How it works
Use the expected number of events in the same interval you evaluate. With λ = 2 and k = 1, P(X ≤ 1) = e⁻²(1 + 2), about 0.40600585. The model assumes independent occurrences at a constant rate. At λ = 0, zero events have probability one. The second result is strictly more than k events.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Expected count λ for the interval | 3 | Enter a numeric value. Use a non-negative value. Allowed range: 0–100. |
| Maximum events k | 2 | Enter a numeric value. Use a whole number. Use a non-negative value. Allowed range: 0–170. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- Expected count λ for the interval
- 3
- Maximum events k
- 2
Complete example results
- Probability of at most k (0–1)
- 0.42319008
- Probability of more than k (0–1)
- 0.57680992
Reading the result
Check the probability scale, sample size and assumptions stated by the method. A decimal probability of 0.5 represents 50%. Mean and spread inputs must describe the same dataset; the calculation does not validate those estimates.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
Is an hourly rate enough for a two-hour interval?
Convert it to the expected count for two hours first. Under the constant-rate assumption, an expectation of 3 per hour becomes λ = 6 for two hours. Tiny complementary tails may lose floating-point precision.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.
Method sources: itl.nist.gov