CONFIDENCE.NORM in Excel: Calculate a Normal-Model Margin for a Mean

=CONFIDENCE.NORM(alpha, standard_dev, size)

All three arguments are required. alpha is the significance level, so confidence level is 1−alpha. standard_dev is the population standard deviation, assumed known in Microsoft’s reference. size is the sample size.

The normal-model margin is z_(1-alpha/2)*standard_dev/SQRT(size). The division by the square root of sample size converts population standard deviation to the standard error of the sample mean under the sampling assumptions.

An exact normal interval requires an appropriate independent sample from a normal population with known standard deviation; an approximate normal interval needs a justified normal approximation. The function does not establish independence, representative sampling or known population variability from the three inputs.

Put 0.05, 2.5 and 50 in B2:B4. Enter =CONFIDENCE.NORM(B2,B3,B4) in B6. The independent target is 0.6929519122.

If the sample mean is 30, the lower and upper endpoints are =30-B6 and =30+B6, independently 29.3070480878 and 30.6929519122. The full width is twice the margin, about 1.3859038243.

Microsoft’s example displays the margin as 0.692952 and rounds the interval further for prose. Use the unrounded margin cell when deriving or comparing endpoints.

Keeping standard_dev=2.5 and size=50, change alpha from 0.05 to 0.01. The independent margin becomes 0.9106931839 for a 99% interval.

A higher confidence level requires a wider interval under the same model. Entering alpha=0.95 would request a 5% confidence level, not 95%. Keep confidence level and significance level in separately labeled cells if users supply one and formulas need the other.

The two-sided critical value uses alpha/2 in each tail. Omitting that split gives a different margin and does not reproduce the stated two-sided interval.

At alpha=0.05 and population standard deviation 2.5, increasing sample size from 50 to 200 halves the independent margin to 0.3464759561.

The sample size increased by a factor of four, not two, because margin varies with 1/SQRT(n). Doubling a sample size reduces the margin by a factor of SQRT(2), assuming the same variance and sampling model.

This algebra is useful for sensitivity analysis. It does not fix biased sampling or dependence between observations, and a larger number of correlated measurements may not deliver the same standard-error reduction.

For target margin 0.5, alpha=0.05 and known population standard deviation 2.5, the independent requirement is n≥(z*2.5/0.5)^2, approximately 96.03647052.

Round upward to 97 observations under this model. An illustrative formula is =ROUNDUP((NORM.S.INV(1-0.05/2)*2.5/0.5)^2,0). Check the resulting margin with CONFIDENCE.NORM rather than rounding the sample-size requirement down.

This is a mathematical planning example with assumed known variance, not a guarantee that a study meets every design requirement.

The interval concerns the population mean. It is not a range containing 95% of individual observations or a 95% prediction interval for the next observation. Microsoft’s reference explicitly warns against the latter interpretation.

In repeated sampling under the model, a 95% confidence procedure covers the fixed population mean in 95% of repetitions. It is not necessary to assign a 95% probability to a fixed parameter after one frequentist interval is computed.

If the population standard deviation is unknown and replaced by an estimated sample deviation, a t-based procedure may be appropriate under its assumptions. Do not relabel an estimated deviation as known simply to use this function.

Microsoft documents #VALUE! for nonnumeric arguments, #NUM! for alpha≤0 or alpha≥1, standard_dev≤0 or size<1, and truncation of a noninteger size. Validate whole sample counts before calculation.

Check whether standard deviation was confused with standard error, variance or the sample mean. The function returns only a margin and cannot inspect the dataset. The official equation image was freshly reviewed; the numbers here are independent calculations, with no native Excel execution claimed.

• 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 CONFIDENCE.NORM 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 CONFIDENCE.NORM 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.