T.DIST in Excel: Calculate Signed Student t Probabilities and Density

=T.DIST(x, deg_freedom, cumulative)

All arguments are required. x is the signed evaluation point. deg_freedom is the degree count. TRUE selects cumulative probability, while FALSE selects probability density.

A left-tail cumulative value measures probability at or below x. It increases as x increases and equals one half at zero for this symmetric distribution. Density is instead a curve height per unit of the t-scale variable.

The function does not calculate a t statistic, sample mean or standard error from a dataset. A statistical application must supply a justified statistic and degrees of freedom separately. Merely calling a t distribution does not make an inappropriate small-sample analysis valid.

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

Negative values are meaningful positions below the center. Replacing x by ABS(x) would change the question for the first two rows. Preserve a signed statistic when calculating a signed left-tail event.

Symmetry gives cumulative probabilities at x and −x whose sum is one. Check =B2+B6 and =B3+B5; both mathematical targets are 1. This property concerns the reference distribution, not the shape of a particular observed sample.

In C2 enter =T.DIST(A2,5,FALSE) and fill down. Independent densities are 0.0650903103, 0.2196797974, 0.3796066898, 0.2196797974 and 0.0650903103.

The density values are symmetric: the heights at −1 and +1 match, while their cumulative probabilities differ. At zero, the density is about 0.3796 and the cumulative probability is 0.5.

A continuous model assigns zero probability to any single exact point. The density height is not the probability of exactly that x value. Label the two columns separately rather than giving every result a percentage format.

=T.DIST(2,5,TRUE)-T.DIST(-2,5,TRUE) independently targets 0.8980605212. It is the probability within the interval from −2 to +2.

The complementary probability outside both ends is 0.1019394788, obtainable from =T.DIST.2T(2,5). That function already includes both tails; it should not be doubled again.

Strict versus inclusive inequalities at the endpoints give the same probability in this continuous model. The same reasoning does not apply to integer-valued count distributions.

=T.INV(0.975,5) independently gives 2.5705818356. Passing that full result into T.DIST with five degrees and TRUE targets 0.975, leaving 0.025 above the positive threshold.

With one degree, the t distribution is the Cauchy distribution. The mathematical cumulative expression is =0.5+ATAN(x)/PI(). At x=−1, 0 and 1 its targets are 0.25, 0.5 and 0.75. Use that check only for one degree, not the five-degree table.

The dedicated Microsoft examples use =T.DIST(60,1,TRUE), independently 0.9946953264, and =T.DIST(8,3,FALSE), independently 0.0007369065. The latter is density even though the surrounding prose uses broad distribution terminology.

Microsoft documents #VALUE! for nonnumeric arguments and an error for degrees below one. The current dedicated page does not identify that degree error by code, so this guide does not invent a specific native display.

The syntax requires an integer degree count and a logical mode. Its general nonnumeric-error sentence should not be read as excluding the expressly allowed TRUE/FALSE mode. Fractional-degree coercion and all text/blank conversions were not established by native execution here.

Check sign, mode and degrees before interpreting a surprising number. These independent examples verify arithmetic for stated models, not extreme-tail accuracy or the probability that a hypothesis is true.

• 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, Excel Web App.
• Introduced: Microsoft’s alphabetical catalog marks T.DIST 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 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.