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.

**Syntax**:= POISSON.DIST(x,mean,cumulative)

The POISSON.DIST function syntax has the following arguments:

**X**(required argument) – This is the number of events for which we want to calculate the probability. The value must be greater than or equal to 0.**Mean**(required argument) – This is the expected number of events. The argument must be greater than or equal to zero.**Cumulative**(required argument) – This is the logical argument that specifies the type of distribution to be calculated. It can either be:- TRUE – Returns the cumulative Poisson probability that the number of random events occurring will be between zero and x inclusive.
- FALSE – Returns the Poisson probability mass function that the number of events occurring will be exactly x.

**Example**: Let’s look at some Excel POISSON.DIST function examples and explore how to use the POISSON.DIST function as a worksheet function in Microsoft Excel:

Suppose we are given the following data:

- Number of events:
**20** - Expected mean:
**25**

To find out the Cumulative Poisson probability, we will use the following formula:

**Syntax**: =POISSON.DIST(B1,B2,TRUE)

**Result**: 0.185492303

To find out the Poisson probability mass function, we will use the following formula:

**Syntax**: =POISSON.DIST(B1,B2,FALSE)

**Result**: 0.051917469

**Note**:

- 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: