The Poisson distribution describes the probability of obtaining *k* successes during a given time interval.

If a random variable *X* follows a Poisson distribution, then the probability that *X* = *k* successes can be found by the following formula:

**P(X=k) = λ ^{k} * e^{– λ} / k!**

where:

**λ:**mean number of successes that occur during a specific interval**k:**number of successes**e:**a constant equal to approximately 2.71828

The following example explains how to create a Poisson distribution graph in Excel.

**Example: Poisson Distribution Graph in Excel**

To create a Poisson distribution graph, we need to first decide on a value for λ (mean number of successes):

Next, we need to create a column for each possible number of successes:

Note that we chose k = 10 possible successes. We could have chosen more, but the probabilities become very small for values greater than 10, as we’ll see later in this post.

Next, we can use the **POISSON.DIST()** function to calculate the Poisson probability for the first number of successes:

We can then copy and paste this formula to the remaining cells in column B:

Lastly, we can highlight each of the Poisson probabilities, then click the **Insert** tab along the top ribbon, then click the **Insert Column or Bar Chart** icon in the **Charts** group:

The x-axis of the graph shows the number of successes and the y-axis shows the corresponding probability of that many successes.

Note that if you change the value for λ (mean number of successes), the graph will automatically change to reflect the new probabilities.

For example, if we change the λ value to 4, the Poisson probabilities and the graph will automatically update:

**Additional Resources**

Poisson Distribution Calculator

How to Use the Poisson Distribution in Excel

How to Calculate Poisson Probabilities on a TI-84 Calculator