The Excel EXPON.DIST function returns the exponential distribution — used to model the time between independent events that happen at a constant average rate, such as customer arrivals or component failures.
Syntax
| Argument | Description | |
|---|---|---|
x | Required | The value of the function — the time or distance until the next event. Must be ≥ 0. |
lambda | Required | The rate parameter (events per unit). Must be > 0. Its reciprocal, 1/lambda, is the mean time between events. |
cumulative | Required | TRUE returns the cumulative distribution (probability the event occurs by time x); FALSE returns the probability density at x. |
How to use it
The cumulative flag picks which curve you get. With TRUE, EXPON.DIST returns the probability that the next event happens at or before time x — mathematically 1 − e^(−lambda·x):
With FALSE you get the probability density function (PDF), lambda·e^(−lambda·x). The density can exceed 1 (as above) because it is a rate, not a probability — only the area under the curve is bounded by 1.
The mean of an exponential distribution is 1/lambda. Here lambda is 10, so events occur on average every 0.1 units, and by time 0.2 there is roughly an 86% chance the event has already happened.
Watch the arguments: both x and lambda must be positive (x may be 0), or EXPON.DIST returns the #NUM! error. The legacy name in older Excel is EXPONDIST (no dot).
Try it: interactive demo
Set x and the rate lambda to see the cumulative probability and the density.
Practice workbook
Frequently asked questions
What is the difference between the TRUE and FALSE forms?
TRUE returns the cumulative distribution — the probability the event has occurred by time x, equal to 1 − e^(−lambda·x). FALSE returns the probability density lambda·e^(−lambda·x) at exactly x.Why is the density (FALSE) result greater than 1?
What is lambda and how does it relate to the mean?
1/lambda. With lambda = 10, the average gap is 0.1.How is EXPON.DIST different from EXPONDIST?
EXPON.DIST (with the dot) was introduced in Excel 2010 as the modern name; EXPONDIST is the legacy function kept for backward compatibility.Master functions like this in one day
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