lasts to the end of the bar. Music in a key still uses accidentals for borrowed chords, chromatic passing notes and modulations.
Does a minor key use the harmonic minor scale?
The key signature shows the natural minor scale. In harmonic minor the seventh degree is raised, which appears as a written accidental rather than in the signature. That raised seventh creates the major dominant chord that makes the cadence stronger.