T.DIST.RT in Excel: Calculate a Signed Student t Upper Tail

=T.DIST.RT(x, deg_freedom)

Both arguments are required. x is the signed t-scale evaluation point, and deg_freedom is the integer degree count. There is no density or cumulative flag.

Right tail means probability to the right of the actual signed threshold. It does not automatically mean the smaller of the two tails. For a negative threshold, the right-tail probability is greater than one half.

The supplied x need not be calculated from data, but an inferential use requires a justified statistic and sampling model. This function does not determine the alternative hypothesis, standard error or degrees from a range of observations.

Enter -2, -1, 0, 1 and 2 in A2:A6. Put =T.DIST.RT(A2,5) in B2 and fill down. Independent targets are 0.9490302606, 0.8183912662, 0.5, 0.1816087338 and 0.0509697394.

At −1 the probability to the right is about 0.8184, while at +1 it is about 0.1816. Taking the absolute value in both rows would discard this distinction.

The right tail decreases as x increases. A negative point producing the same small tail as its positive counterpart suggests that a magnitude was substituted somewhere in the formula chain.

In C2 enter =T.DIST(A2,5,TRUE) and fill down. The independent left-tail values are 0.0509697394, 0.1816087338, 0.5, 0.8183912662 and 0.9490302606.

For every row, =B2+C2 targets 1. The TRUE mode is essential: density at the same x is not the complement of a right-tail probability.

A direct right-tail call avoids writing 1-cumulative when the cumulative result is extremely close to one. This can matter numerically, but the independent controls here do not establish native Excel error bounds in extreme tails.

For five degrees, =T.INV(0.95,5) independently gives 2.0150483733. Passing that unrounded value to T.DIST.RT targets 0.05.

A symmetric two-sided 5% cutoff has positive magnitude 2.5705818356, from =T.INV.2T(0.05,5). Its right-tail probability is 0.025, because the other 0.025 lies below the negative boundary.

These are different rules with different tail allocations. Choose the direction and procedure before analyzing the data. The function itself cannot determine whether a one-sided rule is justified.

For nonnegative x=2, =2*T.DIST.RT(2,5) independently gives 0.1019394788, matching T.DIST.2T at magnitude two.

Do not use the same doubling rule with a negative signed input. Twice the right tail at −2 is about 1.8980605212, which cannot be a probability. A symmetric two-tail calculation instead uses the magnitude ABS(−2)=2.

Retain the signed effect estimate beside a magnitude-based p-value. A two-sided probability discards direction by design; it does not say whether the observed difference was positive or negative or whether it matters practically.

Microsoft uses x=1.959999998 with 60 degrees. =T.DIST.RT(1.959999998,60) independently yields 0.0273224650, consistent with its displayed 0.027322.

The corresponding two-tail probability is approximately 0.0546449300. A threshold near 1.96 is not automatically an exact 5% two-tail t cutoff at finite degrees, even though 1.96 is familiar from a normal approximation.

Do not force the result to 0.025 or replace the degree count merely to match a remembered normal-table value. Verify which reference distribution the actual procedure requires.

Microsoft documents #VALUE! for nonnumeric arguments and #NUM! for degrees below one. Its syntax calls for integer degrees; this dedicated page does not describe every fractional-degree conversion or type coercion.

Keep signed x when calculating a directional right-tail event. A probability conditional on a model is not the probability that a hypothesis is true or false. Native execution, localized errors and extreme-tail accuracy remain unverified; these are independent mathematical expectations.

• Current documentation: the dedicated Microsoft reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Introduced: Microsoft’s alphabetical catalog marks T.DIST.RT as introduced in Excel 2010. Exact first build and platform-specific introduction dates remain unverified.
• Last functioning version: unknown; a current help listing is not a last-working-build test.
• Evidence checked: October 15, 2026. Official documentation was freshly retrieved; examples were independently calculated. No native Excel, Mac or web-client execution was performed.

• Microsoft T.DIST.RT reference.
• Microsoft function catalog and introduction-marker explanation.
• Editorial testing standards.

Examples use English function names and comma separators. Expected numbers are rounded independent mathematical calculations; documented error expectations are labeled as such. They are not captured Excel output. All illustrative data and policies are fictional.