Poisson Probability Calculator
The Poisson model calculates the chance of observing exactly a specified number of events when events occur independently at a fixed average rate.
How to use this calculator
- Enter the expected count λ and a non-negative integer event count.
- Confirm that all inputs use the stated units and the same population, period or scope.
- Change one assumption at a time when comparing scenarios.
Formula used by the poisson probability calculator
P(X=k)=e^(−λ) λ^k/k!
- P(X=k)=e^(−λ) λ^k/k!
- The model assumes a stable rate and independent events over an interval.
- Inputs are validated against required ranges and outputs are rounded for readability.
Worked examples
Worked example
An average of 2.5 calls per interval and exactly 3 calls.
P(X=3) is approximately 21.38%.
P(X=3) is approximately 21.38%.
Understanding the result
The Poisson model calculates the chance of observing exactly a specified number of events when events occur independently at a fixed average rate.
The model assumes a stable rate and independent events over an interval.
Important notes
The model assumes a stable rate and independent events over an interval.
Use the result as a calculation aid for the inputs supplied; confirm critical specifications independently.
Frequently asked questions
What is λ?
It is the expected number of events in the interval being modelled.
Does the model predict exact future counts?
No; it calculates a probability under the stated model assumptions.
How do I use this calculator?
Enter the expected count λ and a non-negative integer event count.
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Learn the method behind the number or compare the terminology before using the calculator.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.