T.DIST.RT in Google Sheets: Signed Right-Tail Probabilities

=T.DIST.RT(x, degrees_freedom)

The Google T.DIST.RT reference describes this right-tail function and gives positive and negative input examples. One displayed syntax line instead names T.DIST.2T; the page title, sample formulas and numerical results consistently identify T.DIST.RT. The syntax above follows those agreeing parts.

Both arguments are required. Google documents a numeric error when degrees of freedom is below 1. The page’s explicit negative example establishes that negative x is supported for this function, unlike T.DIST.2T’s documented nonnegative-magnitude domain.

There is no cumulative or tails flag. The reviewed individual page does not establish the treatment of fractional degrees of freedom, so all examples use integers.

Enter -2, -1, 0, 1 and 2 in A2:A6. Put 9 in D1. In B2, enter and fill down:

=T.DIST.RT(A2,$D$1)

Most of the distribution lies to the right of a negative threshold. A large result for -2 is therefore expected, not an indication that the sign was ignored.

The threshold’s sign and the direction of the requested tail are separate ideas. Right-tail means greater than x, even when x itself is negative.

Symmetry gives complementary right-tail values at x and -x. For the two endpoints of the table, 0.9617235881 + 0.0382764119 = 1 within rounding.

At 1 degree of freedom, the t distribution is Cauchy, as documented by NIST. Its right-tail expression is 0.5-ATAN(x)/PI() mathematically. This gives simple expected values:

Google’s own negative example, x = -1.98 with 2 degrees of freedom, gives approximately 0.9068737481, independently reproduced by the right-tail calculation. That is specific evidence for signed input handling.

Suppose E2 contains a signed statistic -2 and E3 contains 9 degrees of freedom. For an alternative aligned with larger values, the right-tail area is:

=T.DIST.RT(E2,E3)

Expected result: 0.9617235881. For the corresponding left-tail area, use:

=1-T.DIST.RT(E2,E3)

Expected result: 0.0382764119. The direction must follow the prespecified hypothesis. Applying ABS to E2 before choosing a directional tail would remove information and could produce the wrong p-value for that hypothesis.

For a symmetric two-sided area, twice the smaller tail gives 0.0765528238. Google’s separate T.DIST.2T function directly handles the nonnegative magnitude for that purpose.

A right-tail function can also produce a finite interval probability by subtracting two right-tail areas in the correct order. Between -1 and +1:

=T.DIST.RT(-1,9)-T.DIST.RT(1,9)

Expected result: 0.6565636039. Subtracting in the reverse order would give a negative number, signaling an ordering mistake rather than a valid probability.

Use unrounded function values for the subtraction. Display rounding should not be carried into subsequent calculations, especially when two probabilities are very close.

Google describes T.DIST.RT as corresponding to TDIST with tails set to 1 and as a replacement alongside T.DIST.2T. The guide preserves the explicit T.DIST.RT negative example without assuming that every historical TDIST boundary behaves identically. Replacement wording alone does not establish retirement of the older spelling.

Check degrees of freedom, the threshold sign and the selected direction before interpreting an unexpected result. Exact native text/blank coercion, fractional-degree handling and all error tokens were not established. A p-value interpretation also requires a correctly constructed test statistic and suitable assumptions.

Current rolling Google Sheets documents the function. Original introduction date, first release and last functioning numbered version were not established.

NOT_TESTED_IN_GOOGLE_SHEETS. Google’s individual reference and NIST mathematics were inspected on October 17, 2026. All original right tails, complements and interval differences were independently calculated. No native execution or screenshot is claimed.

Related published guides: ABS, IF and ROUND.