BETADIST Function (OpenOffice Calc)

• Introduced: First release not established; documented by OpenOffice.org 3.3.
• Supported in: Apache OpenOffice 4.1.16; this is not a final supported version.
• Scope: Desktop Calc with English semicolon-separated formulas. Locale and other-product contracts may differ.
• Checked: October 14, 2026. Eight reference formulas and 5 boundary cases were recalculated in Apache OpenOffice 4.1.16 on Linux x86-64, Build 9816 after XLSX import; other explanatory calculations are independent references.

BETADIST evaluates a beta distribution with positive shape parameters Alpha and Beta. By default its support is 0 through 1 and it returns the lower-tail cumulative probability. Optional bounds rescale the variable to a different interval. The optional sixth argument selects density instead, so this Calc spelling has more options than some legacy spreadsheet implementations. Release implementation.

=BETADIST(X; Alpha; Beta [; Lower [; Upper [; Cumulative]]])

Supply three through six arguments in the displayed order. Alpha and Beta must be positive, and Upper must exceed Lower. Lower defaults to 0, Upper to 1, and Cumulative to TRUE. To request density, supply both bounds and FALSE as the sixth argument. A numeric nonzero cumulative flag selects the cumulative calculation. Brackets denote optional positions and are not entered in formulas.

The numeric helper supplies the corresponding endpoint and evaluation branches.

Values below are rounded to twelve decimal places. These eight formulas were also recalculated in Apache OpenOffice 4.1.16 on Linux x86-64, Build 9816 after XLSX import. Saved results agree with the independent references to the checked precision.

Consider a modeled proportion with Alpha=2 and Beta=3. =BETADIST(0.5;2;3) returns 0.6875, meaning a 68.75% model probability at or below 0.5. =BETADIST(0.5;2;3;0;1;FALSE()) returns density 1.5. A density can exceed 1 because probability is an area over an interval, not the density’s height at one point.

To model the same shape on an interval from 10 to 14, put those bounds in D2 and E2 and evaluate =BETADIST(12;2;3;D2;E2). The midpoint still has cumulative probability 0.6875. Its density is 0.375, because stretching the width to 4 divides the density by 4 while preserving total area.

An interval probability is a difference of cumulative values. =BETADIST(0.5;2;3)-BETADIST(0.25;2;3) gives 0.42578125. For a continuous distribution, including or excluding an isolated endpoint makes no probability difference. This does not mean density is itself a probability.

The standardized variable is z=(X−Lower)/(Upper −Lower). Cumulative probabilities use the beta CDF at z; densities additionally divide by Upper −Lower. Preserve that scale factor when independently checking a formula. For Alpha=Beta=1 the model is uniform: on 10 through 14 its density is 0.25 and its midpoint CDF is 0.5. Choose shape parameters from a defensible model rather than merely selecting a curve that looks convenient.

For valid shape parameters and bounds, cumulative mode returns 0 below Lower and 1 above Upper. Density mode returns 0 outside the support. At a boundary the density may be finite, zero or singular depending on the shape: for example, Alpha<1 at the lower endpoint can cause an invalid-argument error rather than a representable infinite density.

Equal or reversed bounds and nonpositive shapes are rejected. Do not swap the order of the cumulative flag and optional bounds when copying formulas from a dotted BETA.DIST guide. A successful calculation does not validate the distributional model or establish accuracy at extreme shape parameters.

Observed boundary checks

These additional cases were saved from the same 4.1.16 import session. Error displays are errors even where the ODS numeric attribute is zero.

• Function-specific official evidence
• Pinned evaluator and domain checks

The saved import workbook retained the stated formula identities. A deliberately stale SUM cache became 3 and an uncached SUM became 7, confirming recalculation. The observed scope is the named release and method only; explanatory composite formulas are independently calculated unless specifically listed among the native cases. Other releases, locales and extreme-value limits were not established by these ordinary examples.