The Excel POISSON.DIST Function

Poisson Distribution

The Poisson distribution is a discrete probability function that can be used to find the probability of a number of events occurring in a specified time period.

The Poisson probability mass function shows the probability of exactly x occurrences, and is given by :

Poisson Probability Mass Function

where λ is the expected number of occurrences within the specified time period.

The cumulative distribution function shows the probability of at most x occurrences, and is given by :

Cumulative Poisson Probability Function

More information on the Poisson Distribution is given on the Wikipedia Poisson Distribution Page


Basic Description

The Excel POISSON.DIST function calculates the Poisson Probability Mass Function or the Cumulative Poisson Probability Function for a supplied set of parameters.

The function is new to Excel 2010 and so is not available in earlier versions of Excel. However the Poisson.Dist function is simply a new version of the Poisson function, which is available in earlier versions of Excel.

The format of the function is :

POISSON.DIST( x, mean, cumulative )

Where the function arguments are listed in the following table :


x -

The number of events that we want the probability for (must be ≥ 0)

x should be an integer; If supplied as a decimal, Excel will truncated this to an integer
mean - The expected number of events (must be ≥ 0)
cumulative - A logical argument that specifies the type of distribution to be calculated. This can be either:
TRUE - the cumulative distribution function
FALSE - the probability mass function


Poisson.Dist Function Examples

Plot of Poisson Probability Mass Function with Lambda=25
Poisson Probability Mass Function with mean (λ) = 25

Example 1 - Poisson Probability Mass Function

The chart on the right shows the the Poisson Probability Mass Function with an expected value (mean) equal to 25.

If you want to calculate the value of this function at x = 40, this can be done using the Excel Poisson.Dist function, as follows:

=POISSON.DIST( 20, 25, FALSE )

This gives the result 0.051917469.


Plot of Cumulative Poisson Probability Function with Lambda=40
Cumulative Poisson Probability Function with mean (λ) = 40

Example 2 - Cumulative Poisson Probability Function

The chart on the right shows the the Cumulative Poisson Probability Function with an expected value (mean) equal to 40.

If you want to calculate the value of this function at x = 25, this can be done using the Excel Poisson.Dist function, as follows:

=POISSON.DIST( 35, 40, TRUE )

This gives the result 0.242414198.


Further information and examples of the Excel Poisson.Dist function can be found on the Microsoft Office website.


Poisson.Dist Function Errors

If you get an error from the Excel Poisson.Dist function this is likely to be one of the following :

Common Errors
#NUM! - Occurs if either of the supplied x or mean arguments are < 0
#VALUE! - Occurs if either of the supplied x or mean arguments are non-numeric
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