F.INV in Google Sheets: Left-Tail Quantiles and Critical Values
Use F.INV in Google Sheets to find F-distribution cutoffs from left-tail probabilities, handle two-tail boundaries and keep degrees of freedom in the right order.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =F.INV(0.75,2,2) has expected result 3. It finds the F-distribution cutoff with 75% of the area at or below it for numerator and denominator degrees of freedom both equal to 2.
Syntax and documented domain
=F.INV(probability, degrees_freedom1, degrees_freedom2)
All three arguments are required, with no optional defaults. Google’s F.INV reference specifies a left-tail probability strictly between 0 and 1.
The next two arguments are the numerator and denominator degrees of freedom. The page requires each to be at least 1, says fractional inputs are truncated to integers, and requires numeric arguments. It does not state the same upper-limit wording used by the distribution pages; do not silently transfer that restriction to the inverse contract.
The output is an F value. It is not the p-value itself, and it has no cumulative TRUE/FALSE flag.
Worked example: a quantile lookup table
Enter 0.25, 0.5, 0.75, 0.95 in A2:A5. Put 2 in D1 and 2 in E1. In B2, enter and fill down:
=F.INV(A2,$D$1,$E$1)
| Left-tail probability | Expected F cutoff |
|---|---|
| 0.25 | 0.3333333333 |
| 0.5 | 1 |
| 0.75 | 3 |
| 0.95 | 19 |
For this particular (2,2) distribution, the CDF is x/(1+x). Solving that expression for x gives p/(1−p), which independently reproduces the table. NIST’s F-distribution reference gives the general mathematical distribution; the simple inverse above is a special case.
Verify the direction with a forward check
For the cutoff 3:
=F.DIST(3,2,2,TRUE)
=F.DIST.RT(3,2,2)
Expected results: 0.75 and 0.25. The left and right areas complement one another. Google’s F.DIST reference and F.DIST.RT reference document these distinct forward calculations.
If the request is for an upper 5% cutoff, the input to F.INV is 0.95. Entering 0.05 would find a low left-tail cutoff instead.
Advanced application: a two-sided comparison region
For a variance-ratio model with degrees of freedom 6 and 8, a central 95% reference region leaves 2.5% in each tail:
=F.INV(0.025,6,8)
=F.INV(0.975,6,8)
Expected endpoints are approximately 0.1785834509 and 4.6516955373. The F distribution is asymmetric, so these are not equal distances from 1.
For an F statistic of 3, the value lies inside this particular reference region. That observation is not proof that the population variances are equal; it is a comparison against chosen cutoffs under a model. The NIST F-test reference describes how one-sided and two-sided critical regions differ.
Use the intended test’s tail allocation. Applying 0.05 to each tail would leave a central 90% region, not 95%.
Keep the degrees of freedom attached to the ratio
For samples of sizes 7 and 9, the usual sample-variance ratio has degrees of freedom 6 and 8 in that order when the first sample is the numerator. A 95th-percentile cutoff for those degrees of freedom is:
=F.INV(0.95,6,8)
Expected result: 3.5805803198. Swapping the degrees of freedom to 8 and 6 gives 4.1468041623. Do not reorder the parameters alphabetically or by size; their meaning comes from the statistic.
The reciprocal of the lower 2.5% cutoff for (6,8) is the upper 97.5% cutoff for (8,6), approximately 5.5996230050. This is a useful model consistency check, not a reason to reverse a hypothesis after inspecting results.
Errors and troubleshooting
Use probabilities strictly inside (0,1), numeric inputs and whole degrees of freedom whenever possible. Check whether a percentage was entered as 95 rather than 95% or 0.95. Inspect truncation if imported degrees of freedom are fractional.
The reviewed page does not enumerate exact error tokens for every invalid argument, text or blank input. No unsupported native token mapping is asserted. Rounding a cutoff before a later probability calculation also changes the result; retain full precision until the reporting stage.
Availability and verification
F.INV is the left-tail inverse. Google’s F.INV.RT page identifies FINV as the right-tail inverse alias, so FINV and F.INV are not interchangeable spellings. Original introduction date, first release and last functioning numbered version were not established for rolling Sheets.
NOT_TESTED_IN_GOOGLE_SHEETS. Individual Google and NIST references were inspected on October 17, 2026. Quantiles were independently calculated, with closed-form (2,2) checks and forward numerical round trips. No native execution or screenshot is claimed.