F.DIST in Google Sheets: Left-Tail Probability and Density

=F.DIST(x, degrees_freedom1, degrees_freedom2, cumulative)

Google’s F.DIST reference distinguishes the two numerical degrees of freedom and states a FALSE default for cumulative, although its displayed syntax lists all four arguments. Supply TRUE or FALSE explicitly to make the intended result clear.

• x: positive numeric evaluation point.
• degrees_freedom1: numerator degrees of freedom.
• degrees_freedom2: denominator degrees of freedom.
• cumulative: TRUE for the left-tail CDF; FALSE for density.

Google documents integer truncation of fractional degrees of freedom and a permitted range greater than 1 through 10^10 for each. The examples use whole-number degrees of freedom within that stated range, avoiding ambiguity about the validation order near a boundary.

Enter 0.5, 1, 3, 9 in A2:A5. Enter 2 in D1 and 2 in E1 for the numerator and denominator degrees of freedom.

In B2, enter and fill down:

=F.DIST(A2,$D$1,$E$1,TRUE)

In C2, enter and fill down:

=F.DIST(A2,$D$1,$E$1,FALSE)

The CDF grows with x. Density is a curve height, not the probability of exactly x. The values in the last two columns answer different questions and should not receive interchangeable labels.

For this specific degrees-of-freedom pair, the density simplifies to 1/(1+x)^2 and the CDF to x/(1+x). Thus =3/(1+3) gives 0.75, while =1/(1+3)^2 gives 0.0625.

These simple formulas are special to the pair (2,2). They were derived from the general F density in NIST’s F-distribution reference. They are not replacements for F.DIST with arbitrary degrees of freedom.

For the interval between 1 and 3 under this model:

=F.DIST(3,2,2,TRUE)-F.DIST(1,2,2,TRUE)

Expected result: 0.25. For the area above 3:

=1-F.DIST(3,2,2,TRUE)

Expected result: 0.25. Google’s F.DIST.RT reference documents a dedicated right-tail function for that second question.

An F statistic arising from a sample-variance ratio must keep its numerator sample’s degrees of freedom first. For example, a ratio of 3 with degrees of freedom 6 and 8 gives a left-tail probability of approximately 0.9232553018. Swapping only the degrees of freedom to 8 and 6 changes it to 0.90112. The parameters are ordered, not interchangeable labels.

The spelling matters. Google’s F.DIST.RT page identifies FDIST as the right-tail alias. F.DIST with TRUE is left-tailed, and F.DIST with FALSE is a density. Removing the period from F.DIST is therefore not a safe cosmetic edit.

Likewise, a CDF value is not automatically a p-value for every hypothesis test. The test design determines whether the relevant area is left-sided, right-sided or divided between two tails.

Check positive x, numeric inputs, the documented degrees-of-freedom limits and the cumulative flag. If a value seems unexpectedly large or small, confirm which sample supplied the numerator and denominator. For variance-ratio work, degrees of freedom are ordinarily sample sizes minus one, not the sample sizes themselves.

The reviewed page states restrictions but does not enumerate every native error token or text/blank coercion. Its degrees-of-freedom wording differs from the inverse pages, which state at least 1. This guide preserves that function-specific distinction rather than asserting identical boundary handling across the family.

F.DIST is documented in rolling Google Sheets. Original introduction date, first release and last functioning numbered version were not established. No other spreadsheet’s error or omission behavior was used to fill undocumented gaps.

NOT_TESTED_IN_GOOGLE_SHEETS. The individual F.DIST and F.DIST.RT pages and NIST mathematical reference were inspected on October 17, 2026. Original outputs were independently checked with closed-form (2,2) equations and numerical F calculations. No native execution or screenshot is claimed.

Related published guides: VAR.S, COUNT, ROUND and SUM.