# 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.

## Syntax

`POISSON(x,mean,cumulative)`

The POISSON function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

• 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

The example may be easier to understand if you copy it to a blank worksheet.

1. Select the example in this article. If you are copying the example in Excel Web App, copy and paste one cell at a time.Important Do not select the row or column headers.

Selecting an example from Help

1. Press CTRL+C.
2. Create a blank workbook or worksheet.
3. In the worksheet, select cell A1, and press CTRL+V. If you are working in Excel Web App, repeat copying and pasting for each cell in the example.

Important For the example to work properly, you must paste it into cell A1 of the worksheet.

1. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

After you copy the example to a blank worksheet, you can adapt it to suit your needs.

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

Note    The value of the result depends on the number of decimal places that are used in the number format of the cell that contains the formula.

Applies to:
Excel 2010, Excel Web App, SharePoint Online for enterprises, SharePoint Online for professionals and small businesses