BETAINV 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 4 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.

BETAINV 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. Release implementation.

=BETAINV(Probability; Alpha; Beta [; Lower [; Upper]])

Three through five arguments are accepted. Alpha and Beta must be positive. Lower defaults to 0 and Upper to 1. For reliable ordinary quantiles use 0<Probability<1 and Lower<Upper. The inspected 4.1.16 implementation also accepts Probability=0 but returns literal 0, which is an important exception when Lower is not zero. Probability=1 is rejected. Equal bounds are rejected; reversed bounds have the separate implementation caveat below.

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.

For Alpha=2 and Beta=3, =BETAINV(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, =BETAINV(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 =BETAINV(0.5;2;3), then =BETADIST(A2;2;3) 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.

The 4.1.16 source checks Probability<0 or Probability≥1, then handles Probability=0 by pushing 0 before scaling. Thus =BETAINV(0;2;3;10;14) follows a source branch returning 0, not the mathematical lower endpoint 10. Use the known lower endpoint directly when it is the result you need; do not treat this branch as a valid scaled inverse.

The same implementation rejects equal bounds but does not reject Upper<Lower. With uniform shapes, =BETAINV(0.5;1;1;14;10) follows the scaling formula to 12, even though BETADIST rejects that reversed interval. Validate increasing bounds yourself. Extreme parameters may also cause numerical nonconvergence; a failed inverse must not be replaced silently by zero.

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.