We make the first quantitative estimates of the magnetopause reconnection rate at Jupiter using extended<I> in situ </I>data sets, building on simple order of magnitude estimates made some thirty years ago by Brice and Ionannidis (1970) and Kennel and Coroniti (1975, 1977). The jovian low-latitude magnetopause (open flux production) reconnection voltage is estimated using the Jackman et al. (2004) algorithm, validated at Earth, previously applied to Saturn, and here adapted to Jupiter. The high-latitude (lobe) magnetopause reconnection voltage is similarly calculated using the related Gérard et al. (2005) algorithm, also previously used for Saturn. We employ data from the Ulysses spacecraft obtained during periods when it was located near 5AU and within 5° of the ecliptic plane (January to June 1992, January to August 1998, and April to October 2004), along with data from the Cassini spacecraft obtained during the Jupiter flyby in 2000/2001. We include the effect of magnetospheric compression through dynamic pressure modulation, and also examine the effect of variations in the direction of Jupiter's magnetic axis throughout the jovian day and year. The intervals of data considered represent different phases in the solar cycle, such that we are also able to examine solar cycle dependency. The overall average low-latitude reconnection voltage is estimated to be ~230 kV, such that the average amount of open flux created over one solar rotation is ~500 GWb. We thus estimate the average time to replenish Jupiter's magnetotail, which contains ~300-500 GWb of open flux, to be ~15-25 days, corresponding to a tail length of ~3.8-6.5 AU. The average high-latitude reconnection voltage is estimated to be ~130 kV, associated with lobe "stirring". Within these averages, however, the estimated voltages undergo considerable variation. Generally, the low-latitude reconnection voltage exhibits a "background" of ~100 kV that is punctuated by one or two significant enhancement events during each solar rotation, in which the voltage is elevated to ~1-3 MV. The high-latitude voltages are estimated to be about a half of these values. We note that the peak values of order a few MV are comparable to the potential drop due to sub-corotating plasma flows in the equatorial magnetosphere between ~20 R<sub>J</sub> and the magnetopause, such that during these periods magnetopause reconnection may have a significant effect on the otherwise rotationally dominated magnetosphere. Despite such variations during each solar rotation, however, the total amount of open flux produced during each solar rotation varies typically by less than ~30% on either side of the overall average for that epoch. The averages over individual data epochs vary over the solar cycle from ~600 GWb per solar rotation at solar maximum to ~400 GWb at solar minimum. In addition we show that the IMF sector with positive clock angle is favoured for reconnection when the jovian spin axis clock angle is also positive, and vice versa, although this effect represents a first order correction to the voltage, which is primarily modulated by IMF strength and direction.