F Distribution Calculator

What is the F distribution?

The F distribution is a right-skewed curve defined only for values ≥ 0. It describes the ratio of two independent scaled variances, so its shape depends on two degrees-of-freedom parameters: a numerator (df₁) and a denominator (df₂). It underlies ANOVA (comparing means across several groups), the overall F-test for a regression model, and tests comparing two variances.

How to use this calculator

• F → P mode: Enter your F statistic and both df to get the exact corresponding p-value. The shaded area on the graph equals the p-value.
• P → F mode: Enter a significance level (α, e.g. 0.05) and both df to find the critical F-value(s).
• Right-tailed is by far the most common: ANOVA and regression F-tests reject H₀ only for large F. Use two-tailed when comparing two variances (Hₐ: σ₁² ≠ σ₂²).