When to use this calculator
Use a mean count for the same duration or area as the event count being evaluated.
Explore the probability & distributions calculators for other questions in this topic. For a related calculation, use the Uniform Distribution Probability Calculator: Find probability over an interval within a continuous uniform distribution.
PUTTING IT INTO PRACTICE
Poisson Probability: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Expected count per interval | 2 |
| Observed count (integer) | 0 |
| Result | 13.533528 % |
- Check the input labels and enter the example values above.
- Apply the relationship: P(X=k) = exp(−λ) × λ^k/k!.
- The result is 13.533528 %, rounded for display.
How to interpret your result
Assumes independent events with a constant rate over the chosen interval. Large values can exceed numeric limits.
A distribution model is an assumption about the process, not a guarantee about outcomes. Independence, constant probability and fixed interval definitions matter. Exactly-k probabilities differ from cumulative probabilities.
Frequently asked questions
Does exactly two successes mean two or more?
No. Exactly two counts only outcomes with two successes. Two or more is a cumulative probability covering several counts.
When is the poisson probability calculator useful?
Use a mean count for the same duration or area as the event count being evaluated.
How do I use the poisson probability calculator?
Enter expected count per interval, observed count (integer). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
P(X=k) = exp(−λ) × λ^k/k!.
What should I check before using the result?
Assumes independent events with a constant rate over the chosen interval. Large values can exceed numeric limits.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see NIST: probability distributions ↗. This is a topic reference, not an external review or endorsement of this tool.
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