F.INV Function (LibreOffice Calc)

=F.INV(Number; DegreesFreedom1; DegreesFreedom2)

There are no optional parameters and no documented default values. The arguments shown use English function names, semicolon separators, and decimal dots for the tested English-US Calc configuration. A localized installation can use another function display name and decimal or argument delimiter convention. For an F distribution from a ratio of two independent estimated variances, the first df commonly equals the numerator sample size minus one, and the second equals the denominator sample size minus one [LO-FINV].

What an F quantile measures

The function seeks the threshold q for a random variable F with specified numerator and denominator degrees of freedom such that:

P(F ≤ q) = Number,    F ~ F(DegreesFreedom1, DegreesFreedom2)

The F distribution is nonnegative and usually right-skewed. Its quantiles are not symmetric around zero. A returned critical F value is a dimensionless ratio threshold, not a probability, significance percentage, or probability density. Changing the order of the two degrees-of-freedom inputs changes the underlying distribution and, generally, the answer. Compare F.DIST for direct probabilities and F.DIST.RT for right-tail probabilities.

In an empty Calc cell, enter:

=F.INV(0.5;5;10)

Expected result: 0.9319331609. Direct native testing returned 0.9319331608510483, consistent with the example in LibreOffice Help [LO-FINV]. This is the median of the F distribution with 5 numerator and 10 denominator degrees of freedom: the cumulative probability to the left of this value is 50%.

For a conventional upper 5% rejection threshold, however, use 0.95 as the left-tail cumulative probability, not 0.05:

=F.INV(0.95;5;10)

Expected result: 3.3258345304130104 (native-verified). An observed F statistic exceeding this threshold is in the top 5% under the relevant null F model.

The following expressions were entered directly in native LibreOffice Calc 25.2.3.2 and checked against independently prepared values. They show the effects of different probabilities and df combinations.

Verify a result with the cumulative F distribution. For example:

=F.DIST(F.INV(0.95;5;10);5;10;TRUE())

Expected result: 0.95 in the native test. The final TRUE() selects the cumulative distribution, not the probability density. The separate formula =F.DIST(F.INV(0.5;5;10);5;10;FALSE()) returned approximately 0.5294890785: that is a density, not a 52.95% probability that a continuous random variable equals that exact value [LO-FDIST].

Make a reusable critical-value calculator

Prepare the following example sheet:

Expected G2: 3.3258345304130104. The cell-reference formula was separately asserted in the native test, not just inferred from the constant-value example. Changing the inputs recalculates the threshold.

Suppose you plan an upper-tail F test using a 5% significance level, a numerator df of five, and a denominator df of ten. The critical value follows:

=F.INV(1-0.05;5;10)

Native expected result: 3.3258345304130104. Compare an appropriately calculated F statistic to that boundary. If you need the lower 5% cutoff (for a distinct lower-tail decision), use:

=F.INV(0.05;5;10)

Native expected result: 0.211190428782345. They are not negative/positive reflections: an F distribution is nonnegative and asymmetric. The numerator and denominator df must be calculated consistently with the statistic being tested, not chosen merely to match a convenient lookup table.

When testing model adequacy in analysis of variance, the numerator often represents between-group degrees of freedom and the denominator within-group degrees of freedom. The validity of the resulting F test depends on the design and error assumptions; F.INV does not diagnose model violations.

Suppose two independent random samples from normal populations give a sample-variance ratio s1²/s2² = 1.8, and the numerator and denominator variance estimates have 11 and 15 degrees of freedom, respectively (for example, sample sizes 12 and 16). Under the standard normal-population variance-ratio model, a central 95% confidence interval for the true population variance ratio σ1²/σ2² has bounds:

lower = observed ratio / F.INV(0.975;df1;df2)
upper = observed ratio / F.INV(0.025;df1;df2)

In Calc:

=1.8/F.INV(0.975;11;15)
=1.8/F.INV(0.025;11;15)

Native expected results: lower approximately 0.5984385307 and upper approximately 5.9938826804. Both endpoint formulas were independently expected and directly asserted in the native test. A wide interval reflects sampling uncertainty, not an error in F.INV; whether it is an appropriate statistical summary depends on the independence and normality assumptions. The lower and upper denominators deliberately use different tail percentiles and the same ordered df parameters.

