Poisson Probability Calculator
Find the chance of k events given an average rate.
Counting rare events
The Poisson distribution predicts how many independent events happen in an interval when they arrive at a steady average rate — calls to a help desk, emails per hour, decays per second.
If an average of 3 events occur per interval, the chance of exactly 2 is about 22.4%. Enter your rate and a target count to get the exact and cumulative probabilities.
Exact and private
The calculation runs in your browser, so nothing you enter is uploaded.
Frequently Asked Questions
What is the Poisson distribution?
It models the number of independent events in a fixed interval when they occur at a known average rate.
What do I enter?
The average number of events (lambda) and the specific count k you want the probability for.
Where is it used?
Call-center arrivals, website hits, radioactive decay, and other rare-event counts.
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