*Poisson Distribution Calculator* is an online probability and statistics tool for data analysis programmed to find out the counts of events that occur randomly in a given interval of time. This calculator computes the output values of Poisson and cumulative poisson distribution with respect to the input values of average rate of success and random variables

### Definition

The Poisson distribution, a discrete probability function is used estimate the degree of spread with known average rate of occurrence. When situation arise with the experiment where the great number of possible event occurs, the poisson distribution is employed to designate the probability of a given data set or number of events at a fixed time of interval. It is asymmetric function and has the strong connection with hypergeometric, binomial and exponential distributions

### The Formula for Poisson Distribution

Poisson Distribution with the instances of k = 0, 1, 2, .., n can be calculated from the formula

where

**e** is the base of the natural logarithm equal to 2.71828..

**k** is the number of occurrences of an event; the probability of which is given by the function

**k!** is the factorial of k

**λ** is a positive real number, equal to the expected number of occurrences during the given interval. For instance, if the events occur on average 3 times per minute, and one is interested in the probability of an event occurring k times in a 10 minute interval, one would use a Poisson distribution as the model with **λ** = 10 x 3 = 30

The above illustrations can guide you to understand how to find out the poisson distribution in probability statistics. To make your calculations easy, this online Poisson distribution calculator will help you to figure out counts of events that occur randomly in a given interval of time