CONFIDENCE.T Function

Excel Functions › Statistical

Excel 2010+ Statistical

The Excel CONFIDENCE.T function returns the half-width of a confidence interval for a population mean using the Student's t-distribution — the right choice when the population standard deviation is unknown and estimated from a sample.


Quick answer:
=CONFIDENCE.T(0.05,1,20) ~0.468 (95% margin, t-based)

Syntax

=CONFIDENCE.T(alpha, standard_dev, size)
ArgumentDescription
alphaRequiredThe significance level. Use 0.05 for a 95% confidence interval.
standard_devRequiredThe sample standard deviation.
sizeRequiredThe sample size (must be greater than 1).

How to use it

CONFIDENCE.T mirrors CONFIDENCE.NORM but uses the t-distribution, which has fatter tails for small samples — producing a slightly wider, more honest interval when σ is estimated rather than known.

=CONFIDENCE.T(0.05, 1, 20) // ~0.468

Build the interval as mean ± CONFIDENCE.T(...). As the sample grows, the t-distribution converges to the normal, so CONFIDENCE.T and CONFIDENCE.NORM give nearly identical results for large samples.

Rule of thumb: use CONFIDENCE.T whenever you computed the standard deviation from the sample itself (the usual case). Reserve CONFIDENCE.NORM for the rarer situation where the true population σ is genuinely known.

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Live demo

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Result:

Practice workbook

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Frequently asked questions

How is CONFIDENCE.T different from CONFIDENCE.NORM?
CONFIDENCE.T uses the Student's t-distribution (for an unknown, sample-estimated standard deviation), while CONFIDENCE.NORM uses the normal distribution (for a known population σ). For small samples the t-version is wider.
What does CONFIDENCE.T return?
The margin of error — half the width of the confidence interval. Add and subtract it from the sample mean to get the bounds.
Why must the sample size be greater than 1?
The t-distribution uses size - 1 degrees of freedom. A sample size of 1 leaves zero degrees of freedom, so the function returns an error.
When do CONFIDENCE.T and CONFIDENCE.NORM agree?
For large samples. As the sample size grows the t-distribution approaches the normal, so the two functions converge to almost the same margin of error.

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Related functions: CONFIDENCE.NORM · T.INV.2T · T.DIST · T.TEST · STDEV.S · AVERAGE