Cygnus X-1 is a binary star system that is comprised of a black hole and a massive giant companion star in a tight orbit . Building on our accurate distance measurement reported in the preceding paper , we first determine the radius of the companion star , thereby constraining the scale of the binary system . To obtain a full dynamical model of the binary , we use an extensive collection of optical photometric and spectroscopic data taken from the literature . By using all of the available observational constraints , we show that the orbit is slightly eccentric ( both the radial velocity and photometric data independently confirm this result ) and that the companion star rotates roughly 1.4 times its pseudosynchronous value . We find a black hole mass of M = 14.8 \pm 1.0 M _ { \odot } , a companion mass of { M } _ { opt } = 19.2 \pm 1.9 M _ { \odot } , and the angle of inclination of the orbital plane to our line of sight of i = 27.1 \pm 0.8 deg .