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.



The POISSON.DIST 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.DIST 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.


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

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

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

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

  • POISSON.DIST is calculated as follows.

    For cumulative = FALSE:


    For cumulative = TRUE:



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.




Number of events


Expected mean



R esult


Cumulative Poisson probability with the arguments specified in A2 and A3.



Poisson probability mass function with the arguments specified in A2 and A3.


Applies To: Excel 2016, Excel 2013, Excel 2010, Excel 2007, Excel 2016 for Mac, Excel for Mac 2011, Excel Online, Excel for iPad, Excel for iPhone, Excel for Android tablets, Excel Starter, Excel for Android phones

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