​Poisson Distribution Calculator

Poisson distribution is a term that relates to the chances of an event to occur, and how many times it will be going to happen in the decided time. In the specified period, how likely you will see the train passing in front of you? Or how often will the blue car come into view if you are standing at the corner of the road? All these probabilities are taken under the term of Poisson distribution.

This is the variable term giving us the ratio of occurring and non-occurring of the occasion to happen. The number of the variable will be the whole number every time. The fractional values are not part of the event or happening. In short, it is the measurement of the probability of the event happening in a specified interval of time.


Formula of ​Poisson Distribution Calculator

The mathematical representation of the Poisson distribution is as follows:

P(x; μ) = (e-μ) (μx) / x!


μ = total happening on average in the specified time

x = probability of the future occurring

e = Euler’s constant having the fixed value of 2.718

P = function of the Poisson distribution


To gain knowledge about reference angles, click the Reference Angle Calculator.


To make the term clear, let’s have a look at the example. A person is selling cars. On average, he sells 2 cars per day. What is the probability he will sell his next 3 cars the very next day?

Putting the values in the above formula, we get:

P(x; μ) = (e-μ) (μx) / x!
P(3; 2) = (2.71828-2) (23) / 3!
P(3; 2) = (0.13534) (8) / 6
P(3; 2) = 0.180

Therefore, the probability of selling the 3 left cars the next day will 0.180.

How to use ​Poisson Distribution Calculator?

The steps to use ​Poisson distribution calculator are as follows:

Step 1: Enter the value of a number of occurences in the first required input.

Step 2: Enter the value of the rate of success in the second required input.

Step 3: The calculator will automatically display an answer on the screen.

Calculator use

Using the Poisson distribution calculator, you can save from long derivations and calculations. Simply put the average number of happening in that event in the past and the total number of events to get the answer of possibilities. You do not have to put the value of Euler’s constant again and again. It will automatically adjust the values and you will get the solution with one click.