The coincidence between the Maunder Minimum of solar magnetic activity from 1645 to 1715 and the coldest temperatures of the Little Ice Age raises the question of possible solar forcing of the Earth's climate. Using a correlation which we find between measured total solar irradiance (corrected for sunspot effects) and a Ca II surrogate for bright magnetic features, we estimate the Sun's radiative output in the absence of such features to be 1365.43 w/m2, or 0.15% below its mean value of 1367.54 W/m2 measured during the period 1980 to 1986 by the ACRIM experiment. Observations of extant solar‐type stars suggest that the Ca II surrogate vas darker during the Maunder Minimum. Allowing for this, we estimate the total solar irradiance to be 1364.28 W/m2 or 0.24% below its mean value for the 1980 to 1986 period. The decrease in the global equilibrium temperature of the Earth due to a decrease of 0.24% in total solar irradiance lies in the range from 0.2° C to 0.6° C, which can be compared with the approximately 1° C cooling experienced during the Little Ice Age, relative to the present.