EXPON.DIST in Excel: Waiting Times, Rates and Tail Probabilities

=EXPON.DIST(x, lambda, cumulative)

All three arguments are required. x is the duration or nonnegative model value. Lambda is a rate, with units reciprocal to x; it is not the mean duration. The mean of this model is 1/lambda. Use a logical TRUE or FALSE for cumulative to make the requested output explicit.

For the independent reference calculations, the cumulative probability is 1−exp(−lambda×x), and the density is lambda×exp(−lambda×x). This model assumes a constant event rate; choosing it is a modeling decision that a function cannot validate.

Assume a fictional process has mean waiting time 5 minutes, so lambda=1/5=0.2 per minute. Evaluate a wait of 3 minutes:

=EXPON.DIST(3,0.2,TRUE)
=EXPON.DIST(3,0.2,FALSE)

Expected results are 0.451188364 and 0.109762327. The first is a probability, approximately 45.12%. The second is a density per minute and should not be presented as the probability of exactly 3 minutes.

Putting 5 in the lambda argument would describe a mean duration of 0.2 minutes, a different model. Label parameter cells with units to prevent that mistake.

With the same rate:

=1-EXPON.DIST(3,0.2,TRUE)
=EXPON.DIST(7,0.2,TRUE)-EXPON.DIST(3,0.2,TRUE)

Expected values are 0.548811636 and 0.302214672. The first is the probability of waiting longer than 3 minutes; the second is the probability of a wait between 3 and 7 minutes.

Order the endpoints before subtracting cumulative values. Reversed endpoints produce a negative difference, indicating a setup error rather than a valid negative probability.

Put the mean wait 5 in H2 and durations 0, 3, 5 and 10 in A2:A5. Fill down:

=EXPON.DIST(A2,1/$H$2,TRUE)

Expected probabilities are 0, 0.451188364, 0.632120559 and 0.864664717. The absolute reference keeps the same model across rows. Validate H2>0 before converting the mean to a rate.

A wait equal to the mean does not correspond to cumulative probability 0.5 in this skewed distribution. The cumulative probability at one mean is about 63.21%.

For a target cumulative probability p strictly between 0 and 1, invert the model algebraically:

=-LN(1-0.9)/0.2

Expected 90th-percentile duration: 11.512925465 minutes. Substitute that duration into EXPON.DIST with cumulative TRUE to obtain an expected probability of 0.9.

The formula is an independent algebraic construction, not a separate native exponential inverse function. Keep the units consistent and do not use p=1, which has no finite duration in this model.

Three minutes is 180 seconds; 0.2 events per minute is 0.2/60 per second:

=EXPON.DIST(180,0.2/60,TRUE)

The expected probability remains 0.451188364 because lambda×x is unchanged. A corresponding density is now per second, so its numerical value is the per-minute density divided by 60. Probabilities remain the same; density units change.

Microsoft documents #NUM! for x<0 or lambda≤0 and #VALUE! when x or lambda is nonnumeric. At x=0 with a valid positive rate, the cumulative value is 0 and the density equals lambda. A density can exceed 1 without violating probability rules; for lambda=2 the density at zero is 2 per time unit.

Do not replace a missing rate with zero, or mix minutes with an hourly rate. Extreme-tail cancellation, coercion, blanks and native numerical boundaries remain unverified. For a very small upper-tail value, the independent expression EXP(-lambda*x) avoids subtracting a cumulative value from 1, but its own floating-point limits still apply.

• Current documentation: the dedicated Microsoft reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Introduced: Microsoft’s alphabetical function catalog marks EXPON.DIST as introduced in Excel 2010. The exact first build and platform-specific introduction dates are not established here.
• Last functioning version: unknown; a current help listing is not a last-working-build test.
• Evidence checked: October 15, 2026. Official documentation was freshly retrieved; examples below were independently calculated. No native Excel, Mac or web-client execution was performed.

• Microsoft EXPON.DIST reference.
• Microsoft function catalog and introduction-marker explanation.
• Editorial testing standards.

Examples use English function names and comma separators. Expected numbers are rounded independent mathematical calculations; documented error expectations are labeled as such. They are not captured Excel output. All illustrative data and policies are fictional.