Statistics calculator
Poisson Probability Calculator
Calculate exact and at-most Poisson probability from average event rate and event count.
Formula
Poisson probability
This assumes events occur independently at a stable average rate.
P(X = k) = e^-lambda x lambda^k / k!
Average rate 4 and exactly 2 events gives a Poisson probability.
FAQs
What is lambda?+
Lambda is the expected average number of events in the chosen interval.
What does at most k mean?+
It sums probabilities from zero events through k events.
How does the Poisson Probability Calculator calculate the result?+
It uses the Poisson probability: P(X = k) = e^-lambda x lambda^k / k!. Average rate 4 and exactly 2 events gives a Poisson probability.
What information do I need to use the Poisson Probability Calculator?+
Calculate exact and at-most Poisson probability from average event rate and event count.
How accurate is the Poisson Probability Calculator?+
Poisson Probability Calculator applies the formula and assumptions shown on this page. Results may be rounded for readability, so verify changing rates, thresholds, medical guidance, or legal rules with the cited source or a qualified professional.
What should I check before using the Poisson Probability Calculator result?+
Check that the units, dates, rates, and assumptions match your situation. Change one input at a time to understand which values have the largest effect on the result.
Statistics guide
How to use the Poisson Probability Calculator
Calculate exact and at-most Poisson probability from average event rate and event count. The page also explains the poisson probability and shows a practical example: Average rate 4 and exactly 2 events gives a Poisson probability.
- 1
Enter your details
Enter average event rate and event count, then complete any other fields shown in the calculator.
- 2
Check the calculation
Review the result alongside the poisson probability: P(X = k) = e^-lambda x lambda^k / k.
- 3
Compare scenarios
Change one or more inputs to see how they affect the poisson Probability Calculator result before you use the estimate.
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