The Poisson distribution specifies the probability of a certain number of
events happening when each event occurs with a constant rate of
λ.
Change the value of
λ
to see how the shape of the distribution changes. Hover over the bars in the graph to find the corresponding probability, or look at the table below.

Rate Parameter λ:

Probability Table:

Rate Parameter λ:

Type of Probability:

Value of x:

Value of x_{1}:

Value of x_{2}:

Show Probability Table

Probability Table:

The formula for the distribution function $P(X = x)$ of the Poisson distribution is shown to the right.

The distribution function $P(X=x)$ finds the probability of observing a count of $x$ events, when events occur with rate $\lambda$.

Rate Parameter λ:

Number of Events (x):

For calculations with values of λ or x not selectable via the sliders, please go to the Find Probability tab, where you can enter any values for λ and x.