Both the total amount of precipitation falling on Earth's surface and the fraction of the surface area on which it falls represent two key global climate indicators for Earth's global hydrological cycle. We show that the fraction of Earth's surface area receiving daily precipitation is closely connected to the global statistics of local wet-day frequency as well as mean precipitation intensity. Our analysis was based on the ERA5 reanalysis which also revealed a close link between the global mean of the mean precipitation intensity for each grid box and the total daily precipitation falling on Earth's surface divided by the global surface area fraction on which it falls. The wet-day frequency and the mean precipitation intensity are two important statistical indicators for inferring effects of climate change on society and nature as they represent key parameters that can be used to approximately infer the probability of heavy rainfall on local scales. We also found a close match between the global mean temperature and both the total planetary amount of precipitation and surface area in the ERA5 data, hinting at a dependency between the greenhouse effect and the global hydrological cycle. Hence, the total planetary precipitation and the daily precipitation area represent links between the global warming and extreme precipitation amounts that traditionally have not been included in sets of essential climate indicators.