# (Chapter 6) How to calculate the Probability of Precipitation?

Probability of precipitation is a formal measure of likelihood of precipitation that is often published from weather forecasting model, which is often expressed as the “chance of rain” or “chance of precipitation”. Mathematically, Probability of Precipitation(Pop) 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

For example, if a forecaster says:
“THIS AFTERNOON…MOSTLY CLOUDY WITH A 40 PERCENT CHANCE OF
SHOWERS AND THUNDERSTORMS. WINDY. HIGHS IN THE LOWER 80S. NEAR
STEADY TEMPERATURE IN THE LOWER 80S. SOUTH WINDS 15 TO 25 MPH.
.TONIGHT…MOSTLY CLOUDY WITH A CHANCE OF SHOWERS AND
THUNDERSTORMS IN THE EVENING…THEN A SLIGHT CHANCE OF SHOWERS
AND THUNDERSTORMS AFTER MIDNIGHT. LOWS IN THE MID 60S. SOUTHWEST
WINDS 5 TO 15 MPH. CHANCE OF RAIN 40 PERCENT”

What does this “40 percent” mean? Will it rain 40 percent of of the time? Or Will it rain over 40 percent of the area?
The “Probability of Precipitation” (PoP) describes the chance of precipitation occurring at any point you select in the area

In this case, if the forecaster knows the precipitation will surely occur(C=100%) The forecaster is expressing how much of the area will receive measurable rain. ( PoP = “C” x “A” or “1” times “.4” which equals .4 or 40%.)

However, also, most of the time, the forecaster is expressing a combination of degree of confidence and areal coverage. If the forecaster is only 50% sure that precipitation will occur, and expects that it will produce measurable rain over about 80 percent of the area, the PoP (chance of rain) is 40%. ( PoP = .5 x .8 which equals .4 or 40%. )

Either way, the correct way to interpret the forecast is: there is a 40 percent chance that rain will occur at any given point in the area.