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Poisson Probability — result sheet
Exact and cumulative probabilities for counted events at a known average rate.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: P(X=k) = e^(-L) L^k / k!; cumulative sums 0..k.
Models independent arrivals at a constant average rate. Factorials use exact integer products up to k = 10000 within safe-integer bounds.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Average rate — Mean events per interval.; minimum 1.0E-6; maximum 1000
- Events (k) — minimum 0; maximum 10000
Worked example
| Input | Value |
|---|---|
| Average rate | 3 |
| Events (k) | 2 |
P(X = 2) = 0.2240; P(X <= 2) = 0.4232.
Assumptions and limits
- Constant rate, independent events, one interval.
- k a whole number; lambda positive.
- Very large lambda*k may overflow and is rejected.
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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