F Distribution Calculator (p & Critical F)

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F Distribution Calculator

The F distribution is the ratio of two scaled chi-square variables and is the reference distribution for ANOVA, for the F-test of two variances and for the overall test in regression. This calculator gives P(F ≥ x), P(F ≤ x) or a two-tailed probability for a statistic with df₁ (numerator) and df₂ (denominator) degrees of freedom, and in critical value mode gives the F cut-off for any α.

Enter the two degrees of freedom, the mode, and either the F statistic or α. The result comes with a shaded density plot and the steps that go from the cumulative probability to the tail you asked for. Because printed F tables cover only a few α levels and df combinations, the calculator is the practical way to get exact values for, say, F(3, 47) at α = 0.025.

The order of the degrees of freedom matters: df₁ belongs to the numerator (between-groups mean square in ANOVA, or the variance on top in an F-test). A printable F-table at α = 0.05 and 0.01 is available, and the one-way ANOVA calculator runs the whole test.

Frequently asked questions

Which degrees of freedom go first?

The numerator df (df₁) first, then the denominator df (df₂). Swapping them gives a different distribution.

How is the p-value for ANOVA found?

It is P(F ≥ observed F) with df₁ = k − 1 and df₂ = N − k. Choose the right tail in probability mode.

What is the critical F value at 0.05 for (2, 27) df?

3.354. Critical values fall as df₂ grows and rise as α shrinks.

Why does the calculator offer a two-tailed option?

The F-test for two variances is two-tailed when the alternative is simply “the variances differ”; the p-value is twice the smaller tail.

Last reviewed: September 25, 2026. Calculations run in your browser and were validated against SciPy.