# Microsoft Knowledge Base

## Excel: POISSON() Function Returns #NUM! Error Value

Last reviewed: September 12, 1996
Article ID: Q104583

• Microsoft Excel for Windows, versions 4.0, 4.0a, 5.0
• Microsoft Excel for the Macintosh, versions 4.0, 5.0

## SUMMARY

In Microsoft Excel, the POISSON() function will return a #NUM! error value if the mean argument (the second argument), raised to the power of the x argument (the first argument), exceeds 9.999E+307.

You will also receive a #NUM! error value if the x argument (the first argument) exceeds 170.

The POISSON() function returns the Poisson probability distribution. You can use this function to predict the number of events over a specific time, such as the number of cars arriving at a toll plaza in one minute.

Microsoft Excel computes the Poisson probability distribution with the following formula,

```   (e^-y) * (y^x)
--------------
(x!)
```

where:

• e is the base of the natural logarithm, or 2.71828182845904
• y is the expected number of successes (the mean)
• x is the number of actual successes (x)

One of the components of the formula is y raised to the power of x (y^x). If this component exceeds 9.999E+307, the maximum possible positive number in Microsoft Excel, you will receive a #NUM! error value.

Another component of the formula computes the factorial of x (x!). If x exceeds 170, the factorial of x will exceed 9.999E+307, resulting in a #NUM! error.

In general, these errors only occur when you use numbers greater than 100 for the mean and x arguments.