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Poisson Probability Calculator — result sheet
Calculate the probability of exactly k events for a Poisson process with a known mean rate.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: P(X = k) = e^(-λ) λ^k/k!; mean and variance = λ.
The Poisson model describes counts in a fixed interval when events occur independently at a stable average rate.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Mean event count λ — minimum 0; maximum 100000
- Event count k — minimum 0; maximum 1000
Worked example
| Input | Value |
|---|---|
| Mean event count λ | 3 |
| Event count k | 2 |
P(X = 2) ≈ 0.2240; mean = 3; variance = 3.
Assumptions and limits
- The mean rate is stable across the chosen interval.
- Events are independent and the count is nonnegative integer-valued.
- The result is a model probability, not a forecast guarantee.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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