F.INV.RT Function (LibreOffice Calc)

• Introduced: LibreOffice 4.2, explicitly stated in official F.INV.RT Help.
• Availability: Supported in LibreOffice 26.8.1.1, confirmed by the versioned function registry. This is not a final supported version.
• Scope: Desktop Calc; formula names and separators depend on language/settings. Other spreadsheet products need separate compatibility checks.
• Checked: October 14, 2026. Documentation/source evidence; saved 25.2.3.2 native observations and supplementary development-build XLSX tests are scoped separately below.

Validation scope: The saved native observations in this guide were produced in LibreOffice Calc 25.2.3.2 on Linux on October 13, 2026. This revision verified the corresponding saved ODS values against the result ledgers; it did not rerun that historical installation. Supplementary numerical cases were recalculated through imported XLSX files in LibreOfficeDev 26.8.0.0.alpha0 (build 2c87e51eeaa2b413ff4ae097b2705eea1995d8e5). That development-build/import check is separate from direct formula entry and from the stable-release support evidence.

F.INV.RT returns an F statistic cutoff whose right-tail probability equals a requested probability. It is the inverse (quantile) counterpart of F.DIST.RT, not a function for directly calculating a p-value from an observed ratio. official function Help

If a random variable F follows an F distribution with numerator degrees of freedom df1 and denominator degrees of freedom df2, this function finds x satisfying P(F >= x) = probability. It is often used to find an upper critical value before a one-sided F test of variances or another F-statistic-based procedure. The mathematical model and selected tail must match the proposed hypothesis.

Quick example — native-tested:

=F.INV.RT(0.5;5;10)

Result: 0.931933160851048 (approximately 0.9319331609), matching the official LibreOffice Help example. Because this is the 50% right-tail cutoff, it equals the median; the agreement with F.INV(0.5;5;10) at this one probability does not make the two functions interchangeable for other probabilities. official function Help

For the 5% upper-tail critical value with the same degrees of freedom:

=F.INV.RT(0.05;5;10)

Result: 3.32583453041301. An observed F ratio must be at least this cutoff to land in the upper 5% tail of this distribution.

=F.INV.RT(Number; DegreesFreedom1; DegreesFreedom2)

There are three required arguments, no optional flags, and no documented default values. The Number argument means probability; despite its name it is not a raw observation. An input probability of 0.05 represents 5%. The English-language locale examples use semicolons and decimal points; other Calc formula configurations may display localized separators and names. official function Help

Fractional degrees of freedom: In Calc 25.2.3.2, native tests showed decimal inputs such as 2.5 were truncated to 2, and 10.5 to 10. That can materially alter a critical value. Use valid integer degrees for ordinary F distributions and check the model’s assumptions; do not pass fractional degrees of freedom from an unrelated approximation without assessing the interpretation. This is a version-specific observation, not a blanket guarantee for all releases.

The following results were tested by entering the shown formulas directly in Calc through UNO (not by importing an XLSX) and comparing with SciPy’s F distribution inverse-survival function. Display is rounded; machine-readable evidence stores full values.

Build a parameterized critical-value calculator

Place these inputs on a sheet named Inputs:

Then enter on another worksheet:

=F.INV.RT(Inputs.D2;Inputs.B2;Inputs.C2)

Native-tested result: 3.32583453041301. Use Data → Validity to constrain the probability cell to a sensible open interval and degrees-of-freedom inputs to positive integers. A basic guard, also entered and numerically tested with the indicated values, is:

=IF(OR(Inputs.D2<=0;Inputs.D2>=1;Inputs.B2<=0;Inputs.C2<=0);NA();F.INV.RT(Inputs.D2;Inputs.B2;Inputs.C2))

This deliberately excludes the otherwise native-accepted boundary p=1, because the example is intended to return strictly finite positive critical values; it is a model-design choice, not a claim that Calc rejects that input. It does not check for text values or fractional degrees; add ISNUMBER and integer checks for robust user-facing calculators.

