F.INV in Excel: Find a Left-Tail F Quantile

=F.INV(probability, deg_freedom1, deg_freedom2)

All arguments are required. probability is a left-tail cumulative fraction. deg_freedom1 is the numerator degree count, and deg_freedom2 is the denominator degree count.

The result is a quantile on the F-ratio scale, not a probability. It may be much larger than one even though the input probability must be a valid fraction. The function does not calculate sample variances or determine the correct degrees from data.

F.INV reverses F.DIST in cumulative=TRUE mode. It does not invert density. For a 5% upper-tail threshold, use a left-tail probability of 0.95 here, or use F.INV.RT with 0.05.

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

For these degree counts, the inverse has the elementary expression =2*((1-A2)^(-0.5)-1). Put it in C2 and fill down for an independent mathematical check.

The median is about 0.8284, not necessarily one. A model’s ratio interpretation does not force its median to one when numerator and denominator degrees differ. The interval between the tenth and ninetieth percentiles is correspondingly asymmetric.

Enter =F.DIST(B2,2,4,TRUE) in D2 and fill down. Mathematical targets are the original probabilities 0.1, 0.5 and 0.9.

For the same degrees, =1-(1+B2/2)^(-2) independently checks D. Use the full stored B values, not the decimal approximations printed in this guide.

If the round trip gives complements of A instead, check whether a right-tail inverse or forward distribution was used. If it gives unrelated values, verify the degree order and cumulative flag before blaming numerical precision.

The interval from 0.1081851068 to 4.3245553203 contains 80% of the two/four F distribution. Its tails each contain 10%. Subtract the forward cumulative values to verify 0.8.

Equal tail probabilities do not mean equal distances from a center. This is an interval of a specified distribution, not automatically a confidence interval for a population variance ratio. That application requires a separate statistical derivation and assumptions.

Keep probability interval calculations distinct from a decision rule about observed data. A valid quantile calculation alone does not establish that the selected reference model is appropriate.

=F.INV(0.95,2,4) independently targets 6.9442719100, matching =F.INV.RT(0.05,2,4). The input probabilities must be complementary.

A second identity is =1/F.INV(0.05,4,2), which targets the same threshold. Taking the reciprocal exchanges numerator and denominator degrees and complements the left-tail probability.

Changing just the degree order without the other transformations is not equivalent. Record each transformation in a separate cell when auditing an imported workbook, especially if the original ratio convention is uncertain.

The dedicated source uses probability 0.01, degrees 6 and 4. =F.INV(0.01,6,4) independently gives 0.1093099141, matching its rounded 0.10930991.

F.INV.RT with those same arguments instead gives a large upper-tail cutoff. This nonmedian case is a useful control because left- and right-tail inverses happen to agree at probability one half and can hide an incorrect convention there.

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

The documented probability restriction does not exclude zero or one. Mathematically the lower endpoint is zero and the upper-end quantile is unbounded. Actual Excel endpoint outputs and errors were not executed, so the finite examples use interior probabilities.

Use 90% or 0.9 rather than 90. Keep degree inputs as justified integers, and do not infer another function’s maximum-degree or convergence restriction when the dedicated F.INV page does not state it. Independent checks do not certify all native coercions or extreme-probability accuracy.

• 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, Excel Web App.
• Introduced: Microsoft’s alphabetical catalog marks F.INV 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 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.