F.INV.RT in Excel: Calculate an Upper-Tail F Critical Value

=F.INV.RT(probability, deg_freedom1, deg_freedom2)

All arguments are required. probability is the right-tail fraction. deg_freedom1 belongs to the numerator of the F ratio, and deg_freedom2 to its denominator.

The source’s short argument label refers broadly to a probability associated with the F cumulative distribution, but the function definition and inverse equation explicitly identify the right tail. The correct forward partner is F.DIST.RT.

The output is a threshold, not a probability. A smaller upper-tail probability requires a larger cutoff for fixed degrees. The function neither constructs the observed ratio nor chooses degrees of freedom from a dataset.

Put 0.1, 0.5 and 0.9 in A2:A4. Enter =F.INV.RT(A2,2,4) in B2 and fill down. Independent targets are 4.3245553203, 0.8284271247 and 0.1081851068.

For this degree pair, the elementary inverse is =2*(A2^(-0.5)-1). Put that in C2 and fill down for a separate mathematical check.

The quantiles decrease down the table even though the probabilities increase. At probability 0.5 the left- and right-tail inverses coincide, so include a nonmedian case when validating imported formulas.

In D2 enter =F.DIST.RT(B2,2,4) and fill down. The independent targets are 0.1, 0.5 and 0.9.

The elementary right-tail check =(1+B2/2)^(-2) gives the same probabilities. By contrast, F.DIST with cumulative=TRUE gives the complements 0.9, 0.5 and 0.1.

Use B’s full stored results when checking equality. A discrepancy caused by retyping a rounded display is different from a true inverse-convergence problem. Keep the probability convention in the column label.

For an F statistic with two numerator and four denominator degrees, the 5% upper-tail cutoff is 6.9442719100. Evaluating F.DIST.RT there targets 0.05.

A ratio of two under the same model has upper-tail probability 0.25, so it is below that cutoff. This is only an arithmetic comparison under the supplied distribution. It is not a general conclusion about real populations or the truth of a hypothesis.

A two-sided procedure needs its own tail allocation and ratio orientation. Do not assume that a one-tail critical value defines both rejection regions, or select a significance level after seeing the observed statistic.

The right-tail quantile at p with degrees d1,d2 equals the reciprocal of the left-tail quantile at p with degrees d2,d1.

For the quick answer, =1/F.INV(0.05,4,2) independently also gives 6.9442719100. The reciprocal operation exchanges the degrees; simply swapping them while leaving the rest of the formula unchanged does not preserve the question.

The left-tail expression =F.INV(0.95,2,4) gives the same cutoff as well. For extremely small p, direct F.INV.RT avoids explicitly computing 1−p, but these independent examples do not measure native extreme-tail accuracy.

Microsoft uses probability 0.01, degrees 6 and 4. =F.INV.RT(0.01,6,4) independently gives 15.2068648612, matching the displayed 15.20686.

Its forward distribution example uses the rounded x value 15.2068649, whose independently computed tail is approximately 0.00999999995. Rounding explains why a manually reconstructed round trip need not be exactly 0.01.

Microsoft documents #VALUE! for nonnumeric inputs, #NUM! for probability below zero or above one, and #NUM! for either degree below one. Noninteger degree inputs are truncated.

The dedicated page additionally states that denominator degrees at or above 10^10 produce #NUM!. It repeats the lower-bound condition and does not state a matching numerator maximum in that sentence. This guide retains that exact documented scope instead of silently making the bounds symmetric.

The source describes an iterative search whose precision depends on F.DIST.RT, with #N/A if it has not converged after 64 iterations. These are documented expectations, not observed native results.

The probability restriction does not explicitly exclude endpoints. Mathematically the upper-tail inverse at zero is unbounded and at one is zero; actual endpoint handling remains untested. Use interior probabilities for finite checks and validate degree counts explicitly instead of relying on truncation.

• Current documentation: the dedicated Microsoft reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Introduced: Microsoft’s alphabetical catalog marks F.INV.RT as introduced in Excel 2010. Exact first build and platform-specific introduction dates remain unverified.
• Last functioning version: unknown; a current help listing is not a last-working-build test.
• Evidence checked: October 15, 2026. Official documentation was freshly retrieved; examples were independently calculated. No native Excel, Mac or web-client execution was performed.

• Microsoft F.INV.RT reference.
• Microsoft function catalog and introduction-marker explanation.
• Editorial testing standards.

Examples use English function names and comma separators. Expected numbers are rounded independent mathematical calculations; documented error expectations are labeled as such. They are not captured Excel output. All illustrative data and policies are fictional.