If your reported comparison is s2²/s1² instead, the statistic, df order, and target population ratio must all be adjusted consistently. Simply swapping DegreesFreedom1 and DegreesFreedom2 inside an existing formula without reconsidering the ratio can invalidate the interpretation.

LibreOffice includes a separate F.INV.RT function with right-tail semantics. The following native test returned exactly 0 at Calc’s displayed precision:

=F.INV(0.95;5;10)-F.INV.RT(0.05;5;10)

This works because a 5% upper-tail probability corresponds to 95% left-tail cumulative probability, provided both functions use identical df arguments.

The older named function FINV needs particular care. The native diagnostic:

=FINV(0.95;5;10)

returned 0.211190428782345, not the 3.3258345304130104 returned by =F.INV(0.95;5;10). This is consistent with legacy FINV using a different tail convention. It is incorrect to replace FINV with F.INV merely by copying the same probability into the modern function. Preserve the statistical meaning when converting legacy workbooks.

1. Confusing 0.05 and 0.95. To find the high critical F value with 5% of null outcomes above it, use =F.INV(0.95;...), because F.INV uses cumulative left-tail probability. Entering 0.05 returns a low cutoff. Alternatively, use F.INV.RT with a right-tail 0.05 argument.

2. Reversing numerator and denominator df. An F ratio has two roles; df1 belongs to its numerator and df2 to its denominator. Label cells accordingly and use consistent order throughout a workbook.

3. Treating the output as a p-value. An output such as 3.32583453 is a critical F statistic. To find a right-tail probability for an observed statistic, use F.DIST.RT, not F.INV.

4. Using a cutoff without validating assumptions. Standard variance-ratio F tests and intervals assume appropriate normality and independent sampling; ANOVA has additional model and design requirements. The spreadsheet only carries out the stated calculation.

5. Assuming decimals in df are retained. Native Calc 25.2.3.2 truncated 5.5 to 5 (and 10.5 to 10) in the examples below; noninteger df may not represent the continuous mathematical F parameters you intended.

These are direct native observations in LibreOffice Calc 25.2.3.2 on Linux, not promises about every release or import path.

A guarded formula, with probability in D2, numerator df in E2, denominator df in F2, is:

=IF(OR(D2<=0;D2>=1;E2<1;F2<1);NA();F.INV(D2;E2;F2))

For D2=0.95, E2=5, F2=10, this native-tested formula returned 3.3258345304130104. A diagnostic guard with probability zero returned #N/A as intentionally designed. If strictly integer degrees of freedom are required, extend the condition with E2<>INT(E2) and F2<>INT(F2); these extra integer checks are suggested edits and were not executed in the saved test. For production spreadsheets, validate imported types and numeric bounds before analysis.

Numerical precision near 100%

The native diagnostic =F.INV(0.999999999;5;10) returned approximately 203.98455307321035, illustrating rapid upper-tail growth. At exactly one, this tested version yielded a spurious huge finite value instead of a useful infinite quantile. Probabilities extremely close to one can also suffer precision limitations when created by subtraction. For very small upper-tail probabilities, check whether the direct right-tail inverse F.INV.RT better matches the analysis and intended input.

LibreOffice Help states F.INV has been available since LibreOffice 4.2. For file-format compatibility, its documented extension namespace is COM.MICROSOFT.F.INV, and LibreOffice Help states that this spelling is not part of the OpenDocument 1.3 OpenFormula core [LO-FINV]. The namespace is a documentation fact, not a claim of independent execution or perfect workbook interchange with Microsoft Excel, Google Sheets, OpenOffice, or other software. The numeric results and invalid-input behavior reported here were observed only in LibreOffice Calc 25.2.3.2 on Linux using native UNO formula entry and ODS save/reopen; current online help displayed LibreOffice 26.8 Help at research time.

• F.DIST — cumulative left-tail F probability when Cumulative is true, density otherwise.
• F.DIST.RT — probability in the right tail for an observed F statistic.
• F.INV.RT — upper-tail F critical value, accepting the right-tail probability directly.
• FINV — separate legacy function name with different probability convention.
• T.INV — corresponding left-tail inverse t distribution, for a different family of inferential procedures.

See LibreOffice statistical function documentation for syntax, examples, version availability and compatibility details.