Parallel key
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In music, the parallel minor of a particular major key is the minor key with the same tonic; similarly the parallel major of a minor key has the same tonic. For example, G major and G minor have different modes but both have the same tonic, G; so we say that G minor is the parallel minor of G major.
In the early nineteenth century, composers (notably Robert Schumann) began to experiment with freely borrowing chords from the parallel key.
Easily calculating the key signature of the parallel major or minor of a key
To find the parallel minor of a key, add 3 flats to the key signature.
For example, F major has 1 flat (B). Adding 3 flats would yield 4 flats, meaning F minor has 4 flats in its key signature. (B E A D)
B major has 5 sharps (F C G D A). To find B minor, add 3 flats. Since flats cancel out sharps, you are left with 2 sharps. (F C)
To find the parallel major, add 3 sharps.
Em to EM: Em has 1 sharp (F). Add 3 to get 4 sharps. (F C G D)
Fm to FM: Fm has 4 flats (B E A D). Add 3 sharps to get 1 flat. (B)