F-Distribution

F PDF, CDF, and critical values

X ~ F(d₁ = 5, d₂ = 10) · P(X ≤ 2)

Density & probability at x

0.835805

Density f(x)

0.162006

P(X ≤ x)

0.835805

P(X ≥ x)

0.164195

Percentile

83.5805

Distribution mean

1.25

About this calculator

The F-Distribution Calculator draws the density curve for any numerator and denominator degrees of freedom and shades the probability you choose. In density mode it reports f(x), the left tail P(X ≤ x), the right tail P(X ≥ x), and the percentile; in critical-value mode it finds the value F with P(X ≥ F) = α. Useful for ANOVA, regression F-tests, and comparing two variances.

Common examples

F(5, 10) at x = 2: P(X ≤ 2) = 0.8358, right tail 0.1642
Density f(2) of F(5, 10) = 0.1620
Critical value F(5, 10), α = 0.05: F = 3.3258
Critical value F(3, 20), α = 0.01: F = 4.9382
Mean of F(5, 10) is d₂ / (d₂ − 2) = 1.25