F Distribution Calculator

Work out f distribution instantly with clear inputs, formula shown and shareable results.

About F Distribution Calculator

The F distribution is the ratio of two scaled chi-square variables, so it is the natural reference for comparing variances and for ANOVA. It is right-skewed and depends on two separate degrees of freedom.

Formula

F CDF

P(F ≤ f) = I_(d₁f/(d₁f + d₂))(d₁/2, d₂/2)

Worked example

With the default values below, F Distribution Calculator returns P(F > f) — the p value of 0.0496405380. Change any input above and every figure here is recalculated in your browser.

Inputs used

F valueminimum 0: 3.5
Numerator degrees of freedomaccepts 1–1,000: 3
Denominator degrees of freedomaccepts 1–1,000: 12

Results

P(F > f) — the p value: 0.0496405380
P(F ≤ f): 0.9503594620
Critical value at 5%: 3.490295
Mean d₂/(d₂ − 2): 1.200000

Step by step

1Values used
2F CDF
3P(F > f) — the p value= 0.0496405380
4P(F ≤ f)= 0.9503594620
5Critical value at 5%= 3.490295
6Mean d₂/(d₂ − 2)= 1.200000

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For F = 3.5 on 3 and 12 df?

The right-tail p is about 0.0497, just under the 5% critical value of 3.4903.

Why two degrees of freedom?

One for each variance estimate in the ratio; swapping them inverts the F value and its critical points.