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F Critical Value Calculator
Your test setup
Need a level that is not listed? Choose “Custom” and type any significance level below.
In a one-way ANOVA with k groups and N observations, df1 = k − 1 and df2 = N − k.
The F-test is one-tailed: only large F values count against the null hypothesis, so the whole significance level sits in the upper tail.
With 3 and 20 degrees of freedom, an F statistic above 3.098 falls in the top 5% of the F-distribution, so it is significant at the 5% level. The mean of this F-distribution is 1.111.
Example: α = 0.05, df1 = 3, df2 = 20 — F* = 3.098.
Behind the numbers
How the F critical value is calculated
The F critical value F* is the point on the F-distribution with the chosen degrees of freedom that leaves the significance level α in the upper tail. In other words, it is the (1 − α) quantile of the F-distribution: the value where the cumulative distribution function equals 1 − α. This calculator finds it exactly by inverting the F cumulative distribution function, which is built from the regularized incomplete beta function — no rounded table lookup, and it works for any degrees of freedom up to 120 and beyond.
where F is the CDF of the F-distribution with df1 numerator and df2 denominator degrees of freedom. Worked example: α = 0.05, df1 = 3, df2 = 20 means F* is the 95th percentile of the F-distribution with 3 and 20 degrees of freedom: F* = 3.098. The mean of that F-distribution is df2 ÷ (df2 − 2) = 20 ÷ 18 = 1.111.
Worked examples
Example F critical values
| Significance (α) | df1 | df2 | F* |
|---|---|---|---|
| 0.05 | 3 | 20 | 3.098 |
| 0.05 | 1 | 10 | 4.965 |
| 0.01 | 2 | 30 | 5.390 |
| 0.05 | 5 | 10 | 3.326 |
| 0.10 | 4 | 12 | 2.480 |
| 0.05 | 2 | 120 | 3.072 |
As the denominator degrees of freedom grow, F* falls toward 1: with df1 = 2 and df2 = 120 the 5% critical value is 3.072, and with df2 = 1,000 it is 3.005. Smaller significance levels give larger critical values, because less of the distribution is allowed in the upper tail.
Using F* the right way
In a one-way ANOVA, df1 = number of groups − 1 and df2 = total observations − number of groups. Four groups with 24 observations give df1 = 3 and df2 = 20, so the 5% critical value is 3.098.
Compare your F statistic with F*: if F is larger than F*, the result is significant at your chosen level. An F of 4.20 with F* = 3.098 is significant at 5%; an F of 2.50 is not.
Pick the significance level before you run the test. Switching from 0.05 to 0.10 after seeing the result just to reach significance is not honest statistics.
Do not round F* early. A rounded F* of 3.10 instead of 3.098 is harmless, but rounding to 3.0 can flip a borderline decision, so keep three decimals until the final comparison.
Good to know
Your F critical value questions, answered.
What is an F critical value?
An F critical value, written F*, is the cutoff on the F-distribution that leaves the chosen significance level in the upper tail. For example, with 3 numerator and 20 denominator degrees of freedom, the 5% F critical value is 3.098: only 5% of the F-distribution with those degrees of freedom lies above 3.098.
When do I use an F critical value?
Use an F critical value in an F-test, most often a one-way ANOVA that compares the means of three or more groups, or a test that compares two variances. If your calculated F statistic is larger than F*, you reject the null hypothesis at the chosen significance level.
What are numerator and denominator degrees of freedom?
In a one-way ANOVA with k groups and N total observations, the numerator degrees of freedom are k − 1 and the denominator degrees of freedom are N − k. For example, 4 groups with 24 observations give df1 = 3 and df2 = 20, and the 5% F critical value is 3.098.
How is the F critical value calculated?
This calculator inverts the F cumulative distribution function exactly, using the regularized incomplete beta function, instead of reading a rounded table. It works for any degrees of freedom from 1 to 120 and beyond, for significance levels of 0.10, 0.05, 0.025 and 0.01, or any custom level you type.