Probability of precipitation
A probability of precipitation (POP) is a formal measure of the likelihood of precipitation that is often published from weather forecasting models. Its definition varies.
U.S. usage
In U.S. weather forecasting, POP is the probability of exceedance that more than 1/100th of an inch of precipitation will fall in a single spot, averaged over the forecast area.[1] For instance, if there is a 100% probability of rain covering one half of a city, and a 0% probability of rain on the other half of the city, the POP for the city would be 50%. A 50% chance of a rainstorm covering the entire city would also lead to a POP of 50%.
Note that the POP measure is meaningless unless it is associated with a period of time. U.S. forecasts commonly use POP defined over 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:
- 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 might be 50% confident that under the current weather conditions precipitation will occur, and that should rain happen to occur, it will happen over 80% of the area. This results in a PoP of 40%: 
.
So, most of the time, the forecaster is expressing a combination of degree of confidence and areal coverage. The NWS explains this as follows: "Chance of rain 40 percent" means there is a 40 percent chance that rain will occur at any given point in the area. Another way to express "Chance of rain 40 percent" is that on average for all of the points in the area during the specified time period (usually 12-hour periods), chance that rain will occur is 40%.
Explanation
Suppose the forecast were for Maui, HI. One "given" point is your house near the top of Mt. Haleakala, where it rains almost constantly. A forecast of 40% is obviously not accurate for that given point. So assume that Mt. Haleakala is 10% of the area of Maui and that the average chance of rain today for the mountain is 80%. And assume that the average chance of rain for the other 90% of the island is 35%. So for the entire island, the average chance of rain is (0.9 × 0.35) + (0.1 × 0.8) = 0.395 = 40%.
Clearly, Mt. Haleakala pulls up the average for Maui. And clearly, the smaller the area, the more meaningful and accurate "chance of rain" is.
Terms typically in weather forecasts based on POP:
- 0% – No mention of precipitation
- 10% – No mention of precipitation, or isolated/slight chance
- 20% – Isolated/slight chance
- 30% – (Widely) scattered/chance
- 40% or 50% – Scattered/chance
- 60% or 70% – Numerous/likely
- 80%, 90% or 100% – No additional modifiers (e.g. "showers and thunderstorms")