The accurate determination of the solar photospheric radius has been an important problem in astronomy for many centuries. From the measurements made by the PICARD spacecraft during the transit of Venus in 2012, we obtained a solar radius of 696,156±145 kilometres. This value is consistent with recent measurements carried out atmosphere. This observation leads us to propose a change of the canonical value obtained by Arthur Auwers in 1891. An accurate value for total solar irradiance (TSI) is crucial for the Sun-Earth connection, and represents another solar astrophysical fundamental parameter. Based on measurements collected from different space instruments over the past 35 years, the absolute value of the TSI, representative of a quiet Sun, has gradually decreased from 1,371W.m −2 in 1978 to around 1,362W.m −2 in 2013, mainly due to the radiometers calibration differences. Based on the PICARD data and in agreement with Total Irradiance Monitor measurements, we predicted the TSI input at the top of the Earth’s atmosphere at a distance of one astronomical unit (149,597,870 kilometres) from the Sun to be 1,362±2.4W.m −2 , which may be proposed as a reference value. To conclude, from the measurements made by the PICARD spacecraft, we obtained a solar photospheric equator-to-pole radius difference value of 5.9±0.5 kilometres. This value is consistent with measurements made by different space instruments, and can be given as a reference value.