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F.DIST.RT Function (LibreOffice Calc)

Statistical Intermediate LibreOffice Calc

Learn the F.DIST.RT function in LibreOffice Calc: Values of the right tail F probability distribution.

Verification status: Saved LibreOffice Calc 25.2.3.2 observations and supplementary LibreOfficeDev 26.8.0.0.alpha0 XLSX results were reviewed for the identified examples. The historical stable installation was not rerun; the guide distinguishes those evidence sets. How formula examples are checked

Availability and version history

  • Introduced: LibreOffice 4.2, explicitly stated in official F.DIST.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.

What does F.DIST.RT do?

F.DIST.RT returns the probability in the right (upper) tail of an F distribution for a non-negative observed F statistic and numerator/denominator degrees of freedom. The result is a probability between 0 and 1, not an F critical value and not the F probability-density height. An F distribution is frequently used to assess ratios of estimated variances under specific statistical assumptions, as well as in analysis-of-variance (ANOVA) calculations. official function Help

In notation, for an F-distributed random variable with degrees of freedom df1 and df2, the function estimates P(F >= observed_F). Because the F distribution is continuous, > and >= have the same probability. The number is interpreted under the assumed F model; it does not directly measure the probability that a scientific hypothesis is true.

Quick example — native-tested:

=F.DIST.RT(0.8;8;12)

Result: 0.614339643745812 (about 61.43%). The official LibreOffice example rounds this to 0.6143396437. official function Help

Syntax and arguments

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

The English-language formulas here use semicolons as argument separators and a decimal point, matching the environment tested. Localized Calc installations can use different separators or translated function names; follow your installation’s formula configuration. official function HelpOpenFormula standard

Argument Required? What to provide Examples and cautions
Number Yes Non-negative F statistic at which to evaluate the upper-tail probability 2, 0.8, or a cell such as B2; not a significance threshold such as 5% unless that is actually your F statistic.
DegreesFreedom1 Yes Positive numerator degrees of freedom For two sample variances from 6 independent observations in the numerator group, 5.
DegreesFreedom2 Yes Positive denominator degrees of freedom For 11 independent observations in the denominator group, 10.

There are exactly three required arguments, with no optional cumulative/PDF flag. The function is not the four-argument F.DIST, whose fourth argument selects cumulative probability versus density. No argument defaults are documented for F.DIST.RT. official function Help

Integer degrees of freedom: In the tested Calc 25.2.3.2 build, supplying 2.5 or 10.5 as a degree-of-freedom value returned the result for the truncated integer (2 or 10). The official page explicitly describes truncation for the legacy FDIST function, not as a blanket promise about every modern function or every release. Enter valid integer degrees of freedom and confirm version-specific behavior if you receive non-integer values from a statistical model. official function Help

Reproducible examples

All rows below were directly executed as native Calc formulas during the saved 2026-10-13 native test run. Displayed figures are rounded here; the test evidence retains full floating-point outputs and independent expectations.

Question Enter this formula Expected result Interpretation
Official example =F.DIST.RT(0.8;8;12) 0.6143396437 61.43% of this F distribution lies at or above 0.8.
Equal numerator and denominator df =F.DIST.RT(1;4;4) 0.5 With equal degrees, F = 1 divides the distribution at its median.
At the lower boundary =F.DIST.RT(0;4;4) 1 The non-negative F variable is always at or above zero.
Moderate ratio =F.DIST.RT(2;5;10) 0.1641949509 Upper-tail p-value is about 16.42%.
Larger observed statistic =F.DIST.RT(3;5;10) 0.0655575621 Larger F gives a smaller upper-tail probability (same df).
At a 5% upper critical value =F.DIST.RT(3.3258345304;5;10) 0.0500000000 Matches the inverse function’s upper 5% threshold.
Legacy comparison =FDIST(0.8;8;12) 0.6143396437 FDIST gave the same upper-tail result for this tested integer-df case.

A cell-reference example

Enter the following inputs on a worksheet named Inputs:

Cell Value Meaning
A2 2 Observed F statistic
B2 5 Numerator degrees of freedom
C2 10 Denominator degrees of freedom

Then, in another sheet:

=F.DIST.RT(Inputs.A2;Inputs.B2;Inputs.C2)

Native-tested result: 0.164194950899739. A validated variant, also tested with these inputs, is:

=IF(OR(Inputs.A2<0;Inputs.B2<=0;Inputs.C2<=0);NA();F.DIST.RT(Inputs.A2;Inputs.B2;Inputs.C2))

This guard handles negative F statistics and nonpositive degrees, but it is not a complete validator for numeric types or for integer degrees. For editable models, use Data → Validity or add an ISNUMBER/integer check appropriate to the input range rather than silently accepting unsupported data.

Worked example: compare two estimated variances

Before observing the samples, label the groups A and B and choose the one-sided alternative that A has the larger population variance. Always place A in the numerator. Suppose independent samples from approximately normal populations then yield sample variances 56 for A and 11 for B, with sample sizes 6 and 11 respectively:

  1. F statistic: 56 / 11 = 5.0909090909.
  2. Numerator df: 6 - 1 = 5; denominator df: 11 - 1 = 10.
  3. Enter =F.DIST.RT(56/11;5;10).

