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Poisson Probability Calculator

Find the probability of a number of events happening in a fixed interval when they occur at a known average rate. Enter the average number of events, called lambda, and the count you want, and the tool returns the exact probability plus the cumulative chance of at most and at least that many events. The exact value uses the Poisson formula, lambda to the k times e to the minus lambda divided by k factorial. This models arrivals at a queue, calls to a support line, typos per page, or radioactive decays in a second, any time events are independent and the rate is steady. The mean and the variance of a Poisson distribution are both equal to lambda, which the tool also reports. Factorials are handled with a running product to stay accurate for larger counts. Everything is computed locally in your browser, so your data never leaves the page.

How to use Poisson Probability Calculator

  1. Enter the average rate.
  2. Enter the event count.
  3. Read the exact, at most and at least probabilities.

Frequently asked questions

When is the Poisson distribution used?

It models the count of rare events in a fixed interval when they happen at a known average rate, such as calls per hour.

What is the average rate input?

The rate, often called lambda, is the mean number of events expected in the interval.

What do exact, at most and at least give?

Exact is the chance of precisely k events, at most sums up to k, and at least sums from k upward.

What is Poisson Probability Calculator?

Find the probability of a number of events happening in a fixed interval when they occur at a known average rate. Enter the average number of events, called lambda, and the count you want, and the tool returns the exact probability plus the cumulative chance of at most and at least that many events.

Is Poisson Probability Calculator free to use?

Yes. Poisson Probability Calculator is completely free, with no sign-up and no usage limits.

Does Poisson Probability Calculator work in a web browser?

Yes. Poisson Probability Calculator runs in any modern web browser. There is nothing to download or install.

Is my data private with Poisson Probability Calculator?

Yes. Poisson Probability Calculator runs entirely on your device in your browser, so nothing you enter is uploaded to a server.