Before observing data, choose group A as the numerator and the alternative that A has the larger population variance. Suppose independent approximately normal groups A and B of sizes 6 and 11 then have sample variances 56 and 11. For that pre-specified upper-tail, one-sided ratio test, the observed ratio is 56 / 11 = 5.0909090909 and the numerator and denominator degrees of freedom are 5 and 10. official function Help

1. Set the predetermined significance level to 0.05 for the upper tail.
2. Obtain the cutoff with =F.INV.RT(0.05;5;10), which returns 3.3258345304 (native-tested).
3. Compare the observed F ratio 5.0909090909 to that cutoff: it exceeds the critical value.
4. As a cross-check, calculate =F.DIST.RT(56/11;5;10). The companion function returned 0.0140231764204 during the saved 2026-10-13 native test run. This is below 0.05.

Therefore the example rejects the specific upper-tail null at the 5% threshold if the stated independent-normal-population assumptions and chosen ratio orientation apply. A different hypothesis, sampling design, or two-sided test could require a different calculation. A small p-value is not the probability the null hypothesis is true.

Useful reproducibility note: The ratio formula =F.DIST.RT(56/11;5;10) was executed in the shared native test suite. The full original raw-data variance formulas were not independently native-asserted in this batch; this worked example starts from stated sample variances rather than claiming to have measured them from a dataset.

The upper-tail inverse and upper-tail distribution should agree:

=F.DIST.RT(F.INV.RT(0.05;5;10);5;10)

Native-tested result: approximately 0.05. The suite also verified this round trip at several other probabilities and degrees of freedom.

A mathematically related calculation is F.INV.RT(p;df1;df2) ≈ F.INV(1-p;df1;df2) for probabilities away from problematic rounding boundaries. F.INV uses the left-tail probability, whereas F.INV.RT uses the right-tail probability; accidentally passing 0.05 to both functions does not yield the same 5% upper critical value. If p is extremely small, using 1-p can lose precision; the direct F.INV.RT is preferable where supported. official function Help

For a two-sided procedure, the critical values and tail allocations differ: a 5% two-sided test often needs a 2.5% upper-tail cutoff and an appropriate lower-tail cutoff. Do not automatically substitute the 5% one-sided value without defining the statistical procedure. In particular, the opposite tail is not generally the same numerical cutoff for asymmetric F distributions.

The native results below were observed specifically in Calc 25.2.3.2 with semicolon-separated formulas entered directly through UNO. They are not universal cross-application guarantees.

Diagnostics checklist: Confirm the probability is in decimal form (5% or 0.05, not 5), degrees of freedom are in the correct numerator/denominator order, the test is truly upper-tail, text values are not masquerading as numbers, and a one-sided threshold isn’t substituted for a two-sided procedure. If the result looks surprising, substitute the returned cutoff back into F.DIST.RT; it should approximately recover the original probability.

Do not trust a rounded display alone for statistical decisions near the significance threshold. Preserve full-precision values in spreadsheet formulas; format only the visible cell. The inverse may also be numerically sensitive at extreme probability boundaries or degrees of freedom, so verify with a second method for high-stakes analyses.

• LibreOffice support: Official LibreOffice Help lists F.INV.RT as available since LibreOffice 4.2. official function Help
• Formula namespace: The help page places the function in COM.MICROSOFT.F.INV.RT and says it is not a standard OpenDocument 1.3 OpenFormula function. The OASIS ODF 1.4 specification was separately consulted for current standard context, not as a compatibility certification. In the native .ods saved here, its stored formulas used of:=COM.MICROSOFT.F.INV.RT(...). Availability elsewhere must be verified independently. official function HelpOpenFormula standard
• Actual native execution: This function accounted for 36 of 36 passed independent numerical assertions in the shared 2026-10-13 suite, within a total of 73 of 73 assertions for this and F.DIST.RT, plus 34 non-assertion diagnostics. The ODS workbook was reopened and 73/73 recorded numerical outputs matched the saved report.

Choose the ratio orientation before observing sample variances; do not select whichever observed variance is larger and interpret the result as the same one-sided test. NIST variance-test guidance.

• F.INV.RT syntax, version history and examples
• Release-pinned function registration
• Calc formula language and separators