F-Table
F-distribution critical values by numerator/denominator degrees of freedom, with reverse lookup.
Full printable reference table
| df2 \ df1 | 1 | 2 | 3 | 4 | 5 | 6 | 8 | 10 | 12 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 161.448 | 199.500 | 215.707 | 224.583 | 230.162 | 233.986 | 238.883 | 241.882 | 243.906 | 248.013 |
| 2 | 18.513 | 19.000 | 19.164 | 19.247 | 19.296 | 19.330 | 19.371 | 19.396 | 19.413 | 19.446 |
| 3 | 10.128 | 9.552 | 9.277 | 9.117 | 9.013 | 8.941 | 8.845 | 8.786 | 8.745 | 8.660 |
| 4 | 7.709 | 6.944 | 6.591 | 6.388 | 6.256 | 6.163 | 6.041 | 5.964 | 5.912 | 5.803 |
| 5 | 6.608 | 5.786 | 5.409 | 5.192 | 5.050 | 4.950 | 4.818 | 4.735 | 4.678 | 4.558 |
| 6 | 5.987 | 5.143 | 4.757 | 4.534 | 4.387 | 4.284 | 4.147 | 4.060 | 4.000 | 3.874 |
| 7 | 5.591 | 4.737 | 4.347 | 4.120 | 3.972 | 3.866 | 3.726 | 3.637 | 3.575 | 3.445 |
| 8 | 5.318 | 4.459 | 4.066 | 3.838 | 3.687 | 3.581 | 3.438 | 3.347 | 3.284 | 3.150 |
| 9 | 5.117 | 4.256 | 3.863 | 3.633 | 3.482 | 3.374 | 3.230 | 3.137 | 3.073 | 2.936 |
| 10 | 4.965 | 4.103 | 3.708 | 3.478 | 3.326 | 3.217 | 3.072 | 2.978 | 2.913 | 2.774 |
| 12 | 4.747 | 3.885 | 3.490 | 3.259 | 3.106 | 2.996 | 2.849 | 2.753 | 2.687 | 2.544 |
| 15 | 4.543 | 3.682 | 3.287 | 3.056 | 2.901 | 2.790 | 2.641 | 2.544 | 2.475 | 2.328 |
| 20 | 4.351 | 3.493 | 3.098 | 2.866 | 2.711 | 2.599 | 2.447 | 2.348 | 2.278 | 2.124 |
| 24 | 4.260 | 3.403 | 3.009 | 2.776 | 2.621 | 2.508 | 2.355 | 2.255 | 2.183 | 2.027 |
| 30 | 4.171 | 3.316 | 2.922 | 2.690 | 2.534 | 2.421 | 2.266 | 2.165 | 2.092 | 1.932 |
| 40 | 4.085 | 3.232 | 2.839 | 2.606 | 2.449 | 2.336 | 2.180 | 2.077 | 2.003 | 1.839 |
| 60 | 4.001 | 3.150 | 2.758 | 2.525 | 2.368 | 2.254 | 2.097 | 1.993 | 1.917 | 1.748 |
| 120 | 3.920 | 3.072 | 2.680 | 2.447 | 2.290 | 2.175 | 2.016 | 1.910 | 1.834 | 1.659 |
About this tool
Enter numerator and denominator degrees of freedom with alpha for an F cut-off, or enter an F statistic for its p-value.
How to use
How it works
The F distribution is the ratio of two scaled chi-square variables and is used for ANOVA and variance tests. It is right-skewed and has two df. In ANOVA df1 is groups − 1 and df2 is total observations − groups.
Reject H₀ when F > F(α, df1, df2)
Worked example
df1 = 3, df2 = 20
- Input
- Critical value, α = 0.05, right tail
- Output
- 3.0984
- Walkthrough
- An F statistic of 3.1 just exceeds the cut-off and gives p = 0.0499.
Limitations
- df1 and df2 are not interchangeable.
- Left-tail values are rarely needed.
Questions
What is the F critical value for df 3 and 20?
Which df goes first?
What is the F critical value for df 2 and 30?
Features
- Any df pair
- Critical and p-value
- Runs in your browser
Related resources
Guides and videos from around the web—opens on YouTube or the publisher’s site.
Mean, Variance and Standard Deviation
StatQuest with Josh Starmer
Descriptive stats behind table and test tools.
Watch on YouTubeChi-square distribution introduction
Khan Academy
Background for χ² tables and GoF/independence tools.
Watch on YouTube
- Introductory Statistics
OpenStax
Free textbook for hypothesis tests and tables.
- Statistics and probability
Khan Academy
Full intro stats path next to hub calculators.