Recent precise observations of solar global parameters are used to calibrate an upgraded solar model which takes into account magnetic fields in the solar interior. Historical data about sunspot numbers (from 1500 to the present) and solar radius changes (between 1715 and 1979) are used to compute solar variability on timescales of years to centuries. The results show that although the 11 year variability of the total irradiance is of the order of 0.1%, additional, longer-lived changes of the order of 0.1% may have occurred in the past centuries. These could, for example, account for the occurrence of climate excursions such as little ice ages. ¿ 2001 American Geophysical Union