Abstract World extremes in meteorology are important as they can be used as indicators for climate change. This was one of the main reasons for the creation of the World Meteorological Organization’s World Weather and Climate Extremes Archive in 2006. In contrast to temperature, for instance, which can be described by a single parameter, point rainfall must be described by two parameters, for example, precipitation depth and duration. This makes it difficult to directly compare different rainfall records. In this article, however, it is shown that the world’s greatest rainfall events, with durations ranging from 1 min to 2 years, all have nearly the same precipitation intensity duration index, a new dimensionless number. As a theoretical consequence, the intensity of all these record rainfalls is inversely proportional to the square root of their duration. This physically based result is consistent with earlier statistically based findings. The last measured record rainfall on the World Meteorological Organization’s record list is the point rainfall with the largest precipitation intensity duration index since 1860. This 4-day rainfall that began on 24 February 2007 on Cratère Commerson, Réunion Island, can be considered the largest point rainfall within documented records. Significance Statement Floods resulting from extreme rainstorms can be very costly and deadly; thus, understanding such extreme events is very important. Knowledge of extreme rainstorms is also important in determining how much and how fast our climate is changing. In this article, a new dimensionless number, the precipitation intensity duration index (PID) is presented. The world’s greatest point rainfall events, with durations ranging from 1 min to 2 years, all have nearly the same PID. One rainfall event, however, has a considerably larger PID than all others, namely, a 4-day rainfall that began on 24 February 2007 on Cratère Commerson, Réunion Island. Therefore, this rainfall can be considered the largest point rainfall within documented records.