Although I've been using a capo for years, I really don't know how to determine it's placement for playing with open chords shapes in certain key. I just know "play this song using the capo on 4th fret" etc.

Is there a "formula" for calculating which fret to place the capo on?

I have a hunch an answer lies in a circle of fifts. I just can't derive the result with my current knowledge.