WEIBULL Function (OpenOffice Calc)

• Introduced: First release not established. This name is documented in the OpenOffice.org 3.3 function appendix; that establishes historical presence, not introduction.
• Supported in: Apache OpenOffice 4.1.16. No final supported release has been established.
• Scope: Desktop Calc. These examples use English function names, semicolon separators and decimal points.
• Checked: October 14, 2026. Official source/documentation and independent mathematical examples checked; Apache OpenOffice Calc was not run for this guide.

The Weibull distribution is a continuous model often used for nonnegative lifetimes. Alpha is its positive shape parameter and Beta is its positive scale parameter. Scale has the same units as the input time; shape is dimensionless. Official reference.

Let u=(x/Beta)^Alpha. The CDF is 1−exp(−u), and the survival probability is exp(−u). For x>0 the density is (Alpha/Beta)(x/Beta)^(Alpha−1)exp(−u). At x=Beta the CDF is 1−exp(−1), approximately 63.21%, for every positive shape. Scale is therefore not generally the mean or median.

=WEIBULL(Number; Alpha; Beta; Cumulative)

All four arguments are required. Number must be nonnegative, Alpha>0 and Beta>0. Set Cumulative to 0 for density or 1 for cumulative probability. The release evaluator distinguishes zero from nonzero selectors, but using explicit 0 or 1 keeps the documented meaning clear.

The wiki example prose swaps the words density and cumulative beneath its formulas. The release evaluator and independent formulas resolve this: final 1 means CDF and final 0 means density. The two 2.5/3/4 rows below show the corrected interpretation.

Enter each formula in a separate cell. These expected values are independently calculated mathematical references, rounded to twelve decimal places.

Put lifetime 3 in A2, shape 2 in B2 and scale 4 in C2. In D2 use =WEIBULL(A2;B2;C2;1), expected 0.430217175269. If the scale is four hours, A2 must also be in hours. The result is about a 43.02% modeled chance of an event by hour three.

For a survival calculation, =EXP(-(A2/C2)^B2) gives approximately 0.569782824731. It directly computes the modeled probability of exceeding that time. A density call, =WEIBULL(A2;B2;C2;0), gives approximately 0.213668559274 per hour, which is not a point probability.

For cumulative probability p, the mathematical quantile is Beta×(−LN(1−p))^(1/Alpha). With p=0.9, shape 2 and scale 4, enter =4*(-LN(1-0.9))^(1/2). The expected 90th-percentile time is approximately 6.069708517541 hours.

Put that result in F2 and check =WEIBULL(F2;2;4;1), which should recover approximately 0.9. Use the full stored F2, not a rounded visible cutoff. Restrict p to the interior interval 0<p<1 for an ordinary finite positive quantile.

Shape 1 reduces Weibull to an exponential model with mean Beta and rate 1/Beta. For example, =WEIBULL(3;1;2;1) is approximately 0.776869839852. A rate of 0.5 and a scale of 2 express the same model but are not interchangeable argument values.

The Weibull hazard increases with age when shape>1, is constant at shape=1, and decreases when 0<shape<1. Those are properties of the selected model, not evidence that real equipment follows it. Fitting parameters and validating assumptions are separate tasks.

The release rejects negative Number or nonpositive Alpha/Beta as invalid arguments. Density at zero needs care: mathematically it diverges for shape<1, equals 1/Beta for shape=1 and is zero for shape>1. The table deliberately uses positive x; the guide does not promise a native displayed result at the singular boundary.

For extremely small CDFs, subtracting an exponential near 1 can lose precision; extreme inputs may also overflow intermediate powers. The ordinary reference cases do not certify these limits. Preserve units, use the intended selector and validate extreme-value requirements in the installed program.

• WEIBULL function documentation
• Apache OpenOffice 4.1.16 argument handling and calculation