Two methods to automatically detect cloud-free skies from the Earth's surface, which are based on algorithms using surface radiation measurements, are compared with Weather Service ground observations and each other. One algorithm uses total and diffuse shortwave downward radiation (referred to as the shortwave radiation algorithm (SWRA)), and the other uses longwave downward radiation in combination with surface temperature and humidity (referred to as the longwave radiation algorithm (LWRA)). The data used for the comparison originate from five Baseline Surface Radiation Network (BSRN) stations, two in polar regions, one in central Europe, and two at low latitudes, covering time periods of 2--6 years. After determination of the parameterization both algorithms can be applied without further effort, offering a straightforward technique to identify cloud-free skies over long time periods. With Weather Service ground observations as reference, LWRA detects cloud-free skies around 80% of the time. Significant overestimation of cloud cover happens during strong inversions. Thin high clouds on the one hand and dry haze (in an otherwise cloud-free sky) on the other hand can cause LWRA to wrongly calculate a clear sky. The percentage of detected and missed cloud-free skies by SWRA depends on the parameterization (i.e., the definition of cloud-free sky). Compared to Weather Service ground observations, we noticed lower rates of detected cloud-free skies at stations with frequent events with increased turbidity and underestimation of cloud cover occasionally during periods with only thin high clouds, especially if they are accompanied by increased turbidity.