Key signatures

Modulation from tonic to dominant (I→V)

Add sharps or Lose flats

Modulation from tonic to subdominant (I→IV)

Lose sharps or Add flats

Formula for finding Major key from a key signature with sharps

Look at the rightmost sharp on the stave, Go up half a semitone

Formula for finding a Major key from a key signature with flats

Look at the second-to-last flat from the right (or F Major for 1 flat)

Formula for finding relative Minor key from a major key

Go down 3 semitones from the root note

Key signature with No sharps or flats

C Major or A Minor

Key signature with 1 sharp

G Major or E Minor

Key signature with 2 sharps

D Major or B Minor

Key signature with 3 sharps

A Major or F♯ Minor

Key signature with 4 sharps

E Major or C♯ Minor

Key signature with 5 sharps

B Major or G♯ Minor

Key signature with 6 sharps

F♯ Major or D♯ Minor

Key signature with 7 sharps

C♯ Major or A♯ Minor

Key signature with 1 Flat

F Major or D Minor

Key signature with 2 Flats

B♭ Major or G Minor

Key signature with 3 Flats

E♭ Major or C Minor

Key signature with 4 Flats

A♭ Major or F Minor

Key signature with 5 flats

D♭ Major or B♭ Minor

Key signature with 6 flats

G♭ Major or E♭ Minor

Key signature with 7 flats

C♭ Major or A♭ Minor