Critical values for the F-distribution. Used in ANOVA, regression significance tests, and variance comparisons.

F-Critical Values

Select a significance level, then find your df1 (numerator, columns) and df2 (denominator, rows). The cell value is the critical F-value—if your F-statistic exceeds it, reject H0 at that α.

How to Use
Your F-statistic comes from an ANOVA or regression output. Compare it to the critical value at the intersection of your df1 (numerator degrees of freedom) and df2 (denominator degrees of freedom). If Fobs > Fcrit, the result is statistically significant at the chosen α.

Understanding the F-Table

The Two Degrees of Freedom

Unlike the t-distribution (which has one df), the F-distribution has two degrees-of-freedom parameters:

df1 (numerator): In one-way ANOVA, this is k − 1, where k is the number of groups. In regression, it is the number of predictors.

df2 (denominator): In one-way ANOVA, this is N − k, where N is the total number of observations. In regression, it is N − p − 1.

What the F-Test Is Used For

  1. ANOVA (Analysis of Variance): Tests whether the means of three or more groups are all equal. The F-statistic compares between-group variance to within-group variance.
  2. Overall regression significance: Tests whether at least one predictor in a regression model has a non-zero coefficient. This is the F-statistic reported at the bottom of regression output.
  3. Comparing variances: Tests whether two populations have equal variances (Levene’s test, Bartlett’s test). The ratio of two chi-squared variables divided by their df follows an F-distribution.

Relationship to the T-Distribution

F and t Connection F = t²   (when df1 = 1)

When comparing exactly two groups, a one-way ANOVA with df1 = 1 is mathematically identical to a two-sample t-test. The F-statistic is the square of the t-statistic, and the p-values are the same. This means an F-table with df1 = 1 gives you the square of the corresponding t-critical value.

Connecting the Dots
The F-distribution builds on the same math as the t-distribution table. Both use the incomplete beta function under the hood. If you are doing a simple two-group comparison, you can use either table—t is more natural for directional hypotheses, F for omnibus tests. See our Sample Size & Power page for how these distributions feed into study design.

Quick Reference

Need the t-distribution instead? → T-Distribution Table

Need to plan a study? → Sample Size & Power Calculator

F-Critical Value Lookup

Enter your degrees of freedom and significance level to get the exact F-critical value. You can also enter an observed F-statistic to compute its p-value.

Find F-Critical

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F-Critical Value

Find P-Value from F-Statistic

Enter an observed F-statistic along with the degrees of freedom above to compute its exact p-value.

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p-value (upper tail)
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Significant at α?
Tip
The F-distribution is always one-tailed (right tail). An F-statistic is significant when it falls in the upper tail beyond the critical value. There is no “two-sided” F-test—the distribution is non-negative and asymmetric.