A new model of the coronal and interplanetary magnetic field can predict both the interplanetary magnetic field strength and its polarity from measurements of the photospheric magnetic field. The model includes the effects of the large-scale horizontal electric currents flowing in the inner corona, of the warped heliospheric current sheet in the upper corona, and of volume currents flowing in the region where the solar wind plasma totally controls the magnetic field. The model matches the MHD solution for a simple dipole test case better than earlier source surface and current sheet models. The strength and polarity of the radial interplanetary magnetic field component predicted for quiet time samples in each year from 1977 to 1986 agree with observations made near the Earth's orbit better than the hybrid MHD-source surface model (Wang and Sheeley, 1988). The results raise the question of whether coronal holes are the only solar source of the interplanetary magnetic field in the solar wind. If some interplanetary flux originates outside coronal holes, the model can match the observed field using the accepted 1.8 saturation correction factor for &lgr;5250 ¿ magnetograph observations. Requiring open flux to come exclusively from coronal holes requires an additional factor of two. ¿ American Geophysical Union 1995