# Poisson Distribution Calculator

Instructions: Compute Poisson distribution probabilities using the form below. Please type the population mean (λ), and provide details about the event you want to compute the probability for: Population mean ($$\lambda$$)
Two-Tailed:
≤ X ≤
Left-Tailed:
X ≤
Right-Tailed:
X ≥

## Poisson Probability Calculator

More about the Poisson distribution probability so you can better use the Poisson calculator above: The Poisson probability is a type of discrete probability distribution that can take random values on the range $$[0, +\infty)$$. The main properties of the Poisson distribution are:

• It is discrete, and it can take values from 0 to $$+\infty$$.

• The type of skewness depends on the population mean ($$\lambda$$)

• It is determined by the population mean ($$\lambda$$)

• Its mean is $$\lambda$$ and its population variance is also $$\lambda$$

Using the above Poisson distribution curve calculator, you are able to compute probabilities of the form $$\Pr(a \le X \le b)$$, of the form $$\Pr(X \le b)$$ or of the form $$\Pr(X \ge a)$$. Type the appropriate parameter for $$\lambda$$ in the text box above, select the type of tails, specify your event and compute your Poisson probability.

The Poisson probability formula is

$\Pr(X = k) = \displaystyle \frac{e^{-\lambda} \lambda^k}{k!}$

This Poisson distribution calculator with steps corresponds to a solver for a discrete distribution. We have other discrete distribution calculators that you may be interested in, such as our Binomial distribution calculator, Geometric distribution calculator, and Hypergeometric distribution calculator, to mention a few of them.

Also, you can use our general discrete probability calculator which will provide you with the mean and standard deviation of a generic discrete distribution.

In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to contact us. 