The interstellar gas in spiral galaxies can constitute a significant fraction of the baryon mass and it has been demonstrated that the sum of stellar and gas components correlates well with the kinematic signature of the total mass content, the widths of H I line profiles. The correlation of baryonic mass with H I linewidths is used here to obtain distances for 9984 galaxies extending to ~0.05c. The sample is H I flux limited and a correction is required to account for an H I selection bias. The absolute scale is established by 64 galaxies with known distances from studies of Cepheid variables and/or the magnitudes of stars at the tip of the red giant branch. The calibration of the baryonic relationship results in a determination of the Hubble constant of H_0_ = 75.5 +/- 2.5 km/s/Mpc. The error estimate is statistical. This material will be combined with contributions from other methodologies in a subsequent paper where systematic uncertainties will be investigated.