# F Distribution Calculator

Instructions: Use this calculator to compute F-distribution probabilities. Please type in the degrees of freedom $$df_1$$ and $$df_2$$, and specify the event you want to compute the probability for, in the form below:

Numerator Degrees of freedom $$(df_1)$$ =
Denominator Degrees of freedom $$(df_2)$$ =
Variable Name (Optional) =
Two-Tailed:
≤ F ≤
Left-Tailed:
F ≤
Right-Tailed:
F ≥

The F-distribution is one of the most fundamental distributions in Statistics, along with the normal distribution and the Chi-Square distribution. Technically, the F-distribution is obtained by constructing the ratio between two properly scaled variables that have a Chi-Squared distribution

Indeed if $$U_1$$ and $$U_2$$ are two independent random variables that have a Chi-Square distribution, and $$U_1$$ has $$df_1$$ degrees of freedom and $$U_2$$ has $$df_2$$ degrees of freedom, then the variable $$F$$ defined as

$F = \displaystyle \frac{U_1/df_1}{U_2/df_2}$

has an F-distribution, with degrees of freedom $$df_1$$ and $$df_2$$.

The F-distribution is one of the crucial continuous distributions in Statistics. You can use other probability calculators for continuous distributions, such as our normal probability calculator, Chi-Square distribution calculator or our uniform probability calculator, among many others.

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