POISSON function

Returns the Poisson distribution. A common application of the Poisson distribution is predicting the number of events over a specific time, such as the number of cars arriving at a toll plaza in 1 minute.

Important: This function has been replaced with one or more new functions that may provide improved accuracy and whose names better reflect their usage. Although this function is still available for backward compatibility, you should consider using the new functions from now on, because this function may not be available in future versions of Excel.

For more information about the new function, see POISSON.DIST function.

Syntax

POISSON(x,mean,cumulative)

The POISSON function syntax has the following arguments:

• X     Required. The number of events.

• Mean     Required. The expected numeric value.

• Cumulative     Required. A logical value that determines the form of the probability distribution returned. If cumulative is TRUE, POISSON returns the cumulative Poisson probability that the number of random events occurring will be between zero and x inclusive; if FALSE, it returns the Poisson probability mass function that the number of events occurring will be exactly x.

Remarks

• If x is not an integer, it is truncated.

• If x or mean is nonnumeric, POISSON returns the #VALUE! error value.

• If x < 0, POISSON returns the #NUM! error value.

• If mean < 0, POISSON returns the #NUM! error value.

• POISSON is calculated as follows.

  For cumulative = FALSE:

  

  For cumulative = TRUE:

  

Example

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

Data	Description
2	Number of events
5	Expected mean
Formula	Description (Result)	R esult
=POISSON(A2,A3,TRUE)	Cumulative Poisson probability with the terms above (0.124652)	0.124652
=POISSON(A2,A3,FALSE)	Poisson probability mass function with the terms above (0.084224)	0.084224