CONFIDENCE.NORM Function

Excel 2010+ Statistical

The Excel CONFIDENCE.NORM function returns the half-width of a confidence interval for a population mean, using the normal distribution. Add and subtract it from the sample mean to get the interval's bounds.

Quick answer:

=CONFIDENCE.NORM(0.05,2.5,50) ~0.6929 (95% margin of error)

Syntax

=CONFIDENCE.NORM(alpha, standard_dev, size)

Argument		Description
`alpha`	Required	The significance level. For a 95% confidence interval use 0.05; for 99% use 0.01.
`standard_dev`	Required	The population standard deviation (assumed known).
`size`	Required	The sample size.

How to use it

CONFIDENCE.NORM returns the margin of error — half the total width of the confidence interval. Use it when the population standard deviation is known and the sample is reasonably large.

=CONFIDENCE.NORM(0.05, 2.5, 50) // ~0.6929

To build the interval, take your sample mean and go ± this value: mean - CONFIDENCE.NORM(...) to mean + CONFIDENCE.NORM(...). A smaller alpha (higher confidence) or smaller sample widens the margin.

Known vs. estimated σ: use CONFIDENCE.NORM when the standard deviation is known (normal distribution). When you only have the sample standard deviation and a small sample, use CONFIDENCE.T instead.

Try it: interactive demo

Live demo

Pick a CONFIDENCE.NORM example to see the formula and its result.

example

Result:

Practice workbook

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Frequently asked questions

What does CONFIDENCE.NORM actually return?

The half-width (margin of error) of the confidence interval, not the interval itself. Add and subtract it from the sample mean to get the lower and upper bounds.

What alpha gives a 95% confidence interval?

Use alpha = 0.05 for 95% confidence, 0.01 for 99%, and 0.10 for 90%. Alpha is 1 minus the confidence level.

When should I use CONFIDENCE.T instead?

Use CONFIDENCE.T when the population standard deviation is unknown and you're working from a sample standard deviation, especially with small samples. CONFIDENCE.NORM assumes σ is known.

Is CONFIDENCE.NORM the same as the old CONFIDENCE?

Yes — the legacy CONFIDENCE function used the normal distribution, so CONFIDENCE.NORM is its direct modern replacement.

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Related functions: CONFIDENCE.T · NORM.INV · NORM.DIST · STANDARDIZE · Z.TEST · STDEV.P