POISSON Function (OpenOffice Calc)

• Introduced: First release not established. The OpenOffice.org 3.3 appendix documents the name; that is evidence of presence, not its first introduction.
• Supported in: Apache OpenOffice 4.1.16; no final supported release established.
• Scope: Desktop Calc. Argument contracts and boundaries below refer to the cited release.
• Checked: October 14, 2026. Documentation/source and independent mathematics checked; Apache OpenOffice Calc was not run for this guide.

The Poisson model describes nonnegative integer counts of independent events over a fixed exposure interval at a stable average rate. Mean is the expected number of events in that interval, not a rate in unrelated time units. Official reference.

For mean lambda>0, the probability of exactly k events is exp(−lambda)×lambda^k/k!. The cumulative probability sums those masses from zero through k. Because this is a discrete distribution, the exact-count result is a probability mass, not a continuous density.

=POISSON(Number; Mean [; Cumulative])

The release evaluator accepts two or three arguments. Cumulative=0/FALSE selects exact-count mass; 1/TRUE or omission selects P(X≤Number). Number is floored before evaluation and must be nonnegative afterward. Supply integer counts explicitly rather than using flooring to clean measurements.

The wiki illustrates three arguments, but the pinned implementation also accepts the two-argument cumulative form. Use a strictly positive Mean for ordinary calculations and portability.

These values are independently computed from the probability-mass formula and cumulative sums, rounded to twelve decimal places.

Suppose independent calls arrive at an average rate of 12 per hour. For a 15-minute interval, first convert the mean: 12×15/60=3 calls. Put 2 in A2 and 3 in B2. =POISSON(A2;B2;0) gives 0.224041807655, while =POISSON(A2;B2;1) gives 0.423190081127.

The first concerns exactly two calls; the second includes zero, one and two. Entering 12 as Mean while still interpreting the output as a quarter-hour probability would model the wrong interval.

With mean 3, the probability of at least five calls is =1-POISSON(4;3;1), approximately 0.184736755476. The cutoff is 4 because the complement removes zero through four, leaving five and above. Using 5 inside the cumulative term would calculate at least six.

The probability of at least one call is =1-POISSON(0;3;0), approximately 0.950212931632. For a range from two through four, use =POISSON(4;3;1)-POISSON(1;3;1), approximately 0.616114971052. Inclusive discrete bounds require subtracting the CDF at one less than the lower endpoint.

Apache OpenOffice 4.1.16 has explicit Mean=0 branches: cumulative mode returns 1 and exact-count mode returns 0, even at Number=0. The latter differs from the mathematical degenerate distribution, whose mass at zero is 1. This is a source-confirmed implementation convention, not a native result observed here; use positive means in portable models.

Very large means, extreme tails and subtracting cumulative values close to 1 can lose useful precision. The ordinary reference table does not stress-test those conditions. A Poisson model also imposes equal mean and variance; clustering, changing rates or an upper count limit can require a different model.

• POISSON documentation
• Apache OpenOffice 4.1.16 evaluator and argument contract