BETA.INV Function (LibreOffice Calc)

• Introduced: LibreOffice 4.2.
• 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: =BETA.INV(0.5;2;3) has reference value 0.385727568132.

BETA.INV searches for a beta-distributed value whose lower-tail cumulative probability equals the requested Probability. With ordinary positive shapes and increasing bounds, it is the inverse of BETADIST’s cumulative calculation. It returns a value in the variable’s units, not a probability or a density. Pinned calculation logic.

=BETA.INV(Probability; Alpha; Beta [; Lower [; Upper]])

Three through five arguments are accepted. Both shapes must be positive, Lower must be smaller than Upper, and Probability must be in the closed interval 0 through 1. Lower defaults to 0 and Upper to 1. In this LibreOffice evaluator both probability endpoints are accepted and the inverse is scaled to the requested increasing bounds; this differs from Apache OpenOffice 4.1.16’s zero-probability branch.

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.

For Alpha=2 and Beta=3, =BETA.INV(0.5;2;3) is approximately 0.385727568132. That is the median, not necessarily the mean. The mean of this standard beta model is 2/(2+3)=0.4, showing why the two summaries need not match.

For the same shape on 10 through 14, =BETA.INV(0.5;2;3;10;14) is approximately 11.542910272530. The transformation is 10+4×the standard quantile. Store probability, both shapes and bounds in separate labeled cells if building a percentile table; the final column should be labeled in the modeled variable’s units.

A useful check feeds the returned ordinary quantile into the CDF. If A2 contains =BETA.INV(0.5;2;3), then =BETA.DIST(A2;2;3;TRUE()) should be close to 0.5. Carry the unrounded value in A2; rounding the displayed median before reuse can prevent an exact-looking round trip.

A central 90% beta interval uses the 0.05 and 0.95 quantiles. For a uniform beta model on 10 through 14, these bounds are 10.2 and 13.8. These are model quantiles, not automatically a confidence interval for an estimated parameter. The inferential meaning depends on how the beta distribution and its shape parameters were obtained.

A central interval needs two reported endpoints. Subtracting its lower quantile from its upper quantile returns the interval’s width, not the interval itself. To normalize a bounded quantile q from [a,b] to [0,1], calculate (q−a)/(b−a); calling the bounded inverse alone does not perform that normalization. A Bayesian credible-interval interpretation additionally requires a specified prior, likelihood and posterior.

The pinned LibreOffice evaluator rejects Probability<0 or>1, nonpositive shapes and Lower≥Upper. At Probability=0 it returns the lower endpoint, and at Probability=1 the upper endpoint. For example, the scaled uniform model with bounds 10 and 14 has endpoint quantiles 10 and 14. Do not copy the Apache OpenOffice zero-probability exception into LibreOffice.

If an input probability is invalid, find the upstream problem instead of automatically clamping it to 0 or 1. The numerical inverse may also report nonconvergence for difficult parameters. Keep full internal precision for round trips and round only for presentation.

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.