The Ulysses spacecraft has shown that the radial component of the heliospheric magnetic field is approximately independent of latitude. This has allowed quantification of the total open solar flux from near-Earth observations of the interplanetary magnetic field. The open flux can also be estimated from photospheric magnetograms by mapping the fields up to the coronal source surface where the field is assumed to be radial and which is usually assumed to be at a heliocentric distance r = 2.5RS (a mean solar radius, 1RS = 6.96 ¿ 108 m). These two classes of open flux estimate will differ by the open flux that threads the heliospheric current sheet(s) inside Earth's orbit at 2.5RS < r < 1R1 (where the mean Earth-Sun distance, 1R1 = 1 AU = 1.5 ¿ 1011 m). We here use near-Earth measurements to estimate this flux and show that at sunspot minimum it causes only a very small (≈0.5%) systematic difference between the two types of open flux estimate, with an uncertainty that is of order ¿24% in hourly values, ¿16% in monthly averages, and between -6% and +2% in annual values. These fractions may be somewhat larger for sunspot maximum because of flux emerging at higher heliographic latitudes.