By combining the results of SNO and Super-Kamiokande one can derive - in the absence of sterile neutrinos - the total neutrino flux produced from $^8$B decay in the Sun. We use this information to check the accuracy of several input parameters of solar model calculations. Opacity and p-p fusion cross section are constrained by the $^8$B flux measurement to the level of few per cent. The central solar temperature is determined to the one-percent level. We also find an upper limit for the flux on Earth of sterile neutrinos. We discuss the role of nuclear physics uncertainties on these determinations.