Native-tested result: 0.0140231764204 (about 1.40%). The following two-sided decision rule is not implied by this single upper-tail calculation: it is a one-sided upper-tail p-value for a specified variance-ratio model. In the illustrative one-sided test with a prechosen significance level of 0.05, the observed ratio is beyond the upper 5% F threshold, so reject that one-sided null hypothesis provided its independence and normality assumptions apply. Do not choose the numerator by looking for the larger observed variance: that selection changes the test. Keep the pre-specified group orientation. NIST: one-sided and two-sided variance F tests. official function Help

The decision formula was also executed natively and returned the text Reject H0:

=IF(F.DIST.RT(56/11;5;10)<0.05;"Reject H0";"Do not reject H0")

To reproduce the input variances from raw observations, Calc also supplies VAR.S (sample variance); determine your numerator and denominator sample sizes before using this p-value. The worked test above starts from supplied variances; it does not claim a separate raw-data worksheet test.

Advanced use: upper-tail numerical stability

You may see the mathematical identity:

=1-F.DIST(2;5;10;TRUE())

For ordinary F statistics, this agrees (up to floating-point rounding) with =F.DIST.RT(2;5;10). In fact, the directly tested identity =F.DIST.RT(2;5;10)+F.DIST(2;5;10;TRUE()) returned 1. However, subtracting a cumulative probability extremely close to 1 can erase small differences. Prefer the direct right-tail function for tiny p-values.

A native diagnostic in the tested build made that difference concrete:

  • =F.DIST.RT(1E10;8;12) returned approximately 9.56812498769813E-58.
  • =1-F.DIST(1E10;8;12;TRUE()) returned 0.

These are native Calc 25.2.3.2 observations, not promises about every release or alternative evaluator. The right-tail formula avoids the numerically lossy subtraction.

Another direct cross-check is:

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

Native-tested result: approximately 0.05. F.INV.RT supplies the observed F cutoff whose upper-tail probability is 0.05; F.DIST.RT retrieves that probability. official function Help

Function Purpose Relationship and pitfall
F.DIST Left-tail CDF or F density, depending on its fourth argument With cumulative TRUE(), ordinarily F.DIST.RT(x;d1;d2) ≈ 1 − F.DIST(x;d1;d2;TRUE()). FALSE() returns a density, not an upper-tail probability.
F.INV.RT Upper-tail inverse F.INV.RT(0.05;5;10) returns the upper 5% cutoff instead of a probability at a given F value. See the official documentation for its own argument contract.
F.TEST F-test-based comparison of sample variance Takes sample-data ranges; its test interpretation is not automatically equivalent to every one-sided F ratio.
FDIST Legacy right-tail function For this legacy spelling, check its argument contract and the intended upper-tail calculation.
F.INV Left-tail inverse Uses a left-tail probability, unlike F.INV.RT.

Errors, edge cases and troubleshooting

The following error codes and boundary behaviors were observed in direct native testing; they are not guaranteed for older releases, other locales or imported XLSX formula evaluation.

Input or issue Native result in Calc 25.2.3.2 What to check
=F.DIST.RT(-1;5;10) Err:502 Negative F statistic is invalid.
=F.DIST.RT(2;0;10) Err:502 First degree of freedom must be positive.
=F.DIST.RT(2;5;0) Err:502 Second degree of freedom must be positive.
=F.DIST.RT("foo";5;10) #VALUE! (519) Check text in a numeric input cell.
=F.DIST.RT(2;5) Err:511 Missing required third argument.
=F.DIST.RT(2;5;10;1) Err:504 Four arguments supplied to a three-argument function.
=F.DIST.RT(0;5;10) 1 Valid lower boundary of an F distribution.
=F.DIST.RT(2;2.5;10) 0.1859344321 Fractional df1 was truncated to 2 in this tested version; do not assume continuous fractional degrees.
=F.DIST.RT(2;5;10.5) 0.1641949509 Fractional df2 was truncated to 10 in this tested version.

If results appear wrong, confirm the numerator and denominator were not swapped, verify the input is a variance ratio or appropriate F statistic (not raw sample variance), ensure your formula uses upper-tail rather than lower-tail semantics, check numerical cell types and degree-of-freedom assumptions, and format the output as a number or percentage with sufficient displayed decimals. A value like 0.014 represents approximately 1.4%, not 14%.

Compatibility, scope and validation

  • LibreOffice support: Official Help states F.DIST.RT has been available since LibreOffice 4.2 and identifies its function name in the COM.MICROSOFT.F.DIST.RT compatibility namespace. official function Help
  • ODF interoperability: LibreOffice Help explicitly says this function is not a standard function in OpenDocument 1.3 OpenFormula. The separately consulted ODF 1.4 standard does not provide an independently verified cross-application guarantee for this compatibility function. A native .ods file saved in this run recorded formulas using of:=COM.MICROSOFT.F.DIST.RT(...). Do not infer that an unrelated OpenFormula evaluator will run them. official function HelpOpenFormula standard
  • Tested native platform: Linux with LibreOffice Calc 25.2.3.2, directly entered via UNO, recalculated, stored to ODS, and reopened. The shared suite for this guide and the companion F.INV.RT completed 73 of 73 independent numerical assertions; this function accounted for 37. There were 34 additional diagnostics across both functions.

Official references