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F distribution calculator

Choose a calculation and enter numerator and denominator degrees of freedom.

Selected calculation result: —

Fill in the fields above — the result is computed on this page.

x or quantile
—
P(F ≤ x)
—
P(F ≥ x)
—
d₁
—
d₂
—

What do these numbers mean?
  • The upper tail is used by common F tests.
  • Always report both degrees of freedom in the correct order.

The F distribution is one-sided and non-negative. A distribution result does not replace checking assumptions of the specific test.

How do I use this page?
  1. Choose CDF, upper tail or quantile.
  2. Enter d₁ and d₂.
  3. Provide x or a probability and read the result.

What this page does not do: The F distribution is one-sided and non-negative. A distribution result does not replace checking assumptions of the specific test.

Further reading

Theory — what is the F distribution?

The F distribution describes the ratio of two independent, appropriately scaled variances. It is used in analysis of variance, tests comparing variances between two groups, and in evaluating the overall quality of regression models. The shape of the distribution depends on two parameters — the numerator and denominator degrees of freedom — so calculating a probability requires both values. The F distribution's cumulative function is computed using the regularized incomplete beta function.

Frequently asked questions

Why are two df values needed?
The distribution depends on degrees of freedom for the numerator and denominator variances.
What is the 0.95 quantile?
It is the x for which P(F ≤ x) equals 0.95.

See also

← All calculators

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