Poisson Distribution Calculator

Average Rate of Success (μ)

The average number of events expected in the interval.

Poisson Random Variable (x)

The exact number of events you want the probability for.

About This Test

What Is the Poisson Distribution?

The Poisson distribution gives the probability of a certain number of events happening in a fixed interval of time or space, given a known average rate — assuming events happen independently and at a constant average rate.

When to Use It

Number of calls a call center receives per hour
Number of defects found per batch of product
Number of website visits, accidents, or emails in a fixed period
Any count of rare, independent events over a fixed interval

The Formula

P(X = x) = (μ^x · e^−μ) / x!

Worked Example

A call center averages 4 calls per hour. What's the probability of getting exactly 6 calls in an hour?

μ = 4, x = 6
P(X = 6) ≈ 0.1042, or about 10.4%

Your Results

P(X = x)

P(X < x)

P(X ≤ x)

P(X > x)

P(X ≥ x)

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