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
F-distribution density curve with the selected probability region shaded. P(X ≤ 2)F-distribution density curve with the selected probability region shaded. P(X ≤ 2)xf(x)1234560.10.20.30.40.50.60.7

Sobre esta calculadora

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.

Exemplos comuns

  • 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