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) =
≤ F ≤
F ≤
F ≥

More About the F-distribution

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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