F-Distribution
F PDF, CDF, and critical values
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.
How to use the F-Distribution calculator
- Enter the values for your problem into the input fields.
- Read the result — it updates instantly as you type.
- Check the formula and the visual explanation to follow how the answer was found.
- Copy the page URL to share the exact calculation.
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
Frequently asked questions
How does the F-Distribution calculator work?
Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.
When would I use the F-Distribution calculator?
It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.
How accurate are the results?
Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.