EXPON.DIST in Google Sheets: Waiting-Time Probabilities and Rates
Use EXPON.DIST in Google Sheets with the rate parameter, distinguish density from cumulative probability and calculate waiting-time intervals and percentiles.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =EXPON.DIST(5,0.2,TRUE) has expected result approximately 0.6321205588. Under an exponential model with rate 0.2 per minute, it is the probability that the waiting time is at most 5 minutes.
Syntax and the rate parameter
=EXPON.DIST(x, lambda, cumulative)
Google’s EXPON.DIST reference documents all three arguments and also permits the spelling EXPONDIST. No optional default is stated, so supply the cumulative flag explicitly.
| Argument | Interpretation in the model |
|---|---|
x |
Waiting-time threshold |
lambda |
Positive rate per unit of time |
cumulative |
TRUE for probability up to x; FALSE for density |
The rate is the reciprocal of the mean waiting time. Google’s WEIBULL reference explicitly connects a shape-1 Weibull distribution to EXPONDIST with lambda equal to 1 divided by scale. Do not pass a mean waiting time where a rate is required.
Worked example: a five-minute mean wait
Assume a hypothetical mean waiting time of 5 minutes, giving rate 1/5 = 0.2 per minute. Put 0.2 in D1. Enter 2, 5, 10 in A2:A4 as waiting thresholds in minutes.
In B2, enter and fill down:
=EXPON.DIST(A2,$D$1,TRUE)
| Threshold in minutes | Expected cumulative probability |
|---|---|
| 2 | 0.3296799540 |
| 5 | 0.6321205588 |
| 10 | 0.8646647168 |
The mean is not the median: a threshold equal to the mean gives approximately 63.21%, not 50%. The distribution is right-skewed, so long waits pull the mean above the midpoint of cumulative probability.
This is a constructed mathematical model, not measured service performance. Use it only when the underlying waiting-time assumptions are appropriate.
Density and a direct arithmetic check
For density at 5 minutes:
=EXPON.DIST(5,0.2,FALSE)
Expected result: 0.0735758882 per minute. It is a density height, not the probability of waiting exactly 5 minutes.
The zero-location exponential formulas are 1-EXP(-lambda*x) for the CDF and lambda*EXP(-lambda*x) for the density. These follow the density in NIST’s exponential-distribution reference, expressed here with rate equal to reciprocal scale.
For example, =1-EXP(-0.2*5) independently gives 0.6321205588. The calculation checks the parameter convention without relying on a second spreadsheet engine.
Advanced application: tails and waiting intervals
For a wait longer than 10 minutes:
=1-EXPON.DIST(10,0.2,TRUE)
Expected result: 0.1353352832, about 13.53%. The equivalent survival expression =EXP(-0.2*10) avoids subtracting a CDF close to 1 when considering more extreme tails.
For a wait between 2 and 10 minutes:
=EXPON.DIST(10,0.2,TRUE)-EXPON.DIST(2,0.2,TRUE)
Expected result: 0.5349847628. Continuous-model interval probability comes from subtracting cumulative values, not from subtracting density heights.
To find the 90th-percentile wait directly from the model:
=-LN(1-0.9)/0.2
Expected result: 11.5129254650 minutes. Substituting that unrounded result into EXPON.DIST with cumulative TRUE should give approximately 0.9. This is an algebraic inverse calculation, not an undocumented EXPON.INV function.
Keep rate and time units aligned
A rate of 0.2 per minute is 12 per hour. Five minutes is 1/12 hour. Thus:
=EXPON.DIST(1/12,12,TRUE)
has the same expected cumulative result 0.6321205588. Multiplying a minute-based threshold by an hourly rate would change the exponent by a factor of 60 and produce a different, unintended model.
The exponential model has a constant hazard rate. It is not a universal description of repair times, completion times or aging equipment. Check the substantive model rather than selecting the function only because the quantity is a duration.
Errors and troubleshooting
Use nonnegative time thresholds and a positive rate for the mathematical model. The guide’s worked function calls use positive thresholds and rates. The reviewed Google page does not specify a complete native error-token matrix for invalid values, blanks, text or arrays, so no unverified error mapping is claimed.
Check whether TRUE or FALSE was intended, whether lambda is a rate rather than a mean, and whether units match. Very small tail values may require care with floating-point precision. A displayed zero after rounding does not necessarily mean the mathematical probability is exactly zero.
Availability and verification
Google explicitly documents EXPONDIST and EXPON.DIST for this function. Original introduction date, first version and last functioning numbered release were not established for rolling Sheets. Other products’ optional defaults or parameter names are not assumed.
NOT_TESTED_IN_GOOGLE_SHEETS. The individual EXPON.DIST and WEIBULL references and NIST mathematical definition were inspected on October 17, 2026. All outputs, inverse checks and unit conversions were independently calculated; no native execution or screenshot is claimed.