Poisson Distribution in Excel

Poisson Distribution in Excel

Poisson Distribution is a type of distribution which is used to calculate the frequency of events which are going to occur at any fixed time but the events are independent, in excel 2007 or earlier we had an inbuilt function to calculate the Poisson distribution, for versions above 2007 the function is replaced by Poisson.DIst function.


Poisson.Dist Formula

X: This is the number of events. This should be >=0.

Mean: The expected number of events. This is also should be >=0.

Cumulative: This will decide the type of distribution to be calculated. We have two options here TRUE or FALSE.

  • TRUE indicates the probability of a number of events happening between zero and x.
  • FALSE indicates the probability of the number of events happening exactly the same as the x.


You can download this Poisson Distribution Excel Template here – Poisson Distribution Excel Template

Example #1

As a car rental company owner, your average weekend car rental customers are 500. You are expecting 520 customers in the coming weekend.

You want to know the probability percentage of this event occurring in the coming week.

  1. Here, x is 520, and the mean is 500. Enter these details in excel.

    Poisson Distribution Excel Example 1

  2. Open POISSON.DIST function in any of the cell.

    Poisson Distribution Excel Example 1-1

  3. Select the x argument as the B1 cell.

    Poisson Distribution Excel Example 1-2

  4. Then select the Mean argument as B2 cell.

    Poisson Distribution Excel Example 1-3

  5. We are looking at the “cumulative distribution function,” so select TRUE as the option.

    Poisson Distribution Excel Example 1-4

  6. So, we got the result as 0.82070. Now in the below cell, apply the formula as 1 – B5.

    Poisson Distribution Excel Example 1-5

So, the probability of increasing car rental customers from 500 to 520 in the coming week is about 17.93%.

Example #2

In the production of 1000 units of automobile products, the average percentage of defect products is about 6%. Similarly, in a sample of 5000 products, what is the probability of having 55 defect products?

Example 2

First calculate the number of defect products in 1000 units. i.e. λ = np. λ = 1000 * 0.06.

Example 2-1

So, the total number of defect products in 1000 units is 60 units. Now we got the total defects number (x). So x = 60.

Now to decrease the defect products from 60 to 55, we need to find the excel Poisson Distribution percentage.

So, MEAN = 55, x =  60.

Example 2-2

The above formula will give us the Poisson distribution value. In the below cell, apply the formula 1 – Poisson distribution in excel.

Example 2-3

So, the probability of reducing defect items from 60 to 55 is about 23%.

Things to Remember

  • We will get the number error of #NUM! is the supplied x & Mean values are less than zero.
  • We will get #VALUE! If the arguments are non-numeric.
  • If the supplied numbers are decimal or fraction, then excel automatically rounded to the nearest integer number.

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This has been a guide to Poisson Distribution in Excel. Here we discuss how to calculate Poisson distribution in excel using POISSON.DIST function, along with examples and downloadable excel template. You may also look at these useful functions in excel –

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