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FL=(d/2)/tan(a/2)
where FL is the focal length, d is the sensor diagonal and a is the diagonal field of view.
The resolution (Nx and Ny) and the other parameters of the camera don't have any incidence on the focal length.
N.B. this formula is true in the other side of the lens too. For example to get the height of the image (the object that fits in the image) OH at a given distance D given a vertical angle of view av:
OH=2*D*tan(av/2)
More details on angle of view, focal length and image area here.