POISSON.DIST Function (LibreOffice Calc)

• Introduced: LibreOffice 4.2, explicitly stated in function-specific Help.
• Supported in: LibreOffice 26.8.1.1; this is not a final supported version.
• Scope: Desktop Calc with English semicolon-separated formulas. Locale and other-product contracts may differ.
• Checked: October 14, 2026. Official release source and independently calculated examples checked. No new LibreOffice application execution is claimed for this guide.

POISSON.DIST describes the number of events in a fixed exposure interval under a Poisson model. With mean λ, the probability of exactly k events is exp(−λ)×λ^k/k!. Cumulative mode sums those masses from zero through k. A probability mass is for one integer count; the cumulative result is for all counts up to a cutoff. Release implementation.

=POISSON.DIST(Number; Mean; Cumulative)

All three arguments are required for this dotted name. Number is the event count and is rounded down by the evaluator; provide a nonnegative integer deliberately. Mean must be strictly positive. Cumulative=FALSE or 0 selects the probability mass P(X=k); TRUE or another nonzero value selects P(X≤k). Although the legacy POISSON spelling permits omission of its last argument, POISSON.DIST does not.

The pinned dispatcher invokes the strict three-argument mode for this dotted spelling. It must not inherit the optional cumulative argument from legacy POISSON.

Values below are rounded to twelve decimal places. These are independent mathematical references, not newly captured LibreOffice application outputs.

Suppose a help desk averages two independent arrivals in a ten-minute interval. Put 2 in B2 and a candidate count in A2. =POISSON.DIST(A2;$B$2;FALSE()) gives the probability of exactly that count; change FALSE to TRUE for at most that many.

For exactly three arrivals the result is approximately 0.180447044315. At most three has probability 0.857123460499. More than three is =1-POISSON.DIST(3;2;TRUE()), approximately 0.142876539501. At least three uses the cutoff 2 instead, producing 0.323323583817. The difference is the probability mass at three, so those English phrases cannot share the same formula.

The mean belongs to the selected exposure, not automatically to one time unit. At a stable rate of 12 arrivals per hour, a ten-minute interval has mean 12×10/60=2; a half-hour has mean 6. Scale the exposure before entering Mean. Combining intervals is justified only when the model’s independence and rate assumptions fit the process.

For a probability table, list successive integer counts in column A and use an absolute reference for Mean. Sum the masses as a cross-check against the cumulative value at the last row. A finite table may sum to less than 1 because it omits a remaining upper tail; do not renormalize it without stating that you are conditioning on the displayed range.

The implementation rejects Mean≤0 and negative floored counts. A mathematically degenerate Poisson distribution at mean 0 is therefore outside this function’s accepted parameter contract. Fractional counts are floored, not interpolated; 3.9 uses the count 3. Text, errors and array coercions require separate checks.

For very small upper-tail probabilities, subtracting a cumulative result close to 1 can lose useful digits. The ordinary examples do not establish precision in extreme tails or enormous counts. A Poisson model assumes an appropriate count process; clustered, dependent or strongly varying-rate events can violate it even when every spreadsheet formula is syntactically valid.

• Function-specific official evidence
• Pinned evaluator and domain checks

The reviewed scope is the pinned release source and independent mathematical examples. No new application execution is claimed for this guide. Other releases, locales and extreme-value limits were not established by these ordinary calculations.