CONFIDENCE.T in Excel: Calculate a t-Based Margin for a Mean

=CONFIDENCE.T(alpha, standard_dev, size)

All arguments are required. alpha is the total excluded probability: 0.05 corresponds to a 95% two-sided confidence construction. standard_dev is the positive spread input, and size is sample size.

Microsoft labels standard_dev as a known population standard deviation. That wording should not be silently confused with the conventional one-sample t method, which uses an estimated sample standard deviation. The NIST t-interval formula identifies sample spread s and sample size N. The worked application below explicitly uses that conventional t-based construction and labels its results as independent mathematics.

The function has no mean argument. Its single result is a margin, or half-width, rather than two completed endpoints. Correct arithmetic alone does not establish that the t-based interpretation is appropriate for a real dataset.

Put 0.05, 3 and 25 in B2:B4, labeled Alpha, Sample standard deviation and Sample size. In B5 enter =CONFIDENCE.T(B2,B3,B4).

The independent standard error is 0.6, and the two-tail critical magnitude at 24 degrees is approximately 2.0638985616. Multiplying them gives 1.2383391370.

For a transparent reference construction, use =T.INV.2T(B2,B4-1)*B3/SQRT(B4). This explicitly uses sample size minus one and does not halve alpha before passing it to the two-tail inverse.

Use a sample standard deviation for the usual sample-based application rather than replacing it with the standard error. Dividing a standard error by SQRT(size) again would shrink the margin incorrectly.

Put sample mean 40 in B7. Enter =B7-B5 in B8 and =B7+B5 in B9. Independent endpoints are 38.7616608630 and 41.2383391370.

The full interval width is =2*B5, or 2.4766782740. Adding and subtracting that full width would double the intended margin.

The mean, standard deviation, margin and endpoints must use matching measurement units. Alpha is unitless and sample size is a count. A standard deviation in seconds cannot be added directly to a mean measured in minutes.

Keeping spread three and sample size 25, =CONFIDENCE.T(0.01,3,25) independently gives a 99% margin 1.6781637029. Higher confidence requires a wider interval under the same model.

Keeping alpha 0.05 and spread three, increasing size to 100 gives independent margin 0.5952650855. It is not exactly half the size-25 margin, because the critical t value also changes when degrees increase from 24 to 99.

Separate changes in confidence, spread and sample size when comparing scenarios. The function does not determine how many independent observations remain after exclusions or account for a clustered sampling design.

The illustrative construction concerns uncertainty in an estimated mean. It is not an interval intended to contain 95% of individual observations, and it is not a prediction interval for the next observation.

A confidence level concerns repeated-sampling coverage under the procedure’s assumptions. It is not a posterior probability assigned to a fixed mean lying within the particular endpoints on the screen.

Independence and the appropriateness of the underlying small-sample model must be assessed separately. The function cannot inspect the original observations because it receives only three summary inputs.

Microsoft uses =CONFIDENCE.T(0.05,1,50), independently 0.2841968555, matching its displayed 0.284196855.

The reference documents #VALUE! for nonnumeric arguments, #NUM! for alpha≤0 or alpha≥1, and #NUM! for standard_dev≤0. Noninteger size is truncated, and size one produces documented #DIV/0!.

Validate an integer sample size above one for the worked t interpretation. The current dedicated remarks do not enumerate every smaller-size or coercion case, so no additional native error display is invented. All worked numbers are independent calculations; native Excel behavior and extreme-quantile accuracy were not executed.

• 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 CONFIDENCE.T 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. The dedicated Microsoft reference and Microsoft catalog were freshly retrieved; examples were independently calculated. The supplementary NIST formula citation is supported by a cached search excerpt, not a freshly verified full NIST page. No native Excel, Mac or web-client execution was performed.

• Microsoft CONFIDENCE.T 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.