A Probability of Precipitation or POP is a formal measure of the likelihood of precipitation that is often published from weather forecasting models.
In US weather forecasting, POP is the probability that more than 1/100th of an inch of precipitation will fall in a single spot, averaged over the forecast area.
For instance, if there is a 100% probability of rain covering one side of a city, and a 0% probability of rain on the other side of the city, the POP would be 50%.
A 50% chance of a rainstorm covering the entire city would also lead to a POP of 50%.
The POP measurement is meaningless unless it is associated with a period of time. US forecasts commonly use POP that is defined over a 12-hour periods (POP12), though 6-hour periods (POP6) and other measures are also published.
The mathematical definition of Probability of Precipitation is defined as: PoP = CxA
C = the confidence that precipitation will occur somewhere in the forecast area.
A = the percent of the area that will receive measurable precipitation, if it occurs at all.
For example; a forecaster may be 40% confident that under the current weather conditions that precipitation will occur, and that should rain happen to occur it will happen over 80% of the area. This results in a PoP of 32% ((0.4x0.8)x100 = 32%)