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POISSON.DIST Function

Excel 2010+

Summary

The POISSON.DIST function calculates Poisson distribution probabilities, 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.DIST(x, mean, cumulative)

Parameters

Parameter	Type	Required	Description
x	`Number`	Yes	The number of events to evaluate (≥0)
mean	`Number`	Yes	Expected mean number of events (λ > 0)
cumulative	`Boolean`	Yes	TRUE returns cumulative distribution, FALSE returns probability mass function

Using the POISSON.DIST Function

POISSON.DIST is perfect for scenarios involving rare events or counts, such as predicting customer arrivals, equipment failures, or defects in manufacturing. Use FALSE for the exact probability of k events, or TRUE for the probability of k or fewer events.

Common POISSON.DIST Examples

Quality Control - Defect Analysis

=POISSON.DIST(2,5,FALSE)

Probability of exactly 2 defects when expecting 5 per batch (PMF): 0.0842

Customer Arrivals - Cumulative

=POISSON.DIST(3,2,TRUE)

Cumulative probability of 3 or fewer customers arriving when expecting 2 per hour: 0.8571

Call Center Analysis

=POISSON.DIST(A2,$B$1,TRUE)

Cumulative probability referenced from cells for flexible analysis

Exact Probability vs Cumulative

=POISSON.DIST(0,1.5,FALSE)

Probability of zero events when expecting 1.5 (PMF): 0.2231

Frequently Asked Questions

Non-integer values are truncated to the nearest lower integer before calculation.

FALSE returns P(X=x) exact probability; TRUE returns P(X≤x) cumulative probability.

Yes, but very large values may cause precision issues due to computational limits.

POISSON.DIST is the modern replacement with identical functionality but better implementation.

Common Errors and Solutions

#NUM! error

Cause: x < 0 or mean ≤ 0

Solution: Ensure x ≥ 0 and mean > 0

#VALUE! error

Cause: x or mean contains non-numeric values

Solution: Verify inputs are valid numbers

Unexpected results with decimals

Cause: x values truncated to integers

Solution: Use INT() function if you need to force truncation explicitly

Notes

Poisson distribution assumes events are independent and occur at constant rate
Common applications: call centers, traffic flow, radioactive decay, website hits
For cumulative probabilities approaching 1, consider using 1-POISSON.DIST(x,mean,FALSE) for tail probabilities
Excel truncates x automatically but always verify input data types

Compatibility

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

Not available in: Excel 2007, Excel 2003, Earlier versions

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2010+