Poisson Distribution Calculator

The Poisson distribution named after French mathematician Siméon Denis Poisson (1781-1840).

is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event

Examples of the Poisson distribution are: the number of cars passing in a certain place during one hour, number of phone calls etc.

Probability of events for a Poisson distribution

An event can occur 0, 1, 2, … times in an interval. The average number of events in an interval is designated (lambda). Lambda is the event rate, also called the rate parameter. The probability of observing k events in an interval is given by the equation


is the average number of events per interval

e is the number 2.71828... (Euler's number) the base of the natural logarithms

k takes values 0, 1, 2, …

k! = k × (k − 1) × (k − 2) × … × 2 × 1 is the factorial of k.

For example: Salesman sales, in average, 5 products per week. The chance he will sale, in a given week 10 products is 1.8133%

(λ=2; k=10)

Contact Form

Do you have questions or comments for us? We'd love to hear them! Fill out the form and one of the calculators team will get back to you as soon as possible.