When should I use POISSON.DIST instead of other probability functions?

Use POISSON.DIST for modeling the count of events occurring at a known average rate in a fixed time or space interval—like website traffic, customer arrivals, or defect occurrences. It assumes events are independent and occur randomly at a constant rate.

What does cumulative=TRUE actually calculate?

It returns the cumulative distribution function (CDF): the probability of observing x or fewer events. For example, POISSON.DIST(50, 51.75, TRUE) answers 'What's the probability of 50 or fewer conversions?' versus the PMF which asks for exactly 50.

Why do I get #NUM! when my mean parameter looks valid?

Double-check that your mean expression truly evaluates to a positive value. Empty cells in AVERAGE() calculations, hidden zeros, or formulas involving subtraction that produce negatives can all cause this error without being obvious.

Does POISSON.DIST accept decimal values for x?

Yes, most spreadsheet implementations accept decimals for x and automatically floor them (round down to the nearest integer). However, since Poisson models event counts in practice, you typically use whole numbers for meaningful statistical interpretation.

POISSON.DIST function

Returns the Poisson probability of a specified number of events, given the average rate of occurrence in a fixed interval.

=POISSON.DIST(x, mean, cumulative)

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Arguments

How POISSON.DIST reads its arguments

Argument	Required	Description
x	Required	The number of events to calculate probability for; must be a non-negative integer, though decimals are floored by most implementations.
mean	Required	The expected average number of events in the interval; must be a positive number greater than zero.
cumulative	Required	Boolean flag: FALSE returns the probability mass function (probability of exactly x events), TRUE returns the cumulative distribution function (probability of x or fewer events).

Returns

A decimal probability value between 0 and 1, representing a likelihood.

Availability

Excel: All · Google Sheets: Supported

Worked examples

1. Calculate probability of exactly 50 conversions

Campaign	Channel	Spend	Clicks	Conversions
Campaign A	Email	500	1000	45
Campaign A	Social	300	800	32
Campaign B	Email	600	1200	58
Campaign B	Search	800	1500	72

=POISSON.DIST(50, AVERAGE(E2:E5), FALSE)

Result: 0.0631

Uses the average conversion count (51.75) from all campaigns as the Poisson mean. Returns 0.0631, meaning there's approximately 6.3% probability of observing exactly 50 conversion events. The FALSE parameter requests the probability mass function for this specific count.

2. Find probability of 60 or fewer conversions

Campaign	Channel	Spend	Clicks	Conversions
Campaign A	Email	500	1000	45
Campaign A	Social	300	800	32
Campaign B	Email	600	1200	58
Campaign B	Search	800	1500	72

=POISSON.DIST(60, 51.75, TRUE)

Result: 0.7837

With cumulative=TRUE, this returns the probability of 60 or fewer conversion events occurring. The result 0.7837 (78.4%) indicates there's a strong probability the conversion count falls at or below 60, given the historical average rate of 51.75.

3. Estimate probability of 72 conversions

Campaign	Channel	Spend	Clicks	Conversions
Campaign A	Email	500	1000	45
Campaign A	Social	300	800	32
Campaign B	Email	600	1200	58
Campaign B	Search	800	1500	72

=POISSON.DIST(72, AVERAGE(E2:E5), FALSE)

Result: 0.0084

Calculates the probability of exactly 72 conversion events (the value from Campaign B Search). This returns 0.0084 (0.84%), a low probability because 72 is significantly above the mean of 51.75, representing a statistical outlier.

Common errors

Which POISSON.DIST error are you seeing?

Error	Why it happens	How to fix it
#NUM!	The mean parameter is zero or negative. Poisson distribution requires a positive mean to represent a valid average rate of events.	Verify your mean calculation returns a positive number. For example, if using AVERAGE(), ensure your range contains only positive numeric values.
#VALUE!	The x or mean argument contains text that cannot be interpreted as a number, such as =POISSON.DIST("fifty", 51.75, FALSE).	Ensure both x and mean are numeric values or formulas that evaluate to numbers. Use VALUE() if converting text, or reference cells containing numbers.
#N/A	One of the input arguments references a cell containing an #N/A error, or a nested formula returns #N/A before POISSON.DIST evaluates.	Check the cells referenced by x and mean for upstream errors. Use IFERROR() to handle missing data: =POISSON.DIST(50, IFERROR(AVERAGE(range), 1), FALSE).

Tips and when to use something else

Use POISSON.DIST to model discrete count data in fixed intervals: website visitor arrivals per hour, email volume per day, or customer service tickets per week.
For binary success/failure scenarios with a fixed trial count, use BINOM.DIST instead; Poisson is best for open-ended intervals with rare, independent events.
The cumulative parameter saves manual calculation: POISSON.DIST(50, mean, TRUE) replaces manually summing POISSON.DIST(0..50, mean, FALSE) one by one.
Poisson assumes events are independent and randomly distributed at a constant average rate; if events cluster or depend on each other, alternative distributions may be more appropriate.

Related functions

AVERAGEAVERAGE calculates the arithmetic mean of numbers, ignoring text and logical values; returns a single numeric value representing the average.COUNTIFCounts cells in a range that meet a specific criterion, returning a number — use it to tally matching rows like employee counts by department.IFERRORIFERROR returns the result of a formula unless that formula generates an error, in which case it returns a user-specified alternative value.COUNTCOUNT counts the number of cells containing numeric values and dates in one or more ranges, ignoring text and blank cells.IFThe IF function returns one value if a condition is true and another (or nothing) if it is false, letting you branch logic in a cell.

Frequently asked questions

When should I use POISSON.DIST instead of other probability functions?: Use POISSON.DIST for modeling the count of events occurring at a known average rate in a fixed time or space interval—like website traffic, customer arrivals, or defect occurrences. It assumes events are independent and occur randomly at a constant rate.
What does cumulative=TRUE actually calculate?: It returns the cumulative distribution function (CDF): the probability of observing x or fewer events. For example, POISSON.DIST(50, 51.75, TRUE) answers 'What's the probability of 50 or fewer conversions?' versus the PMF which asks for exactly 50.
Why do I get #NUM! when my mean parameter looks valid?: Double-check that your mean expression truly evaluates to a positive value. Empty cells in AVERAGE() calculations, hidden zeros, or formulas involving subtraction that produce negatives can all cause this error without being obvious.
Does POISSON.DIST accept decimal values for x?: Yes, most spreadsheet implementations accept decimals for x and automatically floor them (round down to the nearest integer). However, since Poisson models event counts in practice, you typically use whole numbers for meaningful statistical interpretation.

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Reviewed 2026-09-17