WEIBULL.DIST in Google Sheets: CDF, Density and Survival

=WEIBULL.DIST(x, shape, scale, cumulative)

Google’s WEIBULL.DIST entry specifies these four arguments and points to the detailed WEIBULL reference.

• x: evaluation point.
• shape: positive shape parameter, often called k.
• scale: positive scale parameter, in the units of x.
• cumulative: TRUE for cumulative probability or FALSE for density.

Both shape and scale must exceed zero. The reviewed page does not state an omitted-flag default, so every formula supplies it. The mathematical zero-location lifetime model has nonnegative support; these examples use positive evaluation points and do not infer undocumented native behavior for negative x or singular boundaries.

Assume a component lifetime model with shape 2 and scale 10 months. These are illustrative parameters, not a fit to observed failures. Enter 5, 10 and 20 in A2:A4. Put 2 in D1 and 10 in E1.

In B2, enter and fill down:

=WEIBULL.DIST(A2,$D$1,$E$1,TRUE)

In C2, enter and fill down:

=WEIBULL.DIST(A2,$D$1,$E$1,FALSE)

The first result column estimates failure by the stated time under the chosen model. Density is a height on a continuous curve. It is not the probability of a failure at exactly that time and should not be labeled as a monthly probability without integrating over a month-long interval.

For this shape-2, scale-10 case, verify the cumulative column with:

=1-EXP(-(A2/10)^2)

Verify the density column with:

=2*A2/100*EXP(-(A2/10)^2)

These specialize the zero-location Weibull equations in NIST’s distribution reference. Keeping the explicit ratio x/scale helps prevent mixing months with days.

A useful consequence is that the cumulative probability at x equal to scale is about 0.6321205588 for any positive shape. Scale is therefore not generally the mean or the median lifetime.

The modeled probability of surviving beyond 20 months is:

=1-WEIBULL.DIST(20,2,10,TRUE)

Expected result: 0.0183156389, about 1.83%. An independent survival calculation is =EXP(-(20/10)^2).

The probability of failure between 5 and 10 months is:

=WEIBULL.DIST(10,2,10,TRUE)-WEIBULL.DIST(5,2,10,TRUE)

Expected result: 0.4109213419, about 41.09%. This difference is unconditional: it does not condition on having already survived to month 5.

For very small survival probabilities, subtracting a CDF extremely close to 1 can lose relative precision. The direct mathematical survival expression is useful for checking whether rounding explains an apparent zero.

For the same model, the time by which 90% of failures occur is:

=10*SQRT(-LN(1-0.9))

Expected result: 15.1742712939 months. Feeding that value into WEIBULL.DIST with the same shape and scale and TRUE should mathematically recover 0.9. This is a derived shape-2 inverse equation, not a claim that WEIBULL.DIST itself performs inversion.

Google also documents the shape-1 relationship to EXPONDIST with rate equal to 1/scale. Accordingly, =WEIBULL.DIST(10,1,10,TRUE) has expected result 0.6321205588. Do not pass the scale unchanged into a function that expects a rate.

Check positive shape and scale, consistent units, and the TRUE/FALSE flag. A reversed parameter order can still produce a number while describing a different model. Exact native error codes, coercion and zero-input boundary behavior were not established by the reviewed help page.

The Weibull model does not validate itself against observed data. Parameter fitting, censoring and the suitability of a failure model are separate statistical tasks. This guide demonstrates evaluation, not a reliability guarantee.

Current Google documentation supports WEIBULL.DIST through WEIBULL. Original introduction date, first release and last functioning numbered version remain unestablished.

NOT_TESTED_IN_GOOGLE_SHEETS. Google alias and detailed function pages and NIST equations were inspected on October 17, 2026. All original numbers were independently calculated and cross-checked numerically. No native result or screenshot is claimed.

Related published guides: EXP, LN, SQRT and ROUND.