CONFIDENCE.NORM in Google Sheets: Normal Mean Margins

=CONFIDENCE.NORM(alpha, standard_deviation, pop_size)

The Google reference defines alpha as one minus confidence and standard_deviation as the population standard deviation. It labels the third argument pop_size and calls it population size.

For the usual confidence interval for a mean, the numerical denominator uses the number of sampled observations, n. Google’s linked published example, with alpha 0.05, deviation 6.48 and size 27, yields approximately 2.444225188, matching the normal half-width z*6.48/SQRT(27). The examples here use this sample-size interpretation, rather than substituting the total number of people or items in a population.

• alpha: 0.05 for 95% confidence, 0.01 for 99% confidence.
• standard_deviation: known population deviation, in the units of the measurements.
• pop_size: positive whole-number observation count used in the half-width calculation.

All three arguments are supplied. No omitted defaults are documented.

Enter these synthetic summary inputs:

In B6, calculate the margin:

=CONFIDENCE.NORM(1-B5,B3,B4)

Expected result: 3.9199279691. In B7 and B8, calculate the endpoints:

=B2-B6
=B2+B6

Expected results are 116.0800720309 and 123.9199279691. The full width is =2*B6, approximately 7.8398559382.

Do not enter 0.95 as alpha when intending a 95% interval. The function’s first argument is the excluded total tail probability, not the desired confidence level.

For a two-sided 95% normal interval, the standard-normal critical value is approximately 1.9599639845. The half-width is:

=1.959963984540054*12/SQRT(36)

This reproduces the expected margin. The equation z*sigma/SQRT(n) and the known-population-deviation condition are given in NIST’s confidence-interval explanation.

The Google help note describes a randomly chosen data value falling inside the interval. For statistical interpretation, distinguish an interval for the mean from an interval covering individual observations. NIST’s mean-interval interpretation is the one used here; a confidence level concerns repeated-sampling coverage of the method.

Holding confidence at 95% and population deviation at 12:

Quadrupling n from 36 to 144 halves the margin. Doubling n would not halve it, because the denominator grows with the square root of n.

For a target margin no greater than 2 with these assumptions, (1.959963984540054*12/2)^2 is the mathematical sample-size threshold. Rounding upward gives 139. Checking =CONFIDENCE.NORM(0.05,12,139) gives an expected margin of 1.9949037051. This is a simplified precision calculation, not a complete study-design or power analysis.

At n = 36, increasing confidence to 99% gives:

=CONFIDENCE.NORM(0.01,12,36)

Expected result: 5.1516586071. Greater confidence widens the interval. A smaller numerical alpha does not mean a narrower margin.

If the population deviation is unknown and estimated from the same small sample, a t-based procedure may be more appropriate. Google’s CONFIDENCE.T reference documents the separate t function. Neither function corrects biased sampling, dependence, measurement errors or an unsuitable statistical model.

Use an interior alpha, positive deviation and sensible integer sample count. Native error codes, fractional-count handling and text/blank coercion were not established by the reviewed reference; no cross-product behavior is assumed. Google explicitly documents CONFIDENCE as an alias of CONFIDENCE.NORM.

Current support is documented in rolling Google Sheets. Original introduction date, first release and last functioning numbered version are unestablished.

NOT_TESTED_IN_GOOGLE_SHEETS. Google documentation and its read-only published example were inspected on October 17, 2026. Expected outputs were independently calculated from normal quantiles. Reading Google’s published example is documentation inspection, not execution of this guide’s formulas.

Related published guides: AVERAGE, COUNT, SQRT and ROUND.