We calculate the altitude of the Venus ionopause following the inviscid fluid approach initially introduced by Spreiter et al. (1970) and later modified by Spreiter and Stahara (1980) but incorporate several improved approximations. The calculated altitude is compared with median altitudes measured by the Pioneer Venus retarding potential analyzer. The calculated ionopause shape approximates the measured median shape closely in the solar zenith angle (SZA) range 0¿--135¿ and is a definite improvement over previous calculations. Improved approximations include use of an ionospheric pressure field which varies with SZA in a manner consistent with measurements, use of the modified Newtonian approximation for the pressure exerted on the ionosphere by the ionosheath, use of the Prandtl-Meyer expansion approximation for a short distance downstream from the terminator, and separation of the solar wind terminator from the solar extreme ultraviolet radiation terminator. The calculation is not expected to be accurate for solar zenith angles in excess of approximately 135¿. Use of the improved approximations lowers the terminator ionopause altitude to approximately half that obtained with use of the usual Spreiter approximations. The calculated dawn ionopause is approximately 300 km higher in altitude than the dusk ionipause. Both ionopauses are close to their respective measured median values. The value of the upstream wind momentum flux required to fit the measured median ionopause altitudes is within 15% of the measured median solar wind momentum flux. We conclude that the median altitude of the ionopause between 0¿ and approximately 135¿ SZA may be adequately calculated without including a viscous interaction in the theory.