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POISSON Function

Excel 2007+

Summary

The POISSON function calculates probabilities from the Poisson distribution, ideal for modeling the number of events occurring within a fixed interval of time or space when these events happen independently at a constant average rate.

Syntax

POISSON(x, mean, cumulative)

Parameters

Parameter	Type	Required	Description
x	`Number`	Yes	The number of events to analyze (truncated to integer if non-integer)
mean	`Number`	Yes	Expected numeric value representing average events
cumulative	`Boolean`	Yes	Logical value: TRUE returns cumulative prob, FALSE returns exact prob mass

Using the POISSON Function

POISSON models discrete events occurring randomly over time or space. Use FALSE for the probability of exactly x events, or TRUE for probability of x or fewer events. Perfect for analyzing call center volumes, manufacturing defects, or traffic arrivals.

Common POISSON Examples

Exact Probability Calculation

=POISSON(2,5,FALSE)

Probability of exactly 2 events when expecting 5 (returns 0.0842)

Cumulative Probability

=POISSON(2,5,TRUE)

Probability of 2 or fewer events when expecting 5 (returns 0.1247)

Quality Control Application

=POISSON(A1,10,FALSE)

Probability of exactly A1 defects when average is 10 per batch

Frequently Asked Questions

POISSON returns #NUM! error since event counts cannot be negative.

POISSON works for backward compatibility; use POISSON.DIST for new workbooks as it's more accurate.

Yes, but truncates to nearest lower integer before calculation.

Common Errors and Solutions

#NUM! error

Cause: x < 0 or mean < 0

Solution: Ensure both x and mean are non-negative numbers

#VALUE! error

Cause: x or mean contains non-numeric values

Solution: Verify parameters contain valid numbers

Unexpected probability results

Cause: Using cumulative=TRUE when expecting exact probability

Solution: Use FALSE for exact event probability

Notes

POISSON truncates non-integer x values
Available since Excel 2007 but deprecated
Microsoft recommends POISSON.DIST for new formulas
Cumulative=TRUE sums probabilities from 0 to x inclusive

Compatibility

Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2003, Excel XP, Excel 2000, Excel 97

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+