POISSON Function (LibreOffice Calc)
LibreOffice POISSON calculates exact-count and cumulative event probabilities, with optional mode, positive-mean rules and interval examples.
Verification status: Official release source and independently calculated examples for POISSON were reviewed. No new LibreOffice Calc application execution is claimed for this guide; the stated version and example limits still apply. How formula examples are checked
Quick answer: =POISSON(2;3;0) returns approximately 0.224041807655, the probability of exactly two events when the expected count is three. Omitting the final argument instead gives the probability of at most two.
Availability and version history
- Introduced: First release not established. The LibreOffice 3.3 appendix documents the name; that is evidence of presence, not its first introduction.
- Supported in: LibreOffice 26.8.1.1; 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; LibreOffice Calc was not run for this guide.
Counts, means and output mode
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.
Syntax and default cumulative result
=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.
For this legacy name the dispatcher enables the two-argument form; the dotted POISSON.DIST entry requires its third argument. Mean must be strictly positive in the cited LibreOffice implementation.
Reproducible reference cases
These values are independently computed from the probability-mass formula and cumulative sums, rounded to twelve decimal places.
| Formula | Expected result, approximately |
|---|---|
=POISSON(0;3;0) |
0.049787068368 |
=POISSON(2;3;0) |
0.224041807655 |
=POISSON(2;3) |
0.423190081127 |
=POISSON(4;3;1) |
0.815263244524 |
=POISSON(8;9;0) |
0.13175564001 |
=POISSON(8;9;1) |
0.455652604322 |
=POISSON(2.9;3;0) |
0.224041807655 |
=POISSON(60;50;1) |
0.927839820187 |
Practical worksheet: calls per quarter-hour
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.
Advanced example: staffing for a tail event
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.
Zero mean and numerical cautions
Mean=0 is rejected by the current LibreOffice evaluator. Do not assume its mathematical limiting distribution is accepted as an input.
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.