T.INV.2T in Excel: Find a Two-Sided Student t Critical Magnitude

=T.INV.2T(probability, deg_freedom)

Both arguments are required. probability describes the two outside tails together, and deg_freedom selects the t distribution. The output is the nonnegative threshold magnitude, not the lower signed endpoint.

For a 95% central interval, enter total outside probability 0.05. Do not halve it before calling T.INV.2T; the two-tail inversion already allocates probability across both symmetric tails.

The forward partner is the two-argument T.DIST.2T. It calculates the probability that the absolute t variable exceeds the returned magnitude. A left-tail inverse uses a different probability convention.

Enter 0.2, 0.1 and 0.05 in A2:A4. In B2 enter =T.INV.2T(A2,5) and fill down. Independent targets are 1.4758840488, 2.0150483733 and 2.5705818356.

Smaller total outside probability produces larger magnitudes. A central interval extends from −B to +B; the function returns only B, not both endpoints.

The table is not a ranking of which significance level should be selected. A statistical procedure and its decision rule should be chosen before inspecting the results.

Put =T.DIST.2T(B2,5) in C2 and fill down. Independent targets are 0.2, 0.1 and 0.05.

For the final row, T.DIST.RT at B4 gives 0.025, while T.DIST with TRUE gives 0.975. These are the upper-tail and left-cumulative views of the same positive boundary.

Use the full stored inverse result. A rounded threshold may slightly miss its original probability when passed back through the forward function.

A 5% right-tail threshold at five degrees has magnitude 2.0150483733. It can be expressed as =T.INV(0.95,5) or, deliberately using symmetry, =T.INV.2T(2*0.05,5).

The second expression supplies total probability 0.1, allocating 0.05 to each tail. It does not mean a one-sided 95% statement and a two-sided 90% statement are interchangeable descriptions of the same procedure.

Keep the intended confidence statement, tail allocation and statistic definition alongside the formula. The inverse function evaluates a distribution but does not choose a valid inferential design.

Suppose an illustrative sample has size 25, sample standard deviation 3 and mean 40 under a suitable one-sample mean model. The standard error is =3/SQRT(25), or 0.6.

Use 24 degrees: =T.INV.2T(0.05,24)*3/SQRT(25) independently gives margin 1.2383391370. The corresponding endpoints are 38.7616608630 and 41.2383391370.

The degree count is sample size minus one for this particular construction. The function does not infer sample size from the standard deviation, and the returned critical magnitude is not by itself a margin.

Microsoft’s tabular example uses probability 0.546449 with 60 degrees. =T.INV.2T(0.546449,60) independently gives 0.6065330758, matching its rounded display.

The surrounding prose prints 2.28139 for T.INV.2T(0.05,10). Independent calculation instead gives 2.2281388520; this guide uses the verified mathematical value rather than repeating that apparent digit error.

The same paragraph writes a three-argument T.DIST.2T inverse relation. The dedicated forward syntax requires only x and degrees. The correct check is =T.DIST.2T(T.INV.2T(0.05,10),10), with mathematical target 0.05.

Microsoft documents #VALUE! for nonnumeric arguments and #NUM! for probability≤0, probability>1 or degrees below one. Noninteger degrees are truncated. Probability one is not excluded by that condition; its mathematical critical magnitude is zero, but a native endpoint result was not executed here.

The source states that inverse precision depends on the forward distribution. This is not a measured error guarantee. Validate probability units and integer degrees, and avoid conflating critical magnitudes, margins and complete intervals. All numerical results here are independent calculations, not native Excel output.

• 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.INV.2T 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.INV.2T 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.