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Most of the websites i have looked at, say that the frequency of middle C note is approximately 261.626 Hz. and that middle C on guitar is at the 5th string 3rd fret. but my tuner says the frequency at the 5th string 3rd fret is 130.81 Hz.
In guitar music, middle C (first ledger line below the staff) is the third fret of the A string. In real life, middle C on the guitar is on the first fret of the B string. The reason for this is so that guitar music can be written on a single staff instead of two (like piano music). A lot of instruments have similar issues. All Bb instruments are written a note higher than concert pitch.