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Poisson Distribution Calculator

A free online tool for calculating probabilities of events following Poisson distribution.
Independent random events occuring in a defined time interval or a defined length, area or space volume follow Poisson distribution with parameter λ equal to the average number of events per the defined time, length, space or volume unit. The probability P of seeing exactly x events during the defined time interval or in the defined length, space or volume unit is given by the formula:
P(X=x) = e

λ≥0, x≥0



Expected (average) number of events:λ =

Calculate the probability of x events:
x =
Calculate the total probability of numbers of events from the interval x1 - x2:
x1 = x2 =

P(X = x):

P(X ≤ x):

P(X ≥ x):