POISSON in WPS Spreadsheet: Exact Counts and Cumulative Probabilities
Calculate Poisson point masses or inclusive lower-tail probabilities with explicit TRUE/FALSE modes and independently checked finite sums.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
POISSON calculates probabilities for a Poisson count model. Its mean parameter is the expected number of events in the same exposure interval as the count. The model’s suitability depends on the process; a function call alone does not establish independent events or a stable event rate.
Syntax and two distinct modes
=POISSON(x, mean, cumulative)
The original controls use nonnegative integer x, a strictly positive mean and an explicit Boolean flag. FALSE gives the probability of exactly x events. TRUE gives the probability of a count from zero through x, inclusive.
WPS uses the term “density” for FALSE, but this is a discrete probability mass. Its formula image shows exp(−mean)*mean^x/x!. The cumulative formula sums that mass from 0 through x. A stray parenthetical phrase in the prose refers to 0 and 1; the explicit summation and worked example establish the intended upper limit x.
Original point and cumulative example
Suppose a hypothetical count model has mean 2 events per chosen interval. Enter 2 in B1.
- Use
=POISSON(2,B1,FALSE)for exactly two events. The independent expectation is 0.2706705664732254. - Use
=POISSON(2,B1,TRUE)for at most two events. The expectation is 0.6766764161830635. - The difference is the probability of zero or one event, not a rounding error.
For mean 2, the masses at 0, 1, 2 are respectively e^(−2), 2e^(−2), 2e^(−2). Their sum is 5e^(−2), explaining the cumulative result.
Independent controls
| Formula | Event | Expected probability, approximately |
|---|---|---|
=POISSON(0,2,FALSE) |
Exactly 0 | 0.1353352832366127 |
=POISSON(1,2,FALSE) |
Exactly 1 | 0.2706705664732254 |
=POISSON(2,2,FALSE) |
Exactly 2 | 0.2706705664732254 |
=POISSON(2,2,TRUE) |
At most 2 | 0.6766764161830635 |
=POISSON(3,2,TRUE) |
At most 3 | 0.8571234604985470 |
=POISSON(1,1,TRUE) |
At most 1, mean 1 | 0.7357588823428847 |
Derive an interval or upper-tail event
For mean 2, the independently calculated probability of exactly three is the difference between the cumulative values at 3 and 2: approximately 0.1804470443154835. The probability of more than two is 1 minus the cumulative value at 2, approximately 0.3233235838169365.
These identities are useful for moderate probabilities. They do not certify the accuracy of subtracting nearly equal probabilities in extreme tails. Keep the distinction between “at least x” and “more than x”: their complement boundaries differ by one integer count.
If the observation interval doubles, the mean must be adapted to that exposure under a constant-rate model. Reusing a one-minute mean for a two-minute count changes the question. Do not assume a process follows this model merely because its observations are counts.
Source check and limits
The official example =POISSON(3,8,TRUE) displays 0.042380112. Summing the four masses for 0, 1, 2, 3 independently reproduces that rounded value. All source formula images were inspected; the vendor example is not a native test performed for this guide.
The lesson discusses truncating fractional x and invalid-input errors. Original controls use integer counts and positive means, so they do not establish truncation boundaries, error propagation, very large counts or extreme-tail precision. No dotted spelling is assumed to be an exact alias. See PROB for summing probabilities supplied explicitly for a finite discrete distribution.
Availability and evidence scope
The official WPS lesson is dated 2019-06-18 and explicitly labels WPS Office for Windows Personal. Its numeric build is unspecified. This documents the function by that date; it does not establish first introduction, the last functioning build, other-platform parity or a retirement/deprecation history.
The complete lesson and its formula images and walkthrough were inspected on October 18, 2026. Original examples are documentation-derived independent calculations, not WPS or other spreadsheet-engine executions.