POISSON.DIST in Google Sheets: Exact and Cumulative Counts
Calculate exact, at-most and at-least event-count probabilities with POISSON.DIST in Google Sheets, including interval scaling and checked count-model examples.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =POISSON.DIST(3,2,FALSE) has expected result 0.1804470443. It is the probability of exactly 3 events when the modeled mean is 2 events per observation interval. TRUE returns the probability of 3 or fewer events.
Syntax and cumulative choice
=POISSON.DIST(x, mean, cumulative)
The Google POISSON.DIST reference documents x as the event-count input, mean as the distribution’s average count, and the flag as the choice between exact and cumulative probability. It explicitly allows the spelling POISSON as well.
Use TRUE for at most x events and FALSE for exactly x events. The page does not state an omitted-flag default, so supply all three arguments.
For the mathematical model demonstrated here, x is a nonnegative whole-number count and mean is positive. Google’s sample includes a fractional x but does not explain its treatment. This guide does not infer truncation or rounding from another spreadsheet; it uses integer counts throughout.
Worked example: requests arriving in a 15-minute interval
Assume a synthetic process averages 2 requests every 15 minutes. Enter 0, 1, 2, 3, 4 and 5 in A2:A7. Put 2 in D1 for the mean over that same interval.
In B2, enter and fill down:
=POISSON.DIST(A2,$D$1,FALSE)
In C2, enter and fill down:
=POISSON.DIST(A2,$D$1,TRUE)
| Requests | Expected exact-count probability | Expected at-most probability |
|---|---|---|
| 0 | 0.1353352832 | 0.1353352832 |
| 1 | 0.2706705665 | 0.4060058497 |
| 2 | 0.2706705665 | 0.6766764162 |
| 3 | 0.1804470443 | 0.8571234605 |
| 4 | 0.0902235222 | 0.9473469827 |
| 5 | 0.0360894089 | 0.9834363915 |
The cumulative column is nondecreasing. The exact-count column need not be: it increases and then falls as the counts move through the most likely region. Its six displayed values do not sum to 1 because counts above 5 remain possible.
Unlike a continuous density, the exact-count probability is a probability at that specific integer outcome. It can be directly interpreted as a percentage.
Independently check the arithmetic
The Poisson mass function is exp(-mean)*mean^x/x!, and its CDF sums those masses through x. These equations are documented in NIST’s Poisson reference.
For exactly 3 events with mean 2, the explicit calculation is:
=EXP(-2)*2^3/(1*2*3)
Expected result: 0.1804470443. Summing the exact-count probabilities for 0, 1, 2 and 3 gives 0.8571234605, the at-most-3 result. The factorial at zero is 1; do not substitute zero into the denominator.
Advanced application: at least and between
At least 3 events means the complement of at most 2:
=1-POISSON.DIST(2,2,TRUE)
Expected result: 0.3233235838. Subtracting the CDF at 3 instead would calculate more than 3, excluding the outcome 3.
For 2 through 4 events, including both endpoints:
=POISSON.DIST(4,2,TRUE)-POISSON.DIST(1,2,TRUE)
Expected result: 0.5413411329. The lower CDF input is one less than the first included count. This off-by-one distinction is central to discrete probability formulas.
Match the mean to the interval
If the same stable-rate model averages 2 requests per 15 minutes, its one-hour mean is 8. The modeled probability of no requests in one hour is:
=POISSON.DIST(0,8,FALSE)
Expected result: 0.0003354626. Reusing mean 2 would answer the 15-minute question, even though the formula would remain syntactically valid.
To illustrate estimating a mean, counts 1, 2, 3, 0, 4 and 2 from six equal-length intervals have average 2. Entering them in F2:F7 and using =AVERAGE(F2:F7) supplies that value. It does not establish that the process is Poisson; clustering, changing rates or dependence may make the model unsuitable.
Errors, limits and version scope
Check integer event counts, a sensible mean for the same exposure interval and the cumulative flag. Exact native error tokens, behavior at mean zero, text/blank coercion and fractional-count handling were not established by the reviewed Google page. These gaps are not filled with another product’s conventions.
Small tail probabilities can be affected by displayed rounding or by subtracting a CDF very close to 1. Keep unrounded values for further arithmetic and avoid interpreting a formatted zero as impossibility.
POISSON.DIST and POISSON are currently documented for rolling Google Sheets. Original introduction date, first release and last functioning numbered version were not established.
NOT_TESTED_IN_GOOGLE_SHEETS. Google and NIST references were inspected on October 17, 2026. Original probabilities were independently calculated from factorial masses and cumulative sums, then checked numerically. They are not native spreadsheet executions.