POISSON.DIST in Excel: Exact Event Counts and Inclusive Tails

=POISSON.DIST(x, mean, cumulative)

All three arguments are required. x is the event count. mean is the expected count for the specific interval or exposure being modeled. cumulative is FALSE for P(X=x) or TRUE for P(X≤x), including zero and x.

For a positive mean λ and nonnegative integer k, the mathematical mass is EXP(-λ)*λ^k/FACT(k). A cumulative probability sums the masses from zero through k. The Poisson model describes counts under its event-rate assumptions; the function does not check whether observed events are independent or whether the rate is stable.

The mean is not a percentage. A rate of two events per minute and an interval of five minutes imply mean ten if the constant-rate model is appropriate. Passing two would answer a different question.

Put 2 in A2 and 5 in A3. In B2 enter =POISSON.DIST(A2,A3,FALSE); in B3 enter =POISSON.DIST(A2,A3,TRUE).

Independent targets are 0.08422433749 and 0.1246520195. Microsoft’s source prints rounded values 0.084224 and 0.124652. The cumulative result is larger because it also includes counts zero and one.

Unlike a normal density value, the FALSE result here is a probability mass for an exact discrete count. It is meaningful to ask for the probability of exactly two events.

Suppose the expected count during the chosen interval is 2. The probability of at least three is =1-POISSON.DIST(2,2,TRUE), independently 0.3233235838.

The probability of exactly three is =POISSON.DIST(3,2,FALSE), independently 0.1804470443. These differ because the upper-tail event includes four, five and all larger counts as well.

For at least one event with mean two, use =1-POISSON.DIST(0,2,TRUE), targeting 0.8646647168. The subtraction removes the zero-event case. Do not subtract a cumulative probability through one unless the intended event is more than one.

For mean five, the probability of four through six events is =POISSON.DIST(6,5,TRUE)-POISSON.DIST(3,5,TRUE). Its independent target is 0.4971575477.

Check it by summing POISSON.DIST(4,5,FALSE), POISSON.DIST(5,5,FALSE) and POISSON.DIST(6,5,FALSE). The two calculations express the same event. For a range beginning at zero, use only the upper cumulative result rather than introducing a negative lower count.

An audit table can list counts 0 through a chosen maximum. Its mass sum is generally below one because the Poisson distribution has no finite upper bound. Do not treat omitted tail mass as an arithmetic failure or renormalize it without changing the model’s meaning.

Store rate per minute in D2 and interval minutes in D3, then use =D2*D3 as the mean. With rate 2 and interval 2.5, the expected count is 5, even though the interval is fractional.

This is different from a fractional observed count. A mean can be noninteger; event counts in these examples are integers. Keep units beside the inputs so a conversion from minutes to hours does not accidentally multiply the expected count by sixty twice.

Microsoft documents truncation of a noninteger x. It documents #NUM! for negative x or negative mean and #VALUE! when x or mean is nonnumeric. Validate counts rather than using truncation to hide an invalid measurement.

A mean of zero is not excluded by the reference’s negative-mean rule. The mathematical model is then concentrated at zero; native zero-mean boundary behavior was not executed here. All main formulas use positive means.

A surprising probability may reflect a wrong exposure interval, a TRUE/FALSE mix-up or an unjustified rate model. Extreme upper-tail cancellation and implementation precision were not measured. Preserve full cell precision and label these outputs as model-based probabilities.

• Current documentation: the dedicated Microsoft reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Introduced: Microsoft’s alphabetical catalog marks POISSON.DIST as introduced in Excel 2010. Exact first build and platform-specific introduction dates remain unverified.
• Last functioning version: unknown; a current help listing is not a last-working-build test.
• Evidence checked: October 15, 2026. Official documentation was freshly retrieved; examples were independently calculated. No native Excel, Mac or web-client execution was performed.

• Microsoft POISSON.DIST reference.
• Microsoft function catalog and introduction-marker explanation.
• Editorial testing standards.

Examples use English function names and comma separators. Expected numbers are rounded independent mathematical calculations; documented error expectations are labeled as such. They are not captured Excel output. All illustrative data and policies are fictional.