F Distribution Percent Point Calculator
Find the F distribution percent point (critical F value) from a probability and degrees of freedom d1, d2. Supports lower and upper tail quantiles for ANOVA and F tests.
Input
Enter a probability and degrees of freedom d1, d2 to compute the F distribution percent point (critical F value). Both lower and upper tail methods are supported.
A value strictly between 0 and 1 (e.g. 0.95)
Choose whether the probability is a lower or an upper tail area
Numerator degrees of freedom (positive)
Denominator degrees of freedom (positive)
Result
Percent point F for probability 0.95 and degrees of freedom (5, 10)
3.32583453
Degrees of freedom d1
5
Degrees of freedom d2
10
Input probability p
0.95
Lower tail probability at F
0.95
Upper tail probability at F
0.05
Probability density at F
0.04058624
Mean
1.25
Variance
1.35416667
Probability density (PDF)
Cumulative distribution (CDF)
How it works
- The cumulative distribution of the F distribution is given by the regularized incomplete beta function I_y(d1/2, d2/2), where y equals (d1 F) divided by (d1 F + d2).
- For the target lower probability the value y is found with the inverse incomplete beta function (initial estimate plus Newton iteration, falling back to bisection), then converted using F = (d2 y) / (d1 (1 - y)).
- Choosing the upper tail method reuses the same calculation with the lower probability set to 1 - p.
- The mean equals d2 / (d2 - 2) only when d2 is greater than 2, and the variance is defined only when d2 is greater than 4.
- Degrees of freedom may be any positive real value, not only integers. The probability must lie strictly between 0 and 1.
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F Distribution Percent Point Calculator