BETADIST Function (LibreOffice Calc)

• Introduced: Documented by LibreOffice 26.8.1.1; original introduction not established.
• Availability: Supported in LibreOffice 26.8.1.1, verified against its function registry. This identifies a supported release, not a final working version.
• Scope: Desktop Calc, using the English function name. Availability in other spreadsheet applications is separate.
• Checked: 2026-10-14 — function reference; versioned support. Documentation/source check; not a new native test. Existing example-specific test claims below retain their stated scope.

Quick answer: =BETADIST(0.5;2;3) has reference value 0.6875.

BETADIST evaluates the beta distribution with positive shape parameters Alpha and Beta. It can return either a lower-tail cumulative probability or a density. Optional bounds scale the distribution from its standard 0-to-1 support to a different interval. A density is a height whose integral is probability; it may exceed 1. Pinned calculation logic.

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

Three through six arguments are accepted in the displayed order. Lower defaults to 0, Upper to 1 and Cumulative to TRUE. Alpha and Beta must be positive and Upper must exceed Lower. To request density, supply both bounds and FALSE as the sixth argument. This optional sixth argument is a documented part of Calc BETADIST, not a separate BETA function.

These eight formulas were recalculated through XLSX import in LibreOfficeDev 26.8.0.0.alpha0, build 2c87e51eeaa2b413ff4ae097b2705eea1995d8e5. Saved ODS values agree with independent high-precision references, rounded here to twelve decimal places. This is headless development-build evidence, not stable-release or GUI validation.

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 a Bayesian proportion model, Beta(1,1) is a uniform prior and independent Bernoulli data with s successes and f failures give posterior shapes s+1 and f+1. That specific prior explains the added ones; it is not a universal parameter rule. A posterior CDF at a threshold is one probability, not a central credible interval and not the probability that one A/B variant beats another.

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.

Development-build boundary checks

The following additional formulas were saved from the same headless import run. Error text is retained as an error, not converted to a successful zero result.

• BETA.DIST
• BETAINV
• GAMMALN

The LibreOffice 26.8.1.1 evaluator establishes the product-specific argument and domain rules. Mathematical references and composite examples were independently checked. Native evidence is limited to the eight reference formulas and listed diagnostics in the named development build. A deliberately stale SUM cache changed from 999999 to 3, and an uncached SUM returned 7 after forced recalculation. The earlier ordinary conversion failed the stale-cache control and was excluded. Composite explanatory calculations, stable releases, GUI entry and extreme-parameter accuracy were not established by